Ionizing radiation detection and spectrometry

2.1. Introduction - methodology of ionizing radiation detection
Ionizing radiation is invisible to the eye, so in order to be convinced of its existence at all, it is necessary to detect it using relevant physical methods and appropriate instrumentation, which converts invisible radiation into other visible or measurable quantities.
In addition to "visibility", detection allows us to investigate the properties of this radiation and use it in a number of scientific, technical, industrial and medical applications. It provides us with quantitative information on intensity, energy, spatial distribution and possibly other properties of radiation. In this chapter we will describe the individual methods and devices for the detection of ionizing radiation and for the measurement of its energy - spectrometry. In the introductory §2.1 we will give a basic division of detection methods and devices and summarize some common methodological aspects of ionizing radiation detection. In the next §2.2-2.10 we will describe in more detail specific types of detectors and spectrometers, their principles, properties and technical construction.

Types of ionizing radiation detectors
A number of ionizing radiation detectors have been developed which (in addition to the common basic phenomenon of ionizing radiation effects) use various principles and technical constructions. Instruments for detecting ionizing radiation are sometimes collectively referred to as radiometers. They work either independently, or are part of devices for measuring certain quantities and monitoring certain events using radiation methods.
Dosimeters
A special type of radiometers are the so-called dosimeters. They are usually simple detection devices that are calibrated in radiation dose units (Gray, Sievert) or dose rate. They are used in radiation monitoring to assess the effects of radiation, especially on living tissue (see §5.1 "Effects of radiation on matter. Basic quantities of dosimetry."). For measurement of dosimetric characteristics of radiation, see also §2.8 "Absolute measurement of radioactivity and radiation intensity", section "Measurement of radiation intensity and dose rate".
Ionizing radiation detectors can be divided according to three criteria: the time course of detection, the physical-technical principle of detection and the complexity of the measured radiation information.

× 1. According to the time course of detection, we distinguish two basic groups of detectors :

× 2. According to the detection principle.
Various types of detectors provide a response to the interaction of ionizing particles by various, often very different, mechanisms. They therefore differ in their properties and thus in the possibilities and areas of their use. According to the detection principle, we distinguish three groups of detectors :

Electronics - optoelectronics - photonics
Some special scientific and technical fields deal with the transmission of energy and information :
¨ Electronics is a scientific and technical field dealing with the transmission of energy and information through electrical signals - especially electron currents and electromagnetic fields and waves excited by them.
¨ Optoelectronics, also called photonics, is a scientific and technical field dealing with the transmission of energy and information through photons, especially visible light. It deals with photon sources, such as lasers and light emitting LEDs, light transmission techniques (eg optical fibers), methods detection of photons and their conversion into electrical signals (photodiodes and phototransistors, CCD, photomultipliers) and processing of these signals in electronic circuits, including computer software. Emissions, interactions and detection of photons take place at the quantum level, so there is sometimes talk of quantum photonics.
Electronics and optoelectronics play a key role in the detection of ionizing radiation (§2.4 "Scintillation detection and gamma-ray spectrometry", §3.2 "X-rays - X-ray diagnostics", section "Electronic X-ray imaging detectors"), in electronic sources of ionizing radiation (X-ray tubes, accelerators) as well as in the relevant measuring and control technology.
Significant opto-electronic components or devices are LASERs (Light Amplification by Stimulated Emission of Radiation). They are electronic sources of very intense coherent rays of light (or infrared or ultraviolet radiation), which arises on the principle of stimulated emission, in which excited atoms jump en masse to lower energy levels, which is accompanied by light emission with an avalanche increase (chain effect - emitted light stimulates more and more deexcitation with photon emission). The use of lasers in nuclear physics is mentioned in several places in our treatise - eg §1.3, section "Fusion of atomic nuclei", passage "Inertial thermonuclear fusion", or §1.5, part "Charged particle accelerators", passage "Laser plasma accelerators LWFA" and "Ion sources". However, a more detailed explanation of the physical principles and technical design of lasers lies already outside the scope of our nuclear and radiation physics (and besides, in the laser technology the author is not an expert...).

× 3. Complexity - completeness, details - of the measured information
The ionizing radiation we need to detect often consists of particles and quanta of different kinds and energies that come from different directions and places in space, from different radioactive, electronic or cosmic sources. According to the completeness - details of the measured information, measuring instruments of ionizing radiation can be divided into 4 groups :

In terms of a specific type of sensor sensitivity, we can label simple detectors (and all radiation detectors in general) as radiation-sensitive sensors, spectrometers are also energy-sensitive, imaging and trajectory detectors are position-sensitive radiation sensors.
The basic physical properties of detectors include :
¨ Sensitivity and efficiency of the detector
¨ Temporal resolution detector (its dead time)
¨ Energy resolution of the spectrometer
¨ Spatial (or angular) resolution of the imaging detectors
Furthermore, it is the background of the detector, linearity and homogeneity of response, accuracy and time stability, "resistance" to radiation overload, calibration parameters. These properties of detectors, as well as their quantification, are described in more detail below in the section "General physical and instrumental effects in detection and spectrometry", for imaging detectors in Chapter 4 "Radionuclide scintigraphy", §4.2 "Scintillation cameras", section "Imaging camera features" and §4.5 "Quality control and phantom scintigraphic measurements".

Spectrometry - a powerful tool for physical cognition and applications
We consider it useful to recall here the key role of spectrometric methods of analysis of electromagnetic and corpuscular radiation for physical knowledge and applications of physical methods in various fields of science, technology, industry and medicine. The measurement of energy spectra is the main source of knowledge about stars and galaxies in outer universe, the composition of matter, the properties of atoms and molecules, the structure of atomic nuclei, the nature and interactions of elementary particles. Most of this knowledge is otherwise inaccessible to us - whether for long distances (in space) or submicroscopic dimensions deep inside the microworld. Without spectrometry, we would know much less about the world. A number of analytical methods are also directly based on spectrometry, such as X-ray fluorescence analysis, activation analysis, nuclear magnetic resonance, Mössbauer spectroscopy, and indirectly scintigraphy, Doppler and interferometric methods.

Shielding, collimation and filtration of detected radiation
In many cases it is not enough to place the "bare" detector of the required radiation in a certain place and register the incoming quantum. In addition to the analyzed radiation itself, there is almost always other unwanted and interfering radiation at the measuring place. It is, on the one hand, natural radiation (natural radiation background - cosmic radiation, radioactivity of the environment), radiation from possible other surrounding sources, sometimes even undesirable components in the measured radiation itself. To eliminate or reduce these interfering radiation effects, the detector should be equipped with other suitable mechanical or electronic parts, whereby the beam or field of the detected radiation is basically modified in three ways :
× 1. Shielding of the detector
To suppress unwanted radiation coming from the environment, it is necessary to surround the detector itself with a sufficiently strong envelope made of a substance that absorbs radiation well - place the detector in a suitable shielding. The most common construction material for shielding g radiation is lead, in special cases tungsten and other materials are also used. Sometimes we also use partial shielding of the primary detected radiation - especially in the case of strong radiation (high fluence), which would overwhelmed the sensitive detector.
Influence of detector shielding and radiation collimation on the shape of the spectrum
In the shielding material, the detected radiation interact with the atoms of the substance, which can lead to the formation of secondary radiation. In addition to Compton scattering, which generates radiation with a continuous spectrum, it is also a photo effect, accompanied by the formation of characteristic X-rays with a line spectrum. In Fig.2.1.2 we see the influence of different types of scintillation detector shielding (scintillation detectors are described in detail below in §2.4 "Scintillation detectors", scintillation spectrum in the section "Gamma radiation scintillation spectrum") on the shape of measured spectrum of sample of radionuclide ^99mTc emitting gamma radiation with an energy of 140keV. For a detector without shielding (a), there is a rather weak monotonic Compton continuum in front of the photopeak. To measure low activities, it is necessary to place the detector inside a massive lead shield (b up). A side effect of this useful measure is the interaction of gamma-photons with shielding atoms, among other things, by the photoeffect, which produces secondary characteristic X-rays (lines K_a,b) of lead with an energy of about 70-80keV, which is manifested in the spectrum (b below). A special type of shielding are collimators, used as a primary imaging element in scintigraphy (§4.2, section "Scintigraphic collimators"). The interaction of gamma-photons with a photoeffect with lead baffles between the collimator orifices also produces a characteristic X-ray (lines K_a,b) of lead with an energy of about 70-80keV. If the collimator has relatively thicker baffles (approx. 0.5 mm), the characteristic X-ray of lead is effectively absorbed and we can see a faint X-peak in the spectrum of transmitted radiation (Fig. C). In collimators LE UHR with small holes and very thin baffles are significantly cross-radiation gamma and characteristic X-rays trough the baffles, so that in the spectrum can be X-ray photopeak even more pronounced than the primary photopeak 140keV (d) (at scintigraphy, however, the window of the analyzer set to photopeak 140keV, so that X-rays are not registered, see the spectrum image in the section "Amplitude analyzer " §4.2 "Scintillation cameras").

Fig.2.1.2 Influence of different detector shielding geometry on scintillation spectrum.
a) Basic scintillation spectrum of the ^99mTc sample measured by a detector without shielding. b) Spectrum measured by a detector inside a lead shield (7cm Pb) .
c) Spectrum of the ^99mTc sample measured through a lead scintigraphic collimator type HR. d) Spectrum through a UHR collimator with small holes and very thin septa.

× 2. Collimation of detected radiation
In case we need to detect only radiation coming from a certain direction, we provide the detector with a collimator - such a mechanical and geometric arrangement of materials absorbing a given type of radiation, which transmits only radiation coming from certain desired directions (angles), while it absorbs and does not transmit radiation from other directions. The simplest collimators have the shape of various cylinders - tubes and orifices. Special intricately configured imaging collimators with a large number of holes play a key role in scintigraphy - §4.2 "Scintillation cameras", section "Collimators". Different types of specially shaped collimators are used in radiotherapy; the most important is the multi-leaf collimator MLC (§3.6 "Radiotherapy", part "Modulation of irradiation beams IMRT, IGRT").
Electronic collimation of radiation
In addition to the above-mentioned straightforward "physical" radiation collimation, some special detection systems use another method of directional radiation selection, so-called electronic collimation, without the use of a mechanical collimator. It is based on the specific behavior of quantum ionizing radiation in the detection system - the propagation of pairs (or more) of quantums in certain precisely given directions, their coincidence detection by a system of a large number of detectors and subsequent positional and angular reconstruction of the direction of quantum propagation. This analysis makes it possible to select for further processing only those quants of radiation, that have the desired direction - to perform electronic collimation and display the distribution of radiation in a given field. The electronic collimation method is used in positron emission tomography PET (see §4.3 "Tomographic cameras", part "PET cameras") and in some complex detection systems such as ring imaging Cherenkov RICH detectors (see ....), trackers and muon detection systems for accelerators (see ....).
× 3. Filtration of detected radiation
is used in special cases, where the measured radiation itself contains quantum or particles of different types and energies, while we need to measure only one of the components of the primary radiation and we want to get rid of the others.
An example is the measurement of radionuclide purity of preparations in case a given basic radionuclide emitting low energy radiation g (eg ^99mTc, g 140keV) is contaminated with a small admixture of a radionuclide emitting higher energy g (eg ⁹⁹Mo, g740keV). In direct measurement, the detector would be oweeloaded with basic energy of lower energy, in the "flood" of which the sparsely coming high-energy photons would be "lost". In this case, it is possible to use the method of filtration with a shielding absorbent insert: place the vial with the investigated preparation in a lead shield of suitable thickness (approx. 2-5 mm), which almost completely absorbs intense low-energy radiation g of the basic radionuclide, but transmits a significant portion of the weak but high energy g-radiation of the contaminant. This method is described in more detail in §4.8 "Radionuclides and radiopharmaceuticals for scintigraphy", section "Quality and purity of radiopharmaceuticals".
When using collimation and filtration, we must be aware that a certain part of the incoming radiation will not be detected, the detection efficiency is reduced. For quantitative measurements, it is therefore necessary to make an appropriate correction for this circumstance, or to include it in the calibration of the detection system.

Arrangement and configuration of radiation detectors
Individual types of ionizing radiation detectors are used in various configurations for their own measurements :
¨ One separate detector
In most radiation applications, one detector is sufficient, which we choose according to the type of radiation, its energy, intensity, geometric distribution. We pay particular attention to the optimization of detection efficiency, energy response, linearity and other parameters; sometimes also prices... One detector is used, for example, in personal dosimetry, in some industrial applications, when measuring radioactive samples (Fig.2.1.3 top left).
The geometric design of the detector can be of two types :
l Planar detectors
cylindrical or square in shape, measuring radiation coming from 2p - half-plane; some may also be sensitive to radiation coming from other angles (4p ).
l Well detectors
designed in the shape of a vessel - a "well" into which the measured sample is inserted. The sensitive volume of the detector forms the bottom and walls of the well surrounding the sample (test-tube). Most of the radiation thus passes through the sensitive area, which leads to a higher detection efficiency (it can be close to 100%). These detectors are listed below in §2.7 "Measurement of radioactivity of samples (in vitro)".
¨ Multidetector systems
To measure more complex radiation processes, we usually need to measure radiation in different places of the monitored system Þ the need for the simultaneous use of multiple detectors (Fig.2.1.3 top right). Most of them are detectors of one type, event. two species (eg for g and b ). Several detectors are used, for example, in monitoring systems or in multi-detector sample meters. In §4.2 "Scintillation cameras" and §3.2 "X-ray diagnostics", part "Electronic X-ray imaging" we will see that for electronic radiation imaging a systems of large number of elementary detectors and opto-electronic members (sometimes several thousand) are used. In addition to the requirements applicable to stand-alone detectors, the muttual concurrence and harmonization of the parameters of the individual detectors is important here.

Fig.2.1.3. Arrangement and configuration of ionizing radiation detectors.
Above: Use of one detector and multiple detectors of the same type.
Bottom: A complex system of a large number of detectors of various types for the analysis of high-energy particle interactions.

¨ Detection systems for high-energy particle interactions
The most complex detection systems are used to study the interactions of high-energy particles in large accelerators. Here, during the interactions of accelerated primary particles, a large number of secondary particles and radiation of various kinds arise, which need not only to detect but also to measure their energies, momentum, charge, trajectories (§1.5, section "Analysis of dynamics of particle interactions"). This requires very complexly configured multidetector systems, consisting of a large number (tens and hundreds of thousands) of individual detectors of various kinds, in a complex electronic circuit, often with the participation of strong magnetic fields. These systems of a large number of electronic detectors gradually replace the previously used bubble chambers (described below).
A typical arrangement of such an electronic detection system is simplified schematically drawn in the lower part of Fig.2.1.3. Its task is to capture, if possible, all particles and quantum arising during the studied high-energy interaction .During these interactions, a large number of secondary particles fly out in all directions. The whole detection system is mostly cylindrical in shape and surrounds the place where the accelerated particles interact with the target or in the opposing collided beams. It consists of several axially symmetrical parts - cylindrical layers or "shells" of detectors, whose functions complement each other :
l Internal trajectory detector - tracker
The inner part of the detector starts very close (usually a few cm) from the interaction and consists of a large number of elementary detectors ( detection "pixels" and channels) - semiconductor and ionization chambers, which serve as so-called trackers - electronic path detectors charged particles. They are deposited in several layers so that it is possible to electronically reconstruct the paths of the particles flying out of the interaction site. The best positional resolution is pixel semiconductor detectors, which are placed in the innermost layer, closest to the site of primary interaction. Semiconductor strip and drift detectors are also used (see §2.5 "Semiconductor detectors"). The trajectory, charge and momentum of the particles can be further determined in the next layer of position - sensitive multi - wire drift ionization chambers; the curvature of the trajectory in the magnetic field determines the charge and momentum of the particle.
l Spectrometer - calorimeter
This is followed by a spectrometric layer, called a calorimeter, where the energy of the flying particles is measured. In task is absorb all the energy of the particle and provide an output signal proportional to this energy. This layer is formed absorbent material interspersed with detectors. In the so-called hadron calorimeter, high-energy hadrons (protons, neutrons, pions), when passing through absorbent material through "photonuclear" fragmentation reactions with nuclei, produce a larger number of other secondary hadrons, which further interact with material nuclei in a similar way - creating a gradually expanding spray of ionizing particles, which are registered by interleaved detectors. The so-called electromagnetic calorimeter is optimized for the detection of particles interacting by electromagnetic interaction (photons, electrons, positrons and other leptons). When high-energy electrons and positrons pass through the material, braking radiation is produced in the form of high-energy photons. And high-energy photons as they pass through a substance produce the electron-positron pairs. The result of the interaction of high-energy photons, electrons and positrons with the material of the calorimeter is an electron-photon spray, formed by a larger number of electrons, positrons and photons. Scintillation detectors are suitable for the detection of energetic particles (see §2.4 "Scintillation detectors"), especially high-density materials such as BGO, LSO or PbWO₄ crystals, which have good conversion efficiency even for higher energy photons.
l Muon spectrometer
The last, outer cylindrical layer detects penetrating particles, muons m, which fly out. It consists of a large number of large ionization chambers, located in a magnetic field, which evaluate the curved paths of muons to determine their charge (+, -) and momentum. The detection system further comprises coils (often superconducting) generating a strong magnetic field, curving the paths of the charged particles; it is used to measure the momentum and charges of these particles. As already mentioned, the task of these complex detection systems is to capture as many particles as possible that fly in all directions from the point of interaction. The detection system therefore has the shape of a cylinder, a kind of "pot", surrounding the site of interaction. In order not to escape even particles flying at small angles along the axis, the detectors are also distributed in a circle at both ends of the cylinder - they form a kind of "lids" (they are not drawn in Fig.2.1.3 below). Since the particles formed during interactions at large accelerators generally have high energies, this implies the large size and weight of the detection system so that no particles escape without detection, if possible. In each case, however, neutral, weakly interacting particles such as neutrinos escape freely...
The most complex detection systems of this kind (called ATLAS, ALICE, CMS ) are built at the largest LHC accelerator at CERN (§1.5, part "Large Accelerators").
The complex detection systems a large number of detectors are also used in experiments for detecting neutrinos (§1.2, section "Neutrinos - "ghosts" between particles"), and cosmic radiation, e.g. observatory AUGER (§1.6, section "Cosmic ray" passage "Detection and Spectrometry of cosmic radiation").

Electronic connection and processing signals from the detectors
Electronic detectors of radiation are connected to respective electric circuits, which provide two important functions :
¨ Power supply of detector
For the proper function of the detector, an appropriate supply voltage must be introduced, so that the detected ionizing radiation can cause corresponding electrical changes in the detector, causing an output electrical signal - the detector's response to radiation. We recognize two types of power supplies :
- Low voltage sources of about 5-24 V, used to power electronic circuits equipped with semiconductor components: amplifiers, discriminators, coincidence circuits, counters, indicators, etc.
- High voltage sources of approx. 100-2000 V, which is needed for the function of photomultipliers, some semiconductor detectors, ionization chambers.
For more complex detection devices, an additional supply voltage is required for electromagnets or motor movement of the detector components.
¨ Electronic signal processing and evaluation of results
The primary electrical signal from the detector output is usually very weak (it has a small amplitude, milivolts), so in the first phase it is necessary to amplify it (Fig.2.1.1). Amplification may also be in two stages: at the very output of the detector is sensitive preamplifier, partially amplified signal is then in the evaluation apparatus amplified in the amplifier to a desired level.
This is followed by further processing - signal analysis and its recording or registration in a counter or computer memory. Signal processing may include appropriate pulse shaping and amplitude sorting. For systems of two or more detectors, the signals from the individual detectors are processed either independently (for monitoring systems or multi-detector sample meters) or together. The simplest joint processing is simple signal summation - the system then behaves like one "larger" detector. When detecting more complex structured radiation, especially correlated pairs of quanta, the connection of detectors in coincidence or anticoincidence. In the case of coincidence connection, a signal appears at the output only if the detection occurred simultaneously in both detectors *) - it is used, for example, in PET positron emission tomography. Conversely, in an anticoicidal circuit, the signal only passes if, at a given moment, detection occurs only on one the detector and not on the other (simultaneous detection is excluded). An advantageous feature of the coincidence circuit is the substantial reduction of noise and other disturbing impulses.
*) In special cases, the so-called delayed coincidence is also used - cases are detected when a preset short time (usually less than ms) elapses between the detection on one and the other detector.
In complex systems of many detectors, so-called trigger circuits are included, which trigger the detection process in the system of a large number of detectors only for particles of selected properties (eg trip angle, energy). This helps reduce the large number of "ballast" pulses that would overwhelm the system and make it difficult to find "useful" signals. There is often a very complicated analysis - processing - including arithmetic operations between the magnitudes of individual signals, weighing processes and other manipulations, according to the physical-mathematical model of the investigated radiation process.

General physical and instrumental effects in detection and spectrometry
The task of radiation detection and spectrometry is the objective measurement of the number of quanta, energies, intensities and other characteristics of ionizing radiation. However, a completely accurate measurement with 100% efficiency is only an ideal assumption; in fact, the measuring process manifests itself in a number of unfavorable physical and technical influences, limiting the possibilities of measurement or distorting the results. For individual types of detectors, these effects will be specifically discussed below. Here we will mention some common physical and instrumental influences, which we will discuss mainly for the general case of spectrometry, where the situation is the most complicated; some of these effects are then applied in simpler cases of simple radiation detection.

Detection efficiency and sensitivity
The task of radiometric detection devices is to objectively measure the intensity of radiation or the number of its quants at a given location, or emitted from a radioactive sample. The optimal situation of "100% efficiency", where the device will register every quants of analyzed radiation, is seldom met - a certain part of the radiation for physical or design reasons is usually not detected. An important parameter of the radiometer is its detection efficiency, sometimes called the sensitivity *) of the instrument.
*) However, it is not entirely correct to confuse the sensitivity and efficiency of detection. The word "sensitivity" can also express other properties of the detector. In general, sensitivity means the ability of a sensor to respond on certain stimuli. The sensitivity of the detector expresses the ability of the detector to react to radiation - to generate a processable signal when a given type of radiation enters. The quantitative measure of this sensitivity is then expressed as the detection efficiency. Sometimes the sensitivity of the detector also means the smallest detectable radiation intensity, or the smallest detectable activity of the sample, etc., which the detector is still able to measure (distinguish it from the radiation background in the context of statistical fluctuations and other measurement errors).
We distinguish two types of detection efficiency :
¨ Absolute (total) detection efficiency of measurements
is the ratio of the number of pulses recorded by the detector to the number of quanta emitted by the source in a given time, or the ratio of the frequency of pulses from the detector to the total flux in the field or beam of radiation. The absolute detection efficiency depends on the geometric arrangement of the source and the detector (see below §2.7 "Measurement of radioactivity of samples", geometry 2p, 4p), on event. absorption of radiation in the environment between the source and the detector and, of course, also on the intrinsic internal efficiency of the detector used.
¨ Internal detection efficiency h of detector
is given by the probability of registration of quantum radiation entering the sensitive area of the detector. It is expressed as the ratio of the number of pulses recorded by the detector to the number of quanta of a given type of radiation that entered the detector (its input window); is given as a percentage (0% < h <100%).
The number of pulses registered at the detector output is always slightly smaller (often significantly smaller) than the number of quanta of radiation flying into the detector. On the one hand, some particles arriving at the detector may not reach a sensitive volume at all because they have been absorbed by the material of the package or input window. Other quanta, such as high-energy gamma photons, can in turn fly through the sensitive volume of the detector without interaction (and thus without response and registration). Even if there is an ionization interaction in the detector material, the generated electrons and ions may recombine, or the energy of the electrons may be transferred to other atoms and molecules outside the luminescent centers, - leads to only a slight increase in the temperature of the detector material. These "parasitic" phenomena reduce the number of pulses at the output - they reduce the detection efficiency.
The internal detection efficiency, which is a characteristic of a given detector (its type and even a specific piece), is given by a number of physical and technical circumstances. Above all, it is an effective cross section of the interaction of a given type of quantum with the detector material. Furthermore, it is the size of the sensitive volume, the absorption properties of construction materials - mainly the input window, "competitive" interaction processes without the production of a useful signal, dead time, electronic processing and signal analysis. We will deal with these phenomena specifically for individual types of detectors.
For most applications of ionizing radiation, we naturally require the best possible detection efficiency. However, in the case of high intensity of the measured radiation, high detection efficiency could lead to detector overload, high dead time loss, cumulative effects and other phenomena leading to violation of the linearity of the response, deterioration of the measurement accuracy, in extreme cases even damage of the detector. In such cases, we prefer a detector with less detection efficiency, or we artificially reduce the overall detection efficiency by suitable collimation or filtration of radiation in front of the detector, or by increasing the distance between the source and the detector. We then measure a lower signal flow (response), but correctly. With suitable calibration, we measure a certain representative sample of the analyzed radiation.

Time resolution and dead time
There is a certain time delay between the moment of interaction of the quantum of radiation in the sensitive volume of the detector and the electrical impulse at the output of the detector. It is caused mainly by two factors :
1. Physical processes in the detector itself - energy transfer, formation of ionization, propagation of electrons and ions in the detector material, charge collection by electrodes, deexcitation time, duration of scintillation, etc. The response time of the detector itself depends on the type of detector, the size of the sensitive area (smaller detectors are faster), the material and the design. It ranges from tens of microseconds to G.-M. detectors, per unit of nanoseconds for scintillation detectors.
2. Electrical processes in electronic circuits - steepness of rise and fall of electrical impulses, charging and discharging of capacitors, response speed of semiconductor components. The decisive factors here are mainly the circuits of the input preamplifier. Current electronic circuits are quite fast, their response time is in the nanosecond range.
Individual quants of radiation come to the detector with irregular "time spacings", at higher radiation intensities the particles come in very rapid succession, with only very small time intervals. No electronic detector works "infinitely fast", it has a finite time resolution.
¨ Time resolution
is the time that the detector needs to process and register the response signal from one quantum of radiation.
¨ Dead time
of detector is the time interval from the detection of one quantum, during which the detector is not able to correctly detect another quantum. During this time, the detector is either insensitive to radiation, or the second response signal would be composed of the first (eg pile-up effect, see §2.4, section "Scintillation spectrum" below).
The dead time of the detector causes some quantums, that come "too fast in succession" not to be detected. This leads to a reduction in the detection efficiency, and (worst of all) this detection efficiency is not constant, but depends on the intensity of the analyzed radiation - a non-linearity of the response arises. This can lead to significant errors in measurement procedures.
The issue of dead time, its measurement and correction, will be discussed in more detail below in §2.3, section "Dead time").

Background of the detector
For each of the real measurement device, and therefore the radiometer, over the measured signal is translates and superimposed a "zero" signal - the so-called background. The background of a radiometric detection device generally has three origins :
1.External radiation from the surrounding space - a small amount of ionizing radiation is always present in our environment and in the laboratory. This radiation comes from many sources, such as cosmic radiation and its interaction with the atmosphere, terrestrial radiation from radioactive minerals in soil and rocks, from building materials of buildings (there is mainly potassium ⁴⁰K), from radon gas, from fallout during tests of nuclear weapons and nuclear accidents. Furthermore, it can be radiation from surrounding insufficiently shielded sources, radioactivity of spectrometer components and the like. The background from the outside can be significantly reduced by thoroughly shielding the detector. The background of the unshielded and shielded detector is compared in detail below in Fig.2.1.5.
2.Internal radioactivity of the detector material , which may be of dual origin :
¨ Sensitive detector material may contain long- lived natural radionuclides. These natural radionuclides are ubiquitous and difficult to clean the detector material completely from them. In organic scintillators, a small amount of radiocarbon ¹⁴C is present. Of the commonly used detectors, the LSO scintillator has the highest internal radioactivity (approx. 250Bq/cm³of the natural radioisotope ¹⁷⁶Lu - see the section "Scintillators ...", passage "Internal radioactivity LSO ").
¨ Nuclear reactions and activation of the detector material may occur inside the detector due to external radiation. Both short-term and long-term radionuclides can be formed, which internally contaminate the detector (these phenomena are discussed in more detail below in the section "Aging and radiation wear of detectors", section "Nuclear reactions and induced radioactivity inside detectors").
Radionuclides (natural and induced) contained in the detector material during their radioactive transformations emit quantum radiation, mainly beta and gamma, which are detected with high efficiency. This internal radiation background contributes to the overall background of the detector.
3.Electrical noise of the device arising due to quantum fluctuations in the movement of electric charges in the detector itself, in the photomultiplier (in the case of scintillation detectors) and amplifying electronic circuits. Radiometer noise can be significantly reduced by cooling detector and preamplifier to the temperature of liquid nitrogen or even helium. Electronically, the resulting noise can be reduced by appropriately setting the lower discriminant level, or by using a coincident connection of two or more detectors.
For correct measurement, the background must be subtracted from the resulting measured values. Problems occur when the measured radiation is so weak that it is comparable to the background intensity. The background adversely increases minimally detectable radiation intensity or minimally detectable radionuclide activity - it reduces the sensitivity of detection.
Combinatorial background
In more complex multi-detector systems (as above in Fig.2.1.3), where the resulting measurement response is created by a certain combination signals from individual detectors, when simultaneously detecting a large number of particles, coincidence or anticoincidence signals originating from different, unrelated processes may be incorrectly paired. False data generated in this way is sometimes referred to as combinatorial background. It plays a negative role, especially in complex detection systems for accelerators, where a large number of quanta are created almost simultaneously during interactions and the investigated rare phenomena can then be lost in the combinatorial background...

Spectrum
General physical and instrumental influences have their specifics in radiometers operating in spectrometric mode. Ideally, the measured (instrumental) spectrum n = n(E) should be identical with the actual (physical) spectrum N = N(E) of the emitted radiation. In reality, however, the measured spectrum differs from the actual one due to some distorting physical and instrumental effects :

Other influences that may affect the accuracy of radiometric (and especially spectroscopic) measurements are possible mechanical and thermal instability, influence of external fields (especially photomultipliers in scintillation detectors are highly sensitive to magnetic field ) and detector selectivity (ratio of detector sensitivity for registration of required type of radiation with respect to sensitivity for registration of other types of radiation).

Specific properties and use of different types of detectors
The specific properties of different types and designs of detectors must be carefully considered when using them in different applications of ionizing radiation. Strong radiation fluxes (eg in radiation beams in radiotherapy) are best measured with an ionization chamber, which has a low detection efficiency, but shows a linear response even for high radiation intensities. Operational monitoring of weaker and medium-strong radiation for the purposes of radiation protection, where in principle high accuracy cannot be achieved, is most often performed by GM or proportional detectors. Measurement of radioactive samples, natural materials and environmental radiation is performed using highly sensitive scintillation and semiconductor detectors, with a low background (for example, is not suitable LSO scintillator with relatively high intrinsic natural radioactivity). Semiconductor spectrometers with high energetic resolution are used in neutron activation analysis, X-ray fluorescence analysis, and nuclear physics research. Accurate spectrometry of charged particles - electrons (beta radiation), protons, alpha-particles - can be performed only on magnetic (or electrostatic) spectrometers (in which, however, a non-spectrometric detector can serve as a sensor). Detection of high-energy cosmic rays and neutrinos is performed experimentally mainly using Cherenkov detectors. In nuclear medicine, where we need high detection efficiency without the need for high energy resolution, scintillation detectors and their imaging systems - gamma cameras - are used. For hybrid PET/MRI combinations (positron emission tomography + nuclear magnetic resonance), special semiconductor photodiodes are used in PET camera scintillation detectors, instead of photomultipliers that would adversely affect the magnetic field.
All these aspects of the suitability of using different types of detectors will be discussed in more detail below in this chapter (§2.3 - 2.8), in the relevant parts of Chapter 3 "Applications of ionizing radiation", Chapter 4 "Radionuclide scintigraphy", for neutrinos in §1.2, part "Neutrinos - "ghosts" between particles", for cosmic radiation in §1.6, passage "Detection and spectrometry of cosmic radiation".

Radiation detection by type, energy and intensity
The choice of detection methods and devices naturally depends primarily on the properties of the radiation we want to analyze - the type of radiation, the energy of its quanta and their abundance (radiation intensity). We will mention here some of the problems we generally encounter in detecting radiation of different types, energies and intensities. We first notice the type of radiation :
¨ Photon g and X radiation are relatively easiest to detect with the help of ionization chambers (including GM detectors), scintillation and semiconductor detectors. This applies in particular to radiation of medium energies of tens to hundreds of keV and intensities of approx. 10 ¸ 10⁴ photons /second. Details below §2.4 "Scintillation detection and gamma-ray spectrometry", §2.5 "Semiconductor detectors".
¨ Corpuscular radiation a, b , p⁺ is more difficult to detect - due to its low penetration in the substance it is difficult to get into the sensitive volume of the detector, it is often absorbed in the material of the sample itself - see below Detection of alpha, beta radiation". Effective detection can be achieved using special methods, such as the use of liquid scintillators.
¨ Neutrinos radiation is the most difficult to detect of all known types of radiation, due to the extremely weak interaction of neutrinos with matter. It is possible to detect only in very limited extent, using very voluminous detection systems - see §1.2, section "Neutrinos - "ghosts" between particles".
It also depends on the intensity of the detected radiation :
l Radiation of medium intensity ,
approx. 10 ¸ 10⁵ particles per second, is again relatively easily detected if we have a detector sufficiently sensitive to the given type of radiation (with sufficient detection efficiency).
l Low intensity radiation ,
significantly weaker than 1 particle/second, is difficult to measure accurately. It is often overhelmed by the natural background and noise in the detector, the measured values are significantly affected by statistical fluctuations. It is desirable to use detectors with a high detection efficiency and a low level of self-background, well shielded from external radiation, including natural radiation background. To reduce the effect of statistical fluctuations, the measurement times are quite long - to accumulate a sufficient (statistically significant) number of useful pulses.
l High intensity radiation ,
such as tens of millions of particles/second, can overload the detector (dead time, cumulative processes) and prevent accurate measurements. When exposed to strong radiation, radiation-induced chemical reactions can occur in the detector material, deteriorating the detector's properties - reducing detection efficiency and deteriorating resolution. Immediately after such overexposure, the detector may exhibit an increased intrinsic background, caused by deexcitation of metastable levels and chemiluminescence of molecules released by radiation in the detector during intense exposure. Extreme radiation intensity can damage the detector irreversibly ! Suitable detectors with low detection efficiency and linear response, such as ionization chambers, are used to measure strong radiation. Furthermore, with the help of shielding or collimation, we can select a certain defined "sample" of the analyzed radiation and measure it correctly even with the help of a sensitive detector.
The radiation detection methodology is significantly dependent on the energy of radiation quanta :
× Medium energy radiation ,
keV units up to tens of MeV, can be detected in the case of usual types of radiation (g, b, a, p⁺, ...) without major problems using ionization chambers, scintillation and semiconductor detectors.
× Low energy radiation ,
less than about 1keV, is very difficult to detect. Due to the high absorption in the substance (low permeability), it is difficult to penetrate into the sensitive volume of the detector and causes a low response in it, often overlaid by quantum noise. Low-energy corpuscular radiation is often undetectable (this is absolutely true for neutrinos due to their very small cross-section of the substance interaction).
× Radiation of high energies ,
higher than hundreds of MeV, of the order GeV and TeV, often shows a low effective cross section of the interaction with the detector substance, which reduces the detection efficiency - most quanta can pass through the detector without response. In particular, the spectrometry of such radiation is difficult because high-energy quanta lose only a small part of their energy in conventional detectors. Special robust detection systems, called calorimers, are used here, composed of massive absorption layers interspersed with detectors (these detect emerging sprays of secondary particles). High energies can be encountered in large accelerators or in cosmic rays. In addition to the technical difficulties of measuring high-energy radiation, it is necessary to draw attention to the risk of radiation-induced internal radioactive contamination of the detector material, discussed in more detail in the following paragraph, section "Nuclear reactions and induced radioactivity inside detectors".

Aging and radiation wear of detectors
Like any device (and object and material in general ...) , the ionizing radiation detector is not immutable and eternal. Its properties change over time and during use. Changes in properties can be short-term or long-term, reversible and irreversible. Short-term reversible changes - device instabilities - were mentioned above. Sudden irreversible changes belong to the category of device failures. Here we will briefly touch on longer-term irreversible changes - the "aging" of detectors. In practice, we can distinguish two types of these irreversible time changes of the detector properties :
l Spontaneous temporal changes in the properties of the detector
due to physical and chemical influences inside or by effect of the external environment. A typical example is yellowing of scintillation crystals NaI(Tl) (see Fig.2.4.8 in the section " Inorganic scintillators") , deterioration of optical contact between scintillator and photomultiplier, or gradual changes in gas pressure in ionization chambers (eg gas leakage through chamber leaks).
l Radiation damage and depletion of detection material
due to physico-chemical processes during interactions with detected radiation. When detecting radiation g and b lower and medium energies, low-density excitations and ionizations occur, with subsequent deexcitation and recombination usually leading to the restoration of the original properties of the material. Scintillation or ionization detectors g and b can work for many years without significant wear. When heavy charged particles and neutrons are detected, massive ionizations occur, or even nuclear reactions, in which considerable energy is transferred locally. There is damage to the crystal lattice, chemical changes, or even transmutations of atoms of the detector material (see below "Nuclear reactions and induced radioactivity inside the detectors"). The active area of the detector is thereby radiation damages and depletes.
All these phenomena can lead to a gradual reduction of detection efficiency and in more complex detectors to deterioration of other parameters such as energy resolution, spatial resolution, homogeneity and linearity of the image. Aging and radiation wear of detectors are significantly reflected in systems where detectors are exposed to high energy fluxes for a long time. These are, for example, monitoring detectors in nuclear reactors, detection systems (trackers and calorimeters) of secondary particles on accelerators, dosimetric devices on irradiators in radiotherapy. This leads to a limited lifetime of the detectors.
In normal conditions, detection, spectrometry and scintigraphy of gamma radiation with energies of tens and hundreds of keV and pulse flows up to about 3.10⁵cps, however no radiation "aging or wear" occurs.
Radiation damage to the detector by intense flux of radiation
Strong flux of ionizing radiation in the detector causes radiolysis and dissociation of molecules of the detector material, eg in the NaI (Tl) detector of the NaI ® Na⁺ + I^-. Dissociated molecules can recombine immediately or with a certain time delay. During recombination, light photons are often emitted - chemiluminescence occurs. If the dissociation of the scintillator molecules persists for a long time, these photons, registered by the photomultiplier, can significantly increase the internal background of the detector in the region of low-amplitude-energy pulses. This phenomenon lasts a transient time, after the recombination is completed, the internal background quickly returns to the original value.
Ionization chambers are highly "resistant" to strong radiation fluxes, which can measure over a wide range of intensities with an almost linear response. Scintillation detectors in the "on" mode (with high voltage on the dynodes) must not be exposed to high radiation fluxes (> approx. 10⁷ quant/s) in order to avoid overloading the photomultiplier dynodes with a high flux of electrons and their irreversible damaging !
Nuclear reactions and induced radioactivity inside detectors
If high energy radiation (> 10MeV) or neutron radiation enters the detector, the (photo)nuclear reactions may occur in the detector material (as well as in the construction material of the envelope, shield and collimator) (see §1.3 "Nuclear reactions and nuclear energy" and §1.6 "Ionizing radiation", part "Interaction of gamma and X - rays" and "Neutron radiation and its interactions"). In some of these reactions, radioactive nuclei may be produced - induced radioactivity is formed inside the detector,internal radioactive contamination of the detector occurs. Such an internally activated detector after exposure to high-energy or neutron radiation may have impaired detection properties: it has a higher internal background and spectrometric analysis shows a disturbing artificial spectrum - continuous beta, or gamma or characteristic X-ray peaks. Fortunately, this phenomenon lasts for a transitional period before the induced radioactivity decays with the corresponding half-life. However, this circumstance must be taken into account if we want to measure with a detector that was previously located in the field of high-energy or neutron radiation (either during the actual measurement or even switched off). The induced activity can be many kBq, which can invalidate particularly sensitive measurements of weak radiation fluxes and low activities.
Internal activation of the NaI (Tl) scintillation detector
An example of this phenomenon is the NaI(T1) scintillation detector (discussed in detail below "Scintillation detection and spectrometry"). Due to neutrons, nuclear reactions can occur inside the crystal (n, g): ¹²⁷I + n ® ¹²⁸I + g, in which radioactive iodine-128 is formed from the original inactive iodine-127, which with a half-life of 25 min. by b^- decay (E_b_max = 2.12MeV) it converts to stable ¹²⁸Xe and from 6.5% by electron capture to ¹²⁸Te. In addition to beta radiation with a continuous spectrum, gamma radiation 441keV and characteristic X-radiation are also emitted. This internally induced ¹²⁸I activity produces an artificial continuous b- spectrum extending up to over 2 MeV and a characteristic X-ray peak of tellurium 26 keV. The phenomenon lasts with a decreasing tendency for several hours, until iodine-128 decays.
Similarly, when irradiated with high-energy photon radiation (energy greater than about 15MeV) the photonuclear reactions ( g , n) ¹²⁷I + g ® ¹²⁶I + n can occur inside the NaI(Tl) crystal , which produces radioactive iodine-126, which with a half-life of 13 days is converted by 44% by b^- decay (E_b_max = 1.25MeV) to stable ¹²⁶Xe and 55% by electron capture to ¹²⁶Te. In addition to electron beta radiation with a continuous spectrum (reaching over 1 MeV), gamma radiation of 386keV and 667keV is emitted, as well as characteristic X-radiation of Te with an energy of 26keV. In this case, the detector is internally contaminated for several weeks!
The scintillation spectrum of this internal contamination, measured by the same detector, differs significantly from the spectra of the respective radionuclides from external sources. Some quantum b, g, X are detected coincidentally, so the resulting pulses are summed. As a result, some gamma peaks are not present in the spectrum (the apparent "mystery of lost gamma") - their pulses summed by the signals from the electrons, fall into the continuous beta spectrum; for this reason, we do not see in the spectrum, for example, the g- peak 411keV ¹²⁸I or the peak 386keV ¹²⁶I. Other peaks have shifted energies due to superposition with characteristic X-rays; eg peak g 667keV ¹²⁶I we see an widespread and in a higher position around 690keV, caused by a coincidence sum with a characteristic X-ray of 26keV.
For germanium -based semiconductor detectors, the radionuclide ⁷¹Ge (decays with electron capture, T1/2 = 11.4 days) can be formed either by neutron capture from a stable ⁷⁰Ge, or by a photonuclear reaction (g , n) from ⁷²Ge. Some gallium radioisotopes can also be formed here by neutron capture, eg ⁷²Ga (T1/2 = 14 hours, b^- 3.15 MeV, a number of g lines from 0.6 to 2.5 MeV) and to a lesser extent several other short-term ones.
For silicon semiconductor detectors can induce only a small number of short-term isotopes - neutron or g activation by aluminum isotopes, eg ²⁸Al (T1/2 = 2.3min., b^- 2.85MeV, g 1.78 MeV).
In ionization chambers filled with xenon (which is a mixture of a number of stable isotopes from ^124-136Xe), neutron or gamma activation can produce various radioisotopes of iodine (including the known ¹³¹I) and xenon, but due to the low density of gaseous xenon only in small amounts, usually does not affect the properties of the chamber.

2.2. Photographic detection of ionizing radiation. Material detectors.
All photographic and material detectors operate in a cumulative (integral) mode in the sense of the classification in §2.1. We will first describe photographic detection, which is the most common.
In photographic detectors, the detection medium is photographic material. When ionizing radiation enters this photographic material *) containing silver halides (such as silver bromide AgBr), a photochemical reaction occurs at the ionization sites.
*) The use of photographic materials was the first and oldest method of indicating nuclear radiation; with help of her, H.Beckerel also discovered the radioactivity of uranium ore.
Photochemical reaction
Below the photochemical reaction generally we mean any chemical reaction caused by the incidence of light or other radiation - interaction radiation quanta (photons, electrons, protons, a particles etc.) with atoms and molecules of the substance. The most important photochemical reaction in nature is photosynthesis in plants. Photochemical reactions are used in photography, leading to such chemical changes in the light-sensitive material, which can be used to visualize the spatial distribution of radiation - for photographic imaging.
Photographic (light-sensitive) materials are formed by small crystals of silver halide (now it is almost always silver bromide, crystal size approx. 1 mm, density approx. 10⁹/cm²), which are dispersed in a gelatin layer. This so-called photographic emulsion is coated on the surface of a plastic foil - film; glass photographic plates were also used in the past. In the silver bromide molecule AgBr, the silver and bromine atoms are bound by an ionic bond - Ag⁺ Br^-, which is relatively weak; the AgBr crystal lattice forms a cubic system.
The classical photochemical reaction is caused by the absorption of a light photon f, whose energy h.n releases an electron from the bound bromine atom (bromide ion Br^-): Br^- + f ® Br + e^-. The released electron can be absorbed by some silver ion Ag⁺ bound in bromide: Ag⁺ + e^- ® Ag, thus forming a neutral silver atom. This is the primary photochemical reaction in which the energy of the photon must be higher than the binding energy of the molecule that is cleaved during photolysis. Due to these processes, the disintegration ( photolysis ) of silver bromide occurs. A similar photochemical reaction occurs when irradiation of photographic material with ionizing radiation, which causes the decomposition - radiolysis - of silver bromide. The result is the release of silver atoms from its bond from the AgBr compound and formation the latent image.
At first we would not see anything with the naked eye on the exposed layer, the image is "hidden" (latent), formed only by sparsely distributed silver atoms. The physicochemical change in the tiny silver bromide crystals is made visible only during invocation - development. The development process is an electrochemical reaction in which electrons are primarily transferred from the developing agent to AgBr via the silver atoms in the latent image. Developers (usually methanol and hydroquinone) cleave bromine (which passes into the developer) from exposed bromosilver particles, reducing the original silver bromide to metallic silver. From the hydroxyl group OH bound to the cyclic hydrocarbon (benzene nucleus) of the developing agent, a hydrogen ion is cleaved off, which combines with a bromine ion to form HBr (dissolved in the developer) and a silver atom of Ag. The developing agent penetrates (in dissociated form) to the germs of the latent image, transfers AgBr to its electrons, and silver is reduced . By encountering the transferred electrons with other silver Ag⁺ ions in AgBr, the reduction process is further transferred to the silver bromide crystal and further silver is released. The effect of the microscopic latent image is initiating and catalytic - the chemical process of reduction gradually captures the whole grain of silver bromide, a large number of silver atoms is formed (multiplication factor of about 10⁸). This process occurs only on those AgBr crystals, which already contained several atoms of photolytically excluded silver before development. The different degree of exposure of the photographic emulsion is thus made visible by the density of the colloidal silver grains. The remaining unilluminated and undeveloped silver bromide is removed from the sensitive layer by dissolving in a fixer (aqueous sodium sulfate solution).
After exposure to ionizing radiation, the blackening density of the developed photographic material is proportional to the ionization density at that location, and thus the amount of ionizing radiation energy that has been absorbed at that location. By macroscopic observation or measurement of the total blackening of photographic material, or its individual places, we can determine intensity - amount of radiation in dosimetry and X-ray diagnostics or defectoscopy, by microscopic observation of grains of released silver in the photoemulsion can then observe and evaluate the paths of charged particles in special nuclear emulsions (see below).

Film dosimeters , X-ray films
Simplest use of photographic detection of ionizing radiation, are film dosimeters. The basis of the film dosimeter is a small rectangle of photographic film, tight against of light packed in black paper (it differs from ordinary photographic film in that it has a thicker emulsion with a higher content of silver bromide). The ionizing radiation passes through the film coating and creates a latent image in the photoemulsion, which is visible after development. The optical density of the graying or blackening of the film, which can be evaluated photometrically, is then a measure of the integral amount of radiation that has passed through the film during exposure; this also indicates the dose of radiation that would be absorbed in the substance exposed to this exposure. For small doses of radiation, there is an approximately linear relationship between the dose of radiation and the blackening of the photographic material, at higher doses the blackening grows more slowly and then reaches a state of saturation.
Note: For the objective determination of the radiation dose, a standardized development procedure should be used and the blackening should be compared with a reference film irradiated with a known radiation dose.

Fig.2.2.1. Personal film dosimeter used to monitor workers.
(Thermoluminescent TLD and photoluminescent OSL dosimeters are discussed below , Fig.2.2.2)

Film dosimeters are mainly used for personal dosimetry of workers with ionizing radiation. The film frame itself is inserted into a plastic case (Fig.2.2.1), provided with several small thin rectangles of copper and lead plates of different thicknesses, which serve as filters absorbing radiation g depending on its energy. These filters are used to correct the dependence of blackening on the energy of radiation, and by comparing the blackening under individual filters, it is possible to estimate the type and roughly the energy of radiation (of course, the film itself does not have spectrometric properties). The film dosimeter is worn by workers at the reference point (left pocket on the shirt) and regularly (usually once a month) is exchanged, developed and photometrically evaluated; using a suitable calibration factor, the resulting measured value is the radiation effective dose in mSv.
A similar type of film (usually of much larger dimensions) is used for X-ray imaging in planar X-ray diagnostics (§3.1 "X-rays - X-ray diagnostics"), as well as in defectoscopic measurements (§3.2 and 3.3). After development, the images on these films are evaluated either visually or photometrically.
Autoradiography
This laboratory radiographic method consists in photographically imaging the distribution of the radioindicator in the examined objects in close contact *) of the photographic emulsion with the sample (the prefix "auto" indicates that the radioactive substance is inside the sample). The radioactive sample is attached - pressed to the photoemulsion, which is then exposed in the dark (in a light-tight housing) for some time. Sensitive photographic film photochemically captures the emitted beta or alpha radiation (gamma radiation here contributes only slightly to blackening). After development, differences in the local concentration of the radioactive substance are manifested by varying degrees of blackening of emulsion, on which we can see the distribution of structures with higher or lower accumulation of radioindicator.
*) Image quality
Tight contact of the photoemulsion with the sample is necessary to achieve good sharpness and spatial resolution of the autoradiographic image. Image "collimation" is achieved by each site of the photographic emulsion receiving the largest contribution of radiation from the area of the sample that is closest, while from other - more distant areas - the beta/alpha flux density decreases rapidly (even faster than according to the standard law of the inverse square of distance, because this radiation is strongly absorbed in the substance and has a short range). It is obvious that the image of the radioactivity distribution will be sharper the closer we press the photographic film to the sample. With increasing distance of the photoemulsion from the sample, or its thickness, the sharpness and resolution deteriorate rapidly.
The quality of the image also depends on the energy of the emitted beta radiation. For lower energies with shorter electron range we can achieve better resolution (eg with low-energy phosphorus 33-P we can achieve better resolution on autoradiograms than with high-energy 32-P - see §1.4, passage "Phosphorus, Sulfur").
Beta-radionuclide- labeled radioindicators, such as tritium ³ H, radiocarbon ¹⁴ C, phosphorus^32.33 P, sulfur³⁵ S, are most often used for autoradiography of biological preparations. If selective pharmacokinetics are appropriate, radioindicators labeled with radioiodine¹³¹I (or ¹²⁵ I ), yttrium⁹⁰ Y , in the 1970s also¹⁹⁸Au, and other suitable radionuclides are also used. The required applied activity depends on the radionuclide used, the degree of accumulation of the radioindicator in the investigated structures, the sensitivity of the emulsion, the exposure time. These parameters are influenced by a number of factors, they are optimized empirically (according to experience, to obtain sufficient blackening is per 1cm² photoemulsions need exposure of about 5-10 million beta electrons, or about 2 million alpha particles).
In addition to classical autoradiography, electronic digital autoradiography is now used in larger specialized laboratories, where instead of a photographic emulsion, the imaging is performed using a flat system matrix of semiconductor detectors (similar to so-called flat panels in radiology, see "Electronic X-ray imaging"), attached to the sample. They make it possible to perform online quantitative autoradiographic analysis operatively in a short time.
And if the distribution of the radio indicator does not need to be registered in image form, it is enough to use a simple radiometric detector (possibly several parallel detectors), which passes over the sample and measures the profilogram of the radioactivity distribution. This simple method is routinely used especially in radiochromatography (§2.7 "Measurement of radioactivity of samples", passage "Radiochromatography").
Autoradiography is often used in laboratory methods of molecular biology and genetics. According to the size of the analyzed tissue samples, we have two groups, the third group concerns the imaging of electrophoretic and chromatographic samples :
1. Macro-autoradiography , which shows the distribution of radioactivity in structures the size of millimeters and centimeters (so we can assess differences in blackening with the naked eye). Thus, after previous application of the radioindicator, sections of organs or their parts can be displayed - Fig.2.2.2 a .
2. Micro-autoradiography shows histological tissue sections or cytological samples (coatings on a microscope slide) obtained after previous application of a biologically targeted radioindicator. The structure of blackening after exposure is evaluated under a microscope - Fig.2.2.2 b (and can be confronted with the classical observation of a stained specimen under a microscope). By using thin sections and fine-grained photoemulsions, a high resolution of 3-5 micrometers can be achieved, down to the subcellular level.

Fig2.2.2. Examples of three types of autoradiography. a) Macro-autoradiogram of a kidney section of a laboratory animal after application of the radioindicator ¹³¹I-hipuran.
b) Micro-autoradiogram of a histological section of the liver with a radiolabeled colloid which is taken up in Kuiper cells.
c) Autoradiography of 4 samples of the sequence of DNA fragments labeled with ³²P radiophosphorus and separated by gel electrophoresis.

3. Molecular separation analysis of sequenced samples
Very important is the use of autoradiography in the sample analysis, in which the desired radiolabeled molecules divided - sequenced - by the length of their chains separated in a chromatography column, or more usually by electrophoresis in a gel - see below §2.7, part "Radio-electrophoresis". Gels form a dense network - a "molecular sieve" through which larger molecules pass more slowly than smaller molecules. The analyzed molecules are thus gradually divided according to their size (fragment length) at a distance of several millimeters to centimeters. If they are labeled with beta-radionuclide, after applying the photoemulsion we can display them autoradiographically in the form of "strips", where the separated molecules traveled according to their size (in terms of geometric dimensions it is a macro-autoradiography) - Fig.2.2.2 c. Detected positions of individual fragments are compared with the standard sample analyzed in parallel.
Note:Current routine biochemical DNA sequencing methods use fluorescently labeled nucleotides, which are analyzed by capillary electrophoresis in a large number (several dozen) of parallel capillary sequencers, the fluorescent light being registered by means of a sensitive optoelectronic detector. These new sequencing techniques allow very fast and relatively inexpensive "reading" of entire genomes. A huge amount of sequence data obtained in this way is processed by computer - it becomes the subject of bioinformatics.

Material detectors
Material detectors use some permanent small physical and chemical changes that ionizing radiation causes as they pass through suitable substances (materials). These can be excitations, structural changes in the crystal lattice, polymerization, changes in optical properties (such as color), electrical conductivity. The extent of these effects is proportional to the amount of radiation (number of radiation quanta) transmitted and absorbed by the detection material - it is therefore proportional to the radiation dose at the detector site. They are therefore mainly used for dosimetric purposes.
Thermoluminescence and photoluminescence (OSL) dosimeters
Material radiation detection here is based on the phenomenon of metastable excitation of some dielectric materials: electrons released by ionizing radiation pass from the valence band to the conduction band, from where they are trapped in the places of dislocation of the crystal lattice of the material at energetically excited levels ("capture traps") *) and they remain there for a long time - the levels are metastable. Electrons cannot get out of these levels spontaneously, but are only released by supplying a certain amount of energy (heating or light irradiation). In this way, part of the energy absorbed during irradiation collects in the material . By heating - thermoluminescence (thermally stimulated luminescence) or by irradiation with visible light - OSL (Optically Stimulated Luminescence) deexcitation occur and electrons return to lower energy levels (and to the electron shells of the atoms of the material). The released excitation energy of electrons is emitted in the form of visible light photons - luminescence (fluorescence) of the material occurs, mostly in blue-green light. The higher the radiation dose of the material, the more electrons accumulated in metastable levels and the more photons emitted when evaluated by thermoluminescence or OSL-luminescence: this light yield is therefore proportional to the radiation dose in the irradiated material.
*)The mechanism is to some extent similar to the origin of scintillation in scintillators - §2.4 "Scintillation detectors", part "Scintillators and their properties", Fig.2.4.5 left. The main difference is in the lifetime of excited electron levels: while for scintillators almost immediate deexcitation with the shortest possible afterglow time is desired, for thermoluminescent and OSL materials, on the other hand, the maximum (meta)stability is required, with as little fading as possible. Similar to scintillation materials, although there may be a capture centers made by first base material, a large number of these centers can additionally create introducing ions of the activator in the crystal lattice - these ions cause additional discrete levels in the forbidden band. A common activator, or dopant impurities for TLD and OSL materials are manganese, dysprosium, carbon.
¨ Thermoluminescent dosimetry TLD
As thermoluminescent substances are most often used lithium fluoride LiF (: Mg, Ti, Cu) *), calcium fluoride CaF₂ (: Dy, Mn), calcium sulphate CaSO₄ (: Mn, Dy), alumio-phosphate glass Al(PO₃ )₃ -Mg (PO ₃ ) ₃ , Li ₂ B ₄ O ₇ (: Mn) (low sensitivity, suitable for high doses). A sample of a precisely defined amount of a given TLD substance is encapsulated in a thermoluminescent dosimeter, which is exposed to radiation at the place where the radiation dose is to be determined (TLD material is made differently, on the finger dosimeter in Fig.2.2.1b on the left it is in the shape of a foil - a "chip" about 1 mm thick). At the end of the exposure, the thermoluminescent substance is removed from the housing and heated in the evaluation device to a temperature of about 160-300 °C (depending on the type of material) and the emitted visible light is sensed using a photomultiplier. The electrical signal from the photomultiplier is recorded depending on the temperature - a so-called heating curve is created, the integral of which (area under the curve) is proportional to the dose in the dosimeter.
*) For neutron dosimetry, lithium enriched with the ⁶Li isotope is used instead of natural lithium (with a predominance of ⁷Li).

Fig.2.2.3. Left: Thermoluminescent TLD dosimeter. Middle: Photoluminescent OSL dosimeter. Right: Principle of operation of TLD and OSL dosimeters.

¨ Photoluminescent OSL dosimetry
also called PLD (Photo Luminescence Dosimetry). Optically stimulated luminescence is shown, for example, in the richly distributed silica oxide (quartz), but in dosimetric practice, mainly aluminum oxide Al₂ O₃ (:C), activated by carbon, is used. A defined sample of this substance is exposed to radiation in the dosimeter at the place of radiation monitoring. Irradiation with LED light (longer wavelength - yellow-green light) is used for evaluation, while the resulting luminescence (shorter wavelength - blue light) is detected by a photomultiplier. The total luminescence thus generated is again proportional to the irradiation of dosimeter. Compared to TLDs, the evaluation is simpler and more reproducible (LED irradiation is easier to standardize than controlled thermal heating).
Thermoluminescence and OSL dosimetry is schematically shown in the right part of Fig.2.2.3. These dosimeters can be designed as finger dosimeters for monitoring during laboratory work, or whole-body dosimeters monitoring a sample of total irradiation at a reference site. As with film dosimeters, several separate detection elements, sometimes covered by different filters, are sometimes used - for the analysis of the type and energy of ionizing radiation. Compared to film dosimeters, there is the advantage of higher radiation sensitivity and accuracy, a larger range of measured doses, low sensitivity to external influences (temperature, humidity, chemical fumes), the possibility of continuous operational evaluation and reuse of material (exposure and evaluation is not destructive).
Luminescent archaeological dating
Materials capable of long-term metastable (almost stable!) excitation of electrons in crystal lattices are commonly found in nature. The excitation of these materials occurs slowly and continuously due to natural radioactive radiation (whose intensity is constant for a long time, but may vary for different localities). This phenomenon can be used for archaeological dating. The older the studied material of this kind - the longer the time has passed since its last heating or light irradiation - the more it was "excited" by the excited electrons. It's a kind of "time counter".
Thermoluminescence can be used to determine the age of fired ceramic objects or bricks containing quartz- the most common mineral exhibiting thermoluminescence. All electrons previously trapped in the metastable levels of the trapping centers of the respective material were released by high temperature heat treatment during production. These empty levels are then gradually occupied by electrons released by natural ionizing radiation (thorium and uranium decay series, potassium-40, cosmic radiation). We heat the investigated ceramics (to a temperature of approx. 300 °C) and measure the luminescence it emits. The intensity of this thermally stimulated luminescence depends on the time that has elapsed since its original firing (during manufacture) and the current - new - firing during analysis.
Similarly, small grains of quartz and feldspar, which are commonly found in all layers of archaeological excavations, show optically stimulated luminescence (OSL): metastable electron levels in crystal lattices are gradually and long-term occupied by electrons released by ionizing radiation from natural radioactivity, especially potassium ⁴⁰K. The longer the quartz grain is exposed to this natural ionizing radiation, the more electrons accumulate in these metastable "traps". When irradiated with visible light, the captured electrons then deexcite, measuring the luminescence that is proportional to the time that has elapsed since their last illumination (when they were covered in the landfill from daylight; samples must be taken and processed without access to light! - otherwise premature deexcitation of metastable levels would occur and the accumulated "record" would be "reset").
These luminescence methods allow archaeological dating in the time range of about 100 - 100,000 years.

Other material detectors
This includes, for example, trace detectors, based on the fact that after the impact of densely ionizing particles, especially alpha, there are minor local defects in the crystal lattice of certain materials (eg mica, special glasses, organic polymers). These microscopic defects can be increased to macroscopic dimensions by etching (the damaged material is more chemically sensitive, so it dissolves). The traces etched in this way are then observed under a microscope and their density is determined - either manually or automatically using electro-optical methods. They are mainly used to measure the long-term average concentration of radon in the field (in building interiors) using the density of traces created a-particles from the radioactivity of radon and its daughter products.
The so-called long base silicon diodes (LBSD - Long Base Silicon Diode ), designed for measuring the radiation dose (kerma) from heavy particles, especially fast neutrons, can also be included in this category . When a fast particle collides with a silicon atom, this atom is ejected from its position in the lattice. As a result of this irradiation and ionization, the crystal lattice of silicon is damaged, which changes the lifetime of the minor charge carriers and thus the conductivity of the diode. The voltage drop across the diode is measured in the forward direction before and after irradiation, the change in voltage drop after irradiation relative to the initial value being an approximately linear function of the radiation dose (kerma).

Material detectors, due to their relatively small use in nuclear and radiation physics and technology, we will not deal in the next text of this chapter. For interest, we will mention here only 3-dimensional gel detectors (rare used in radiotherapy) :

3-dimensional gel detectors
The most complex, but physically interesting variant of material detectors are the so-called 3-dimensional gel dosimeters, which allow to record and store the spatial distribution of the radiation dose in the form of a certain dose picture. They are integral (cumulative) chemical detectors in which information is fixed in a gel environment. The measured volume (eg phantom), in which we want to determine the spatial distribution of radiation intensity or dose, is filled with a gel consisting mostly of a gelatin carrier (matrix), in which the radiation-sensitive substance is dispersed. Upon irradiation of this volume, free radicals are generated by the interaction of radiation in the gel, mainly due to radiolysis of water, which by chemical reactions induce permanent physicochemical changes of the sensitive substance at the irradiation site, the intensity of which is proportional to the local absorbed radiation dose. In particular, two types of sensitive substances dispersed in the gel are used, differing in the mechanism of the radiation effect :
w Radiochromic gel dosimeters ,
where the sensitive substance changes its color by irradiation. The most frequently used iron sulfate [ferro ammonium sulfate (NH₄)₂SO₄.FeSO₄.6H₂O in the so-called Fick's solution with sulfuric acid H₂SO₄ ], where free radicals and hydrogen peroxide, formed by irradiation of an aqueous solution in a gel, cause oxidation of Fe⁺² ions to Fe⁺³. This leads to increased light absorption, especially at a wavelength of around 300 nm. A certain disadvantage of this substance is the diffusion of radiation products - iron ions - from the place of their origin to the surroundings in the gel, which soon blurs the information about the spatial distribution of the dose. To reduce the diffusion effect, the chemical composition was improved by the addition of xylenol, forming a color complex (xylenol-orange ) with Fe⁺³ ions. In this so-called FXG dosimeter, in addition to reducing the diffusion effect, an increase in the optical response is achieved by absorbing the wavelength of 585 nm.
Note: Plastic 3-D dosimeter: Instead of a gel, the radiochromic substance is sometimes fixed in a low-melting plastic; with optical evaluation.
w Polymer gel detectors
consist of a monomeric substance dispersed in a gelatin carrier. Free radicals formed in the gel upon irradiation induce local polymerization of the monomer at the site of irradiation, in proportion to the absorbed dose. The gel carrier causes the radiation-formed polymer (with large molecules) to remain permanently localized at the site of interaction. This polymerization leads to changes in optical properties - the originally transparent gel acquires turbidity at the site of irradiation, the opacity of which is proportional to the absorbed dose. The density also increases slightly. The most commonly used sensitive substance here is methacrylic acid, resp. a mixture of acrylamide and N, N-methylenebisacrylamide. Compared to ferro-sulphate gels, polyacrylamide gels have the advantage that the polymerization chains remain permanently fixed at the site of their formation, so that the record of the spatial distribution of the dose is stable for weeks and months. Therefore, polymer gel dosimeters appear to be more promising.
A certain disadvantage of polymeric gel dosimeters is their sensitivity to atmospheric oxygen, which can inhibit polymerization. Their material must therefore be prepared in a nitrogen atmosphere and filled into hermetically sealed containers. Sometimes oxygen absorbers are added to the gel.
The resulting irradiation effect of both types of 3D gel dosimeters is local material changes proportional to the local absorbed dose. These changes manifest themselves in three ways, which allows the evaluation of the spatial distribution of the dose in the irradiated gel dosimeter by three methods :
× Transmission optical CT
The non -irradiated gel is optically almost transparent. The sites with the higher absorbed dose where the radiochemical reaction occurred show variety of optical properties - discoloration, turbidity - have increased light absorption, higher opacity. By irradiating the detector gel with light rays at different angles 0-360°, with the measurement of the transmitted intensity, resp. attenuation of the beam, using photodiodes (or CCD detectors) and subsequent reconstruction based on the Radon transformation by the method of filtered back projection, we obtain transversal images of opacity and thus the local distribution of the dose in cross sections. The set of these cross-sections will create a three-dimensional image of opacity and thus the spatial distribution of the radiation dose in the sensitive volume of the gel detector. This optical CT scan and reconstruction is analogous to X-ray CT, described in §3.2 "X-ray diagnostics", part "Transmission X-ray tmography (CT)". The gel dosimeter is mounted in a special holder, rotating by means of a stepping electric motor. The irradiation is realized either by a thin laser beam - an accurate but lengthy method, or by a wide beam of light - a fast but less accurate method (usually sufficient in practice). For better optical contact, irradiation is suitable with a dosimeter immersed in an aqueous enviroment.
× Nuclear magnetic resonance NMRI
At the sites of radiochemical reaction, chemical properties change, which leads to subtle changes in magnetic behavior. There are changes in the interaction of nuclear moments, manifested by changes in relaxation times T1 and T2 of magnetic moments of hydrogen nuclei when imaging a gel detector by nuclear magnetic resonance (see §3.4, section "Nuclear magnetic resonance"). With appropriate modulation (sequence and "weighing"), the intensity in the NMRI image will be proportional to the local radiation dose in the gel.
× X-ray CT
The radiochemical reaction may lead to slight changes in the density of the material. In places where radiation-induced polymerization has taken place, the volume of the sensitive substance decreases and thus the detector material density increases. This leads to an increase in the linear attenuation factor for X-rays, which can be shown by CT transmission tomography. With use an X-ray CT of gel detector, using the soft tissue CT settings, we obtain an image whose density expressed in Housfield CT units will be modulated by the spatial distribution of the radiation dose in the gel dosimeter material.
3D gel detectors are rare used in dosimetric measurements in radiotherapy, especially in measuring intricately shaped spatial distributions of radiation doses in advanced radiotherapeutic techniques IMRT, stereotactic radiotherapy, high-density brachytherapy or hadron radiotherapy - see §3.6 "Radiotherapy". With dosimetric gel may be filled vessel modeling anatomic various organs and body parts for the purpose phantom dosimetric measurements. A significant advantage of gel dosimeters is their energy independence, tissue equivalence (density of the gel is approximately equal to the density of soft tissues), and almost linear response of the size the radiation dose even in high doses. The disadvantage is, as with all material detectors, low sensitivity, they work only from relatively high doses of about 4 Gy.
3D gel dosimetry is relatively complex and demanding method both in the stage of laboratory preparation (including high demands on the homogeneous distribution of the sensitive substance in the gel), as well as the evaluation of the response in the dosimeter material. It is therefore used only sporadically.
For comparison and interest, see §3.6, passage "Make the 'invisible visible' - display of radiation beams", where pictures of the optical response of electron, photon and proton radiation using Cherenkov radiation in water and scintillation radiation in a liquid scintillator are shown.

Particle trace detectors
In addition to "one-time" detection of radiation quanta and spectrometry of their energy, important information about the physical properties of particles can carry their behavior and motion in substances and magnetic and electric fields. To study the properties of particles, it is therefore useful to capture - "make visible" - analyze the path of their movement in matter, with the possible participation of a magnetic field.
Nuclear photoemulsions for particle trace detection
The oldest and easiest way is to record photographically the trajectory - the trace that the particle left in its movement in matter. To detect traces of particles, a photographic emulsion with a relatively large thickness (approx. 0.1-1 mm) and a high content of silver halide in gelatin is applied to the film or glass plate. When a fast charged particle enters this emulsion, it leaves an ionization trace along its path of movement, in which a photochemical reaction releases silver in the grains of silver halogens dispersed in the gelatin of the emulsion. The particle thus leaves traces of released silver on its path in the emulsion from grain to grain, ie a latent image of its path is formed; upon development, a visible trace of a more or less dense sequence of black particles is formed, the density of the silver grains along the path depending on the species and energy of the particle.
  Viewing and measuring these traces in exposed and developed nuclear photoemulsions is performed using special microscopes equipped with micrometric shifts. The range of the particle (if its path ends in the emulsion) and the density of the silver grains are measured along its path. From these measurements, the energy and mass of the particle that has flowed through the emulsion can be determined. The greater the particle's energy, the greater the range of the particle. The density of silver grains, i.e. the relative number of grains per unit length of the path, is proportional to the relative loss of energy of the particle in a given section of the path. According to the so-called Bragg curve (see §1.6, Fig.1.6.1), each charged particle causes more and more ionization towards the end of its path with a maximum just before the end of the path (stopping), so that the end parts of the particle track appear the highest blackening density (the largest number of silver grains).
If during the exposure a nuclear emulsion is placed in a strong magnetic field of a given intensity and direction, the paths of the charged particles are curved by the action of the Lorentz force; from the curvature of particle paths it is then possible to determine the ratio of charge and momentum of the particle (images are similar to Fig.2.2.4, but negative - the trace is black on a white background). If a fast particle interacts with another particle within the emulsion, important quantitative data on the dynamics of this interaction can be determined from the angles of travel, curvature, blackening, and trajectory of the individual secondary particles formed.
  Another option is to stack several photographic emulsions (films or plates) on top of each other. The passage of a particle through this system causes a small island of blackening at the corresponding point (the intersection of the particle's path with the emulsion) on each of the plates. By evaluating these traces from the individual emulsions, the spatial trajectory of the particle can be reconstructed.
Note: Now, even electronic position-sensitive detectors (trackers) are spatially assembled into blocks or other structures.
  Nuclear emulsions were also used to study nuclear reactions, while the emulsions were filled with compounds of some elements - lithium, boron, uranium, etc., with the nuclei of which the reactions were examinated.
Nuclear photoemulsions played an important role in the study of nuclear processes and elementary particles in the first generations of accelerators and in cosmic rays; a number of elementary particles were discovered using these emulsions. The disadvantages of nuclear emulsions are their small dimensions (especially thickness) and low operability of use - particle paths are only visible later, after development, and their evaluation is slow and laborious *). Therefore, they were gradually pushed out primarily bubble chambers, which provide significantly faster and more complete information about the motion and interactions of elementary particles. And now the bubble chambers are being pushed out by electronic detection systems, see below.
*) ECC photoemulsion chambers
However, nuclear photoemulsions are still used in some particle experiments, where a very high spatial resolution of registered particle paths, on the order of micrometers, is required. Often a "sandwich" arrangement of photoemulsions is used in a series of layers of films applied close to each other, with possibly interleaving with layers of target material (eg lead). This arrangement is referred to as the Emulsion Cloud Chamber (ECC) - a kind of "photoemulsion cloud chamber" which, after evaluation, provides similar images of particulate traces as a conventional cloud chamber (described below). The evaluation of photoemulsions in modern detection systems is fully automated, performed by microscopic scanning, electronic digitization and computer evaluation. The largest detection system based on nuclear photoemulsions is currently OPERA in the Gran Sasso underground laboratory for the detection of neutrinos and the study of their oscillations (see §1.2, section "Neutrinos - "ghosts" between particles", passage "CNGS + OPERA").

Cloud and bubble chambers for the detection of trace particle
Wilson cloud chamber
First type of detector, providing continuous visible traces of flight of charged particles, is the Wilson cloud chamber. It consists of a closed glass cylinder filled with a gas (perhaps air) with saturated vapors of suitable liquids - water vapors are used with an admixture of vapors of organic substances, most often alcohol. Sometimes the chamber space is also filled with rare gases, such as argon. The cylinder is provided on one side with a piston or diaphragm, the displacement of which allows a rapid change in volume and pressure inside the cylinder. If we perform a rapid expansion of the working space of the chamber (to about 1.2-1.4 times the original volume), it will occur due to adiabatic expansion of the gas in the cylinder to drop the temperature and the saturated vapors present with the resulting cooling below the dew point become supersaturated. Supersaturated vapors tend to precipitate in the form of droplets (mist) on the walls of the vessel, as well as on dust particles and ions which are contained in the gas and form condensation nuclei for formation of droplets. If condensation nuclei are not present (dust-free environment in the cylinder), supersaturated vapors will last for a short time without condensation.
  If a charged particle passes through such a working space either just before expansion or during expansion, it will form a number of ions along its path, which attract and thus locally concentrate vapor molecules. Supersaturated vapors precipitate on these ions as condensation nuclei - the path of the particle is covered by a series of small droplets. With suitable side lighting, the ionization paths are clearly visible as light traces on a dark background and can be observed or photographed in this way.
  The supersaturated mist chamber remains sensitive to particle path registration for only tenths of a second. After photographically capturing the traces of particles, the chamber must be set to the initial state - reseted: the gas in the working cylinder is back-compressed, the droplets evaporate or flow down along the walls of the cylinder, the steam becomes saturated again. Then a new work cycle of expansion - exposure - compression can occur, which may be repeated periodically.
  The length of the nebula track and its "fulness" (density) is characteristic for different types of ionizing particles and their energy. In order to be able to derive quantitative parameters of particle motion from the observed trajectory, stereoscopic images of the trajectory are taken by two cameras oriented at appropriate angles. Then, the reconstruction of the captured paths, their accurate measurement and evaluation of the quantities characterizing the motion and interaction of the detected particles are performed. To determine the electric charge of the particles, the fog chamber is placed in a strong magnetic field and the curvature of the particle paths is evaluated.
Diffuse could chambers
The disadvantage of the classical Wilson could chamber is the short sensitive registration time of the particles during the working cycle. Therefore, types of fog chambers operating not cyclically but continuously - diffuse cloud chambers have been developed. A vertical temperature gradient is achieved in the working cylinder of this chamber by heating the upper plate of the chamber with a heating element, while the bottom of the chamber is cooled, for example, with solid carbon dioxide (the opposite temperature gradient can also be used). The alcohol vapors generated in the hot part of the chamber diffuse into the cold part of the chamber. In a certain part of the chamber space, a zone is formed in which a state of supersaturated steam occurs, needed to condense vapors on ions along particle paths. The vapors are constantly replenished by drops of supplied alcohol (it evaporates in the upper part, the condensed alcohol is discharged from below), they diffuse against the direction of the temperature gradient, so that the diffusion cloud chamber can operate continuously in a steady state.
Note: The air in the chamber itself contains many ions and charged dust particles, which would be disruptive (reduce the contrast or even prevent the visibility of traces); other ions and charged particles are formed during the actual measurement. Therefore, a direct voltage (of the order of one hundred to a thousand volts) is inserted between the lids of the chamber - the generated electric field cleans the working space of the chamber from disturbing charged particles.

Fig.2.2.4. Example of photographic image from a bubble chamber. The primary particle (proton) from the accelerator, arriving from the left, leaves an ionization trace and then collides to produce other particles, of which the electrically charged ones again leave ionization traces. The chamber is inserted into a magnetic field, so that according to the sign of the charge, the particle paths are curved to the left (here negative particles) or to the right (positive particles).

The bubble chamber for detecting trace particles
is based on a similar principle as the nebula chamber, but for the visualisation of ionization trace of particles uses the opposite states than the fog chamber: the formation of gas (or vapor) bubbles in superheated liquid along the ionization trace of the particle. Compared to cloud chambers, in which the gas is too sparse, the bubble chambers have the advantage of a higher liquid density with which high-energy particles can interact more effectively. Furthermore, it is a faster work cycle speed.
If we heat a clean liquid to a temperature slightly higher than the boiling point, it may not start to boil immediately, but it may remain in a superheated liquid state for some time (a few seconds); then it starts boiling violently. If, during the unstable state of the superheated liquid, before the onset of boiling, a charged particle passes through the liquid, it forms a number of ions along its path. Microscopic bubbles of steam begin to form on these ions, which, if the liquid overheats sufficiently, can grow to macroscopic dimensions - a sequence of visible small bubbles is formed along the path. These bubble traces are photographed, reconstructed and evaluated in a similar way as in fog chambers under suitable side lighting (discharge flash) (the formation of bubbles along the tracks can also be monitored in time - the growth of bubbles can be stroboscopically filmed).
The first types of bubble chambers were filled with ether heated to a temperature of about 140 °C and by regulating the pressure (approx. 20 atm) a suitable state of superheating was achieved. Today's bubble troughs are filled with liquid hydrogen, or deuterium (for monitoring interactions with neutrons), propane, freon, liquid xenon, etc., according to the specific type of studied particles and their interactions. They often reach considerable dimensions of several meters and contain hundreds and thousands of liters of liquid gas. The superheat state of the liquid gas is very precisely regulated by pressure changes by mechanical movement of the piston (electronically controlled). As the pressure increases, the bubbles disappear, the boiling stops and the chamber is brought to its initial quiescent state. By reducing the pressure, a superheated liquid is created again, particle paths, etc. are registered periodically. The cyclic phases of the bubble chamber operation are synchronized with the accelerator duty cycle so that the particles enter the chamber at a time when the pressure is momentarily reduced and the liquid is in a superheated state.
Bubble chambers are almost always placed in a strong magnetic field, so that by measuring the curvature of the paths due to the Lorentz force, it is possible to analyze the charge and some other dynamic parameters of the registered particles - Fig.2.2.4. From the direction of curvature, we determine whether the particles have a positive or negative charge, the magnitude of the curvature (Larmor 's radius) makes it possible to determine its momentum; if the path of the particle ends inside the chamber, the energy of the particle can be determined from the range.
For high-energy particles that fly through the chamber and continue to move, the velocity of the particle can be determined using two or more detectors (preferably fast-response scintillators) located at defined distances in the path of the particles. The particle velocity can be determined from the time differences (delayed coincidences) of the pulses from the individual detectors. From the relationship between velocity and momentum (relativistic) it is then possible to determine the mass of the particle, which together with other parameters allows the particle to be identified.
Photographic emulsion, could and bubble chambers are now being pushed out in research practice by electronic particle trajectory detectors, so-called trackers (show the track of trajectory, path). The conceptual diagram of such a detector is above in the section "Arrangement and configuration of radiation detectors" in Fig.1.1.2 below. They are significantly more flexible, their advantage is high scanning speed and direct electronic information processing.

2.3. Ionization detectors
Ionization chambers with gas filling
The ionization chamber is the simplest electronic detector of ionizing radiation; it directly uses the basic property of this radiation contained in the name - ionizing effects on the substance. The basic scheme of a simple ionization chamber is on the left in Fig.2.3.1. :

Fig.2.3.1. Left: Schematic drawing of the ionization chamber principle for detecting the flow of ionizing radiation. Right: Ionization chamber in a well design as a meter of activity of radioactive preparations.

The ionization chamber consists of two metal plates (or wires) - electrodes - anode and cathode, located in a gaseous environment *) and connected in an electrical circuit to a voltage of the order of hundreds of volts. Usually a cylindrical arrangement is used (resembling differently shaped coaxial "cylindrical capacitors"; but the electronic function of the capacitor is not used here...), where the outer metal shell is one electrode and the inner wire or cylinder is the other electrode.
*) The gas filling of the ionization chamber can in principle also be ordinary air, but special gas fillings formed by inert chemically stable gases show better properties, whose molecules are not subject to chemical changes during radiation ionization and the passage of an electric current. The most commonly used argon, krypton, xenon.
Under normal circumstances (without the presence of radiation) no current passes through the system - the gas between the electrodes is non-conductive, the electric circuit is not closed. However, when ionizing radiation enters the space between the electrodes, it ejects electrons from the originally neutral gas atoms and converts them into positive ions. Negative electrons travel in the electric field immediately to the positive anode, positive ions are set in motion to the negative cathode - a weak electric current begins to flow through the circuit caused by the ionic conductivity of the ionized gas between the electrodes. The current measured by the microammeter is directly proportional to the intensity of the ionizing radiation; can be calibrated in units of radiation intensity or dose rate (Gy/s). Thus, the detection of the flow of invisible ionizing radiation is realized by converting it into a measurable amount of electric current trough the circuit of the ionization chamber. The electrical signal from the ionization chamber is measured in the evaluation circuit either as an ionization current - ionization chambers with continuous ionization (these are discussed in this section), or a short current or voltage pulse - pulse ionization chambers (described below in the section "Geiger-Müller detectors" and in the passage "Proportional detectors").
The electric current flowing through the ionization chamber is generally very weak (approx. 10^-16 ÷ 10^-9 A) - the ionization chamber has a low sensitivity (low detection efficiency), so it is not suitable for detecting low flux radiation. However, its advantage is the linear dependence of the current even in the area of high intensities of ionizing radiation. The ionization chambers therefore have a very good linearity of response to the intensity of the detected ionizing radiation in a very wide range. It is therefore used, for example, to measure the distribution of intensity (dose rate) in radiation beams in radiotherapy. The most common use of the ionization chamber is in dosimetry for measuring the dose of ionizing radiation.
Activity meters with a well ionisation chamber
Ionisation chambers in a well design are often used in activity meters for radioactive preparations (these meters are sometimes incorrectly called "dose calibrators") - Fig.2.3.1 on the right. It is a hollow cylindrical chamber filled with an inert gas (mostly argon), in the center of which is formed an inter-cylindrical depression - a "well" for the insertion of the measured radioactive sample. Inside the chamber are electrodes to which a direct voltage (several hundred volts) is applied. Until radioactivity is present, the gas is not ionized and virtually no electric current passes - except for a slight current caused by the ubiquitous radiation background. There should be lead shielding around the chamber to reduce unwanted background.
The vial or syringe with the measured radioactive substance is inserted into the opening of the well ionization chamber, which then registers the outgoing gamma radiation in a geometry close to 4p. The activity of the measured radionuclide determines the intensity of gamma radiation in the chamber space, and thus the density of gas ionization and the value of the electric current between the electrodes. The electrical signal I from this chamber is then proportional to the activity of preparation A and G- constant of the given radionuclide: I ~ A. G. The gamma-constant is different for each radionuclide, it depends mainly on the number of photons emitted per radioactive conversion and on the energy of these photons. The electronic circuits of the activity meter are calibrated (via the G- constant) so that for the selected radionuclide the display shows its activity directly in [MBq] *).
*) In order for this measured activity value to be correct and accurate, a careful metrological calibration is required for the activity meters. The result of this calibration is the values of the "isotope factors" for the dividual radionuclides, which are multiplied by the measured ionisation current for obtaining the activity [MBq]. These multiplication factors are stored in the memory of the device and then are used by entering the type of radionuclide to be measured.
Activity meteres with a well ionization chamber have very good linearity to high activity hundreds of TBq (at our workplace we measured the linearity of several types of activity meters up to about 40GBq, we did not have higher activity). Common activity meters (such as Curiementor or Bqmetr) with measuring times around 5-10 sec. are able to reliably measure activities only greater than about 100kBq. Only those activity meters that have the option of extending the measurement time for low activities (such as Mediac by Nuclear Chicago ) are able to measure activities of the order of kBq units - but the measurement can take several minutes. To measure samples of even lower activities, the well scintillation detectors must be used (see below §2.7 "Measurement of sample radioactivity").
The detection efficiency of the well ionization chamber, and thus the accuracy of measuring the activity of the preparations, significantly depends on the position of the sample in the well, the sample volume and the absorption of gamma radiation inside the sample, in the vial walls and the inner wall of the ionization chamber. Problems of positional and volume dependence of measurement in the well detector is discussed in §2.7, passage "Detection efficiency", Fig.2.7.2. For these circumstances, it is necessary to apply the appropriate correction - multiplication of the measured value by an experimentally determined correction factor.
Well ionization chambers are basically used to measure the activity of radioisotopes emitting g radiation - either pure gamma emitters (such as ^99m Tc ) or mixed b + g (such as ¹³¹ I ) or a + g. Even pure beta emitters with higher energies (such as ⁹⁰Y) can be measured in an emergency despite the resulting braking radiation, but with significantly worse accuracy, significantly dependent on geometric influences. Also for radionuclides with low gamma radiation energy (such as ¹²⁵ I ), the measurement accuracy deteriorates due to absorption. The main use of activity meters with a well ionization chamber is for the measurement of radiopharmaceuticals applied to patients in nuclear medicine for scintigraphic diagnostics and radionuclide therapy (§4.8 "Radionuclides and radiopharmaceuticals for scintigraphy").
Electroscope
The historical predecessor of the ionization chamber was the leaf electroscope used in electrostatics. This simple device consists of a vertical insulated metal rod to which a thin metal sheet is conductively attached. If we apply an electric charge to this system, due to the repulsive electric force (the rod and the ticket are uniformly charged) the ticket will deviate from the rod; the angle of deflection depends on the size of the charge. If the air were a perfect insulator, the charge of the electroscope would not change and the angle of deflection of the leaf would remain the same for an indefinite period of time. In reality, however, a certain amount of ions is contained in the air, so that the electroscope slowly discharges and its leaf gradually returns to its original suspended position. If the air around the electroscope is exposed to ionizing radiation, the ion concentration will increase significantly and the electroscope will discharge significantly faster: the rate of decrease of the electroscope leaf thus becomes a measure of the intensity of the ionizing radiation.
With the help of these electroscopes, many important experiments were done in the early researches of ionizing radiation and radioactivity. Until recently, the simple principle of discharging the electroscope was maintained in pencil personal dosimeters, where the ticket was replaced by a thin fiber ("fiber electroscope"), which also served as a hand-arrow for immediate reading of the radiation dose.

Electret detectors
This is a simple variant of gas ionization chambers, in which the electric field is not excited by an external electronic voltage source, but by a so-called electret *). The charge of the electret creates an electrostatic field in the chamber. Radiation entering the chamber (or generated by radioactivity directly inside the gas charge - air) ionizes the gas and the resulting negative electrons are attracted to the electret, which is gradually discharged. The rate of discharge of an electret is directly proportional to the amount of radiation (radiation dose) that has entered the chamber and been absorbed there. The discharge of the electret (ie the difference in polarization charge before and after exposure) is measured via the electrical voltage between the electrodes of the respective evaluation device ("reader"), where the electret removed from the exposure chamber is inserted. Electret detectors work in a cumulative (integral) mode in the sense of the classification in §2.1 .
*) Electret is such an electrically non-conductive substance - dielectric, which maintains a permanent electrical polarization even after the removal of the external electric field. It is the electrical equivalent of a permanent magnet .
These simple detectors are mainly used to measure the average concentration of radon in terrain (in the interiors of buildings) - in the air that forms the "gas filling" of the chamber. After several days of exposure, the discharge of the electret is evaluated, which is directly proportional to the concentration of radon in the object.

Electrical properties of the ionization chamber
For a better understanding of the operation of individual types of ionization detectors, we will only briefly mention the electrical properties of the ionization chamber. The dependence of the ionization current on the voltage between the electrodes of the ionization chamber is schematically shown in Fig.2.3.2 - we assume a constant intensity of flux of quants radiation.

This dependence, sometimes called the "volt-ampere characteristic" of the ionization chamber, can be divided into three areas :

Geiger-Muller detectors
The Geiger-Müller (G.-M.) detector is an ionization chamber, hermetically sealed, filled with a gas with a pressure usually lower than atmospheric (however, there are also chambers with a higher pressure); works in pulse mode. The electrodes of this chamber are connected in the electrical circuit to such a voltage that the chamber works in the area III B of the characteristic in Fig.2.3.2 (voltage is about 600-1000V), in the so-called Geiger mode. Schematic chart of G.-M. detector is in Fig.2.3.3 :

Fig.2.3.3. Left: Schematic diagram of Geiger-Müller detector. Middle: Some shapes and designs of G.-M. detectors ; Right: G.-M. (or proportional) detectors in a planar arrangement as a meter of radioactive contamination (in the shape of an "flatiron" ).

Upon entry of a quantum of ionizing radiation, ionization occurs in the gas, after which the electrons begin to move toward the anode and positive ions toward the cathode. Because the gas is diluted, or the voltage at the electrodes is high enough, the mean free path of each electron is long enough to gain such kinetic energy in the electric field, that it is able to eject additional electrons (and ions) when it strikes a next gas atom. These secondary electrons then emit other secondary electrons, etc. This process of secondary ionization is avalanche (up to 10¹⁰ secondary electrons are formed from one primary electron) - small electric discharge is generated in the space between the electrodes. A relatively strong current pulse passes through the circuit and a relatively high voltage pulse is generated on the working resistor R , which is processed via a separating capacitor C in the appropriate electronic unit (amplifier, counter, integrator) - the quantum of the respective ionizing radiation is detected by conversion to electric impulse. The resulting electrical impulses have the same size and shape, regardless of the type and energy of the detected quantum - the GM detector has no spectrometric properties.
The discharge that occurs when a particle is detected in the space between the electrodes must be interrupted as soon as possible, because no other particles can be registered during the discharge (prolonged discharge could also damage the gas charge of the detector and the electrode itself!). Two circumstances are involved in the interruption of the discharge. The first is the voltage drop across a relatively high operating resistance R (of the order of MW ), which reduces the voltage at the electrodes and reduces the production of secondary electrons. However, in the ionized gas, ions recombine and deexcite, emitting ultraviolet photons. Photons of UV radiation are able to ionize and eject additional electrons from the cathode, which tends to prolong the discharge. Therefore, a quenching agent (usually methyl alcohol, bromine vapors, ...) is added to the gas filling, the molecules of which absorb ultraviolet photons and thus contribute to the rapid interruption of the discharge.
G.M. gamma detectors are most often designed as cylindrical tubes filled with a suitable inert gas. The inner metal wall of the cylinder serves as a negative electrode, a positive electrode in the form of a wire is guided in the middle of the tube. G.-M. beta detectors have a different design, with a thin inlet window at one end of the tube.
Detection efficiency G.-M. detectors
it generally depends on the walls (or inlet window) of the detection tube and on its gas filling. They differ diametrically for charged particle radiation and for photon radiation.
For heavier charged particles (eg for alpha radiation) and for beta electrons, the detection efficiency can be close to 100%, provided that they reach the gas charge, ie the sensitive volume of the detector. In order to penetrate there, the entrance window must be made of the thinnest possible light material; there is talk of "windowless" detectors.
For photon radiation X and especially gamma, the detection efficiency of the gas charge itself is very low, due to its low absorption in the gas. The vast majority of g-photons pass through a sensitive volume of gas without interaction. Photons with higher energies can be detected by a gas-filled detector practically only if they interact with the wall material of the detection tube. Then some electrons released by Compton scattering or photoeffect penetrate the gas charge, where they are already effectively detected. The detection efficiency of G.M. detectors for photon radiation therefore depends on the material and wall thickness of the tube (most often a few tenths of a millimeter thick aluminum is used), of course in relation to the radiation energy. For medium energy photon radiation, the detection efficiency is usually about 0.1-10 %.
The use of G.-M. detectors
G.-M. detectors played an important role in the development of nuclear and radiation physics - it was the first type of detectors that could register individual quanta of ionizing radiation, not just the intensity or flux of radiation, as is the case with ordinary ionization chambers. Even today, G.-M. detectors used for their simplicity, but mostly only for less demanding measurements. E.g. in radiation protection they are contamination meters, radiation alarms, monitoring systems, etc. For more accurate and demanding measurements, they were replaced mainly by scintillation and semiconductor detectors, which are of course much more expensive, but have significantly better parameters in all respects (see below §2.4 "Scintillation detectors", §2.5 "Semiconductor detectors").

Dead time of detectors
It is clear that for the duration of the avalanche discharge in G.-M. tube, the detector is insensitive to other incident quanta. Similarly, for other types of detectors (scintillation, semiconductor) there is a certain period of insensitivity, during which the device is "busy" by processing the response from the currently registered quantum. The time from the registration of one pulse, during which the detector is not able to register further pulses is called detector dead time, denoted by t or DT (Dead Time) and is measured in microseconds *). An alternative name is the time resolution of the detector ("counter" of radiation quantum). In G.-M. detectors, the dead time is of the order of 10^-4 seconds, ie t @ 100 ms (which is a relatively long dead time!), for scintillation detectors it is often shorter than 1 ms.
*) For radiometers and spectrometers, the dead time, resp. total dead time loss - "Dead Time" is often expressed in % of the total measuring time.

Dead time in general (also applies to other types of detectors - scintillation, semiconductor)

Dead time causes that not all interacting quantum of radiation to be detected, but there is some loss of detected pulses, wherein the loss due to dead time increases with the frequency (flux, intensity) of the measured radiation quanta. This disrupts the linearity of the response of radiometric instruments in the higher frequency range. Instead of the actual average input (theoretical) frequency N [imp./s] of the incoming radiation quanta, we measure the registered pulse frequency n [imp./s], where n <N. Functional dependence of n = n(N) registered pulse frequency n on actual (theoretical) frequency N expresses response function detector in terms of the measured number of pulses. According to the nature of this dependence, dead time is sometimes divided into two types: non-paralyzable and paralyzable (cumulative) :
¨ The above dead time is so-called non-paralyzable, characterized in that during this dead time the detector does not register incoming particles, wherein these particles have no effect on its operation, and after the dead time has elapsed, the detector is immediately ready to detect another pulse. The dependence between the registered n and the actual (theoretical) pulse frequency N is given by the relation *)
n = ^N / _{(1
+ N.}_t₎ .
With a linear increase in radiation intensity (frequency) N the registered frequency of pulses n first increases practically also linearly (in practice with the coefficient given by the detection efficiency, which we, howevwr, consider here as 1), then the growth begins to slow down and at high frequencies N >> 1/t almost no longer increases and reaches saturation: lim_N_®_¥n(N) = 1/t (Fig.2.3.4 left).

Fig.2.3.4. Influence of detector dead time on detector response function. Left: Non-paralyzable; Right: Paralyzable.

¨ Paralyzable dead time (also called cumulative) is such that during it the detector not only does not register other particles, but each such particle that flies into the detector during the dead time, prolongs its insensitivity by the same time - "paralyzes" the detector, dead time "cumulates". In other words, each pulse entering the detector generates a "new" dead time t, regardless of whether or not it is registered. The dependence between the measured and the actual pulse frequency is here *)
                   n = N . e ^-^N.^t .
As the input frequency of the particles increases, the response first increases linearly again, then slows down and reaches a peak, after which, as the input frequency increases further, the response of the detector begins to decrease (Fig. 2.3.4 on the right). For too high frequencies N , the detector even stops counting pulses completely: lim_N_®_¥n(N) = 0 - the detector is "paralyzed" (overloaded).
*)The general mathematical derivation of the influence of dead time on the functional dependence of n = n(N) between the input (theoretical) and measured (registered) pulse frequency is based on a statistical analysis of the time distribution of incoming pulses according to the Poisson distribution. If the detected quantum comes with the actual (theoretical) average frequency N, then the probability of occurrence of the pulse in the time interval dt is N.dt, while the probability that the pulse falls outside the time interval t is P(t).dt=N.e^-N.^t.dt. More complex manipulations with integrals _tò^{^¥}P(t) dt and time intervals can then be used to derive the corresponding functional dependences n = N . e ^-^N.^t .
  In the case of a non-parillable detection system, this derivation can be substantially simplified by a simple consideration from the "opposite side": Each registered pulse is accompanied by a detector insensitivity time equal to the dead time value t . Therefore, if we register with the non-paralyzable detection system n pulses per second, then for input (theoretical) pulses of frequency N there is an effective shortening of the measuring time from 1 second to (1-n. t) -seconds. This means that instead of theoretical N pulses we measure n = N. (1-n. t) pulses per running second. From this, a simple modification gives the resulting functional dependence n = N / (1 + N. t) .
  (For a paralyzable detection system, the dependence is nonlinear, so a differential analysis must be used. As the incoming frequency of quanta increases by DN, the registered frequency changes by Dn = DN- DN. t. ........)

Dead time sources
In general, all parts of the detection system contribute to the dead time effect: own detector - GM tube, scintillator, photomultiplier, semiconductor detector; preamplifier or amplifier; amplitude analyzer; pulse counter; analog-to-digital converter. For scintillation detectors, one of the causes of pulse loss by "dead time" is so-called pile-up effect (discussed below in §2.4 "Scintillation detectors", section "Scintillation spectrum").
With a GM detector, the relatively long dead time is given by the detection principle and cannot be shortened too much. However, for scintillation and semiconductor detectors, technical developments in the field of electronics and materials have led to a significant reduction in dead time. While in the past (60s) the dead time of scintillation detectors was about 5-10 ms, in the 80s and 90s this value was reduced to about 1 ms due to the use of fast electronic components. The slowest link in the detection chain gradually becomes the scintillator itself. For this reason, in some devices, NaI(Tl) or BGO scintillation crystals are replaced by faster scintillators based on rare earth doped silicon oxides, especially LSO (see "Scintillators and their properties" below). Gradually, the photomultiplier becomes the limiting factor of dead time- however, it will be replaced in some applications by special photodiodes (see below "Photomultipliers", fig.2.4.2G ).
......??.......... forced dead time ...- add .... ?? ........

Measuring of dead time (non-paralyzable)
There are basically three ways to measure the dead time of a detector (if we have a shielded detector, we can neglect the background) :

Note:
For all these dead time measurements, there is a risk of large systematic errors due to other physico-electronic influences that can simulate dead time ! Before measuring the dead time and interpreting the results, it is recommended to examine the following two circumstances :
a) Dependence of the position of the photopeak on the frequency of pulses - determine the position of the photopeak for the range of input frequencies about 10² -10⁶ imp./s.
b) Temporal stability of photopeak position at high frequencies. Some scintillation detectors show a kind of "fatigue effect" of the photomultiplier: at high electron fluxes, the photomultiplier gradually decreases its gain (mostly reversible), which is manifested by a gradual decrease in the position of the photopeak. We recommend loading the detector with a pulse flow of approx. 10⁶ imp./s. and for about 60min. monitor the position of the photopeak.
Partial leakage of the photopeak position from the analyzer window leads to a reduction in the detected pulse frequency, which simulates the effect of dead time.

Dead time correction
If we measure such high frequencies of radiation quantums that the dead time of the detector is significantly applied, it is necessary to make a correction for this dead time in order to obtain objective and accurate results. To perform this correction, it is of course necessary to know the specific value of the dead time for the given detector, ie the measurement must be performed according to the previous paragraph. If it is a non-paralyzable detector, we perform a correction for the dead time, ie determining the actual frequency N based on the measured frequency of n pulses, according to a simple relation N = n/(1 - n.t). In general, dead time correction can be performed by applying an inverse relationship between theoretical and actually registered pulse frequency; we can also use the measured dependence between the theoretical and registered frequency, obtained by the above-mentioned method of continuous change of pulse frequency. In the case of a paralyzable dependence, the correction can in principle only be performed for lower frequencies in the ascending area of the graph, for the descending area it is usually not possible to make the correction (the correction becomes ambiguous).

Proportional detectors
Proportional detectors also use secondary ionization, but due to the lower voltage there is no avalanche microdischarge, but they work in the IIIA region on the volt-ampere characteristic according to Fig.2.3.2 - in the proportional region. The gain coefficient is about 10⁴-10⁴, the dead time is usually of the order of 10^-6s. The connection and design is similar to G-M detectors, they work in pulse mode. The output voltage pulses are proportional to the energy of the detected radiation (more precisely, the energy absorbed by the interaction of the quantum of radiation with the gas charge), so that these detectors can in principle be used for spectrometry, although their resolution does not reach the quality of scintillation and not semiconductor detectors at all.
...............

Spark detectors
For some applications, detectors operating in the last (highest) area of the volt-ampere characteristic of the ionization chamber according to Fig.2.3.2 - in the area of the spark discharge - are also seldom used. If a voltage is applied to the electrodes of the ionization chamber only slightly lower than the breakdown voltage leading to spontaneous discharge and spark jump, nothing will happen at rest. However, if a quantum of ionizing radiation enters the space between the electrodes, it will immediately initiate a jump of the spark, which is manifested both by the passage of a strong electrical impulse through the circuit and by the appropriate light and sound of the spark discharge.
Spark detectors in an arrangement with many electrodes distributed over a larger area form so-called spark chambers for the registration of traces of charged particles (ie for a similar purpose as, for example, bubble chambers - cf. §2.2). The spark chamber consists of a large number of electrodes in the form of plates or wires, to which a voltage of approx. 10 kV *) is applied. The charged particle, which passes through the spark chamber, by its ionization gradually causes spark discharges in the individual sections of the chamber between the electrodes, which follow the trace of the particle in the chamber. On the one hand, these discharges are visible and can be captured photographically (eg stereoscopically by two cameras); however, they are also audible and can be registered electroacoustically, for example, via piezoelectric sensors. After registration, an electric field is applied to remove the generated electrons and ions, and the measurement cycle can be repeated. The spark chambers are able to operate in very fast cycles, while high voltage can be applied to the electrodes for a correspondingly short time via gate circuits triggered by synchronization detectors monitoring the primary particle beam before entering the spark chamber (so-called triggering).
*) High voltage is applied either between adjacent electrodes (with opposite polarity of even and odd electrodes) or between electrodes forming eg a cathode and a base plate forming opposite polarity, eg anode.

Drift ionization chambers (TPC)
When an ionizing particle passes through a gas-filled chamber, the released electrons and ions do not reach the collecting anode and cathode immediately, but "penetrate" gradually through the gas - they drift at a certain speed (depending on voltage, distance from anode and gas density) to anode or cathode. The time of electron drift to the anode carries information about the position of the place where the particle passed in the tube and where it caused ionization. The drift chambers have several electrodes in the shape of wires or strips, and according to the place - the specific electrodes - where the electrons travel and the time of drifting, the course of the path of the ionizing particle in space can be determined. The most advanced detectors of this type are multi-wire drift time-projection chambers (TPC), composed of a large number (even several thousand) wires -electrodes, stretched in a gas filling in several layers (in each layer the wires are stretched in a different direction - they form a spatial grid). Drift ionization chambers used to have a mostly cylindrical shape, but for larger systems the flat quadrangular shape is also used more recently (Fig.2.3.5).
As the charged particle passes, ionization occurs along its path. Electron clouds drift at each location to the nearest electrodes, where an electrical signal is generated. The intersections of the electrodes from the different layers, which thus received the signal, indicate the (x, y)-coordinates of the passage point of the detected particle, its 2D projection. The ionization cloud of electrons can reach several nearby electrodes; the evaluation electronics then determine the coordinates using the weighted averages of the signals from the various electrodes. The place of passage of the charged particle can thus be determined with an accuracy of about 0.1 mm. The third spatial (z)-coordinate of the ionization site is determined by measuring the electron drift time from the ionization site to the wire electrodes. 2D projection of the ionization path from the electrodes, supplemented by the time data of the electron drift, thus enables the implementation of a 3-dimensional reconstruction of the trajectory when the particles interact with the sensitive volume of the chamber..

Fig.2.3.5. Basic principle of multi-wire drift time-projection ionization chamber TPC.
The simplified diagram shows only 6 places of ionization electron drift and the formation of coordinates (x₁,y₁), ... , (x₆,y₆).

Multi-wire drift ionization chambers are now used in complex detection systems (such as above in Figure 2.1.3 below) in accelerators. As a rule, several layers of chambers placed in a strong magnetic field are used. The magnetic field changes (curves) the paths of charged particles, depending on the charge and momentum of the particle. From the changes in the path of the particles registered in the individual layers of the chambers, it is then possible to determine the momentum of the respective particle (if we know its charge). The more accurately we can measure the momentum of secondary particles flying out of the point of interaction, the more accurately we can determine the rest masses and other characteristics of the resulting investigated particles.
Drift time projection ionization chambers, together with semiconductor trackers (see below "Multidetector semiconductor systems" in §2.5) have become significantly more advanced replacement of fog and bubble chambers for particle path detection (§2.2, "Particle Detectors").
Drift time-projection ionization chamber with liquid argon (LArTCP)
Instead of gas, liquid argon (at -185.8 °C, i.e. 87.3 °K) is used as the sensitive ionization medium. The main advantage here is the high density of liquefied argon 1.4 g/cm³, which is about 1000 times higher than the gas charge of standard ionization chambers. This increases the detection efficiency for particle interactions about a thousand times. This is especially important when measuring processes where the effective cross-sections of particle-mass interactions are very low - detection of neutrinos, WIMP particles, or the search for very rare processes such as proton decay. Argon, as an inert element with zero electronegativity, does not absorb ionizing electrons when drifting towards the electrodes. Argon exhibits scintillations as it passes through charged particles, which can be registered by photomultipliers to obtain additional information about the process, as well as to trigger electron drift time detection. Liquefied argon is well obtained by fractional separation from air and is cheaper than other rare gases, so even large-volume detectors are economically realizable.
A large cryogenic underground detector LArTCP, which will contain 70,000 tons of liquid argon, is being built as part of the international neutrino detection project DUNE (§1.2, passage "DUNE (Deep Underground Neutrino Experiment)").

2.4. Scintillation detectors
Scintillation detectors of ionizing radiation are based on radioluminescence - the properties of some substances react with light flashes or scintillations (lat. scintilla = spark, flash ) to absorb quantums of ionizing radiation; these flashes are then electronically registered using photomultipliers. Substances exhibiting this property are called scintillators. The oldest used radioluminophore is zinc sulfide activated with silver ZnS (Ag), from which the screens of sciascopic X-ray devices were used, in the past platinum-barium cyanide was also used. However, for the purpose of detecting g radiation, thallium - activated sodium iodide - NaI(Tl), in the form of a single crystal, is most often used. Other scintillators (including liquid scintillators) will be listed below, where the mechanism of scintillation formation will also be discussed (see section "Scintallators and their properties"). Fig.2.4.1 schematically shows the basic principle of operation of a scintillation detector/spectrometer :

Fig.2.4.1. Schematic diagram of a scintillation detector with a fixed scintillator.
On the left, the formation of scintillations in the crystal, the emission of electrons from the photocathode and their multiplication by the dynode system are shown.
In the middle part is the electronic processing of the generated signals. The upper branch of the scheme represents simple detection using a "single-channel" amplitude analyzer and pulse counter. The lower branch of the diagram shows spectrometric measurements using an analog-to-digital converter and computer acquisition of the energy spectrum ("multichannel" analyzer). The typical shape of the scintillation spectrum of gamma radiation is plotted on the screen - compared to the actual line spectrum above.
Right is assembled a scintillation detector (probe) with a crystal, light-tightly encapsulated with a photomultiplier and at the bottom with a resistive divider.

The quantum of the measured invisible radiation penetrates into the scintillation crystal material, where it interacts with the substance (eg the most frequently detected gamma radiation is a photoeffect, Compton scattering or electron-positron pair formation, as explained in more detail in §1.6., section "Interactions gamma radiation and X"). Due to these interactions, the ionizing quantum is partially or completely absorbed and part of its energy is converted in the scintillator into a flash (scintillation) of visible light (Fig.2.4.1 top left). The resulting scintillation consists usually of several hundred of these secondary photons, depending on the absorbed energy of the primary detected quantum and the conversion efficiency of the scintillator. The total number of scintillation photons is directly proportional to the energy of the detected quantum absorbed in the scintillator.
A photomultiplier is optically attached to the scintillation crystal - a special optoelectronic component that converts scintillation light into an electrical signal with high sensitivity. The construction and properties of photomultipliers are discussed below in the section "Photomultipliers". In the classic design, the photomultiplier is a vacuum tube, on the entrance window of which a thin metal layer is applied from the inside - a photocathode (thickness approx. 10^-7cm, the material is cesium and antimony with low electron output work), which converts light photons into electrons. Furthermore, the photomultiplier contains a system of electrodes - the so-called dynodes (their number is about 8-12), which acts as an electron amplifier. There is, of course, a high vacuum inside the entire tube. Positive voltage is applied to the individual dynodes - they gradually increase and increase for each dynode.
The photons from a light flash in a scintillator impinge on the photocathode, from which by the photoelectric phenomenon eject out the electrons e^-. Each such electron in an electric field begins to move rapidly to the first (nearest) dynode, to which a positive voltage of, say, about 100V is applied. It hits this dynode with a kinetic energy of about 100eV, which causes at least 2 or more secondary electrons to be ejected from the metal surface of the dynode. These electrons set out on the path to the next dynode, on which there is a higher positive voltage - about 200V. The energy to which it accelerates (given by the voltage difference, here again about 100eV), again ejects 2 or more secondary electrons for each electron - so we already have at least 4 electrons, which move to the next dynode, where twice more electrons eject, etc. Thanks to this repeated multiplication was originally a small number of electrons released from the photocathode multiplies greatly and about 10⁵ -10⁸ electrons fall on the last dynode (already anode), which is already a sufficient number to induce a well-measurable electrical pulse of amplitude A on the working resistance R (has a value of the order of magaohms) in the electrical circuit. This pulse trough the decoupling capacitor C leads to the amplifier and other electronic circuits for processing.
Special photodiodes or arrays of matrix photodiodes ("semiconductor photomultipliers") can also be used to register and convert light scintillations into electrical pulses, event. hybrid combination of a tube photomultiplier with a photocathode and subsequent semiconductor registration of photoelectrons - see the section "Special types of photomultipliers" below.
Thus, a scintillation detector works in this way, which can be used either separately (one detector) or can be part of multidetector systems (cf. the section "Arrangement and configuration of radiation detectors" above, Fig.2.1.3). Systems of a large number of elementary detectors and opto-electronic elements (sometimes several thousand) are used for electronic radiation imaging - §4.2 "Scintillation cameras" and §3.2 "X-ray diagnostics", part "Electronic display of X-rays ", specifically it is a so-called flat-panel with indirect conversion of X-rays.

The design of the scintillation crystals and photomultipliers
Scintillators
can be inorganic crystals, organic plastic materials, liquid solutions of organic substances, respectively also rare gases. Here in the basic text we will consider inorganic scintillators, plastic and liquid scintillators will be described below (§2.6 "Detection and spectrometry of radiation a and b . Liquid scintillators"). The mechanisms of scintillation formation and the properties of scintillation materials will be discussed in the section "Scintillators and their properties". The most commonly used inorganic scintillators are thallium-activated sodium iodide crystals - NaI(Tl).
For general detection and spectrometry of g- radiation, planar scintillation crystals of cylindrical shape with a diameter of about 2-7 cm and a height of about 2-8 cm are used . For the detection of soft g and X radiation, thin crystals 1-5 mm thick with a thin aluminum or beryllium entrance window. On the other hand, large-volume scintillation crystals (approx. 20 ´ 15 cm and larger) are suitable for the detection of high-energy radiation g. In addition to the generally used planar cylindrical scintillators, the well or transversely drilled scintillation crystals with a hole for measuring samples in test tubes are also produced (see below §2.7 "Measurement of sample radioactivity"). For the measurement of larger volumes of sample are used large-volume well scintillation detectors with a diameter of 18 cm and a height of about 12 cm with a measuring well space volume of approx. 250 ml. Special purpose scintillators (such as positron emission tomography PET, or spectrometers-calorimeters detection systems for accelerators) will be given at the appropriate places in the description of its methods.
Scintillator NaI (Tl) is placed in a light tight aluminum housing which protects the crystals particularly against the penetration of external light into the photomultiplier and also from moisture from the air (NaI is hygroscopic and may cause its hydrolysis by air humidity, see below "Inorganic scintillators", fig.2.4.8). At the bottom of the housing is a transparent glass exit window through which scintillation photons penetrate the photomultiplier. Photons from scintillation flashes are emitted isotropically in all directions, often outside the output window and photocathode of the photomultiplier. The inner sides of the scintillator housing are therefore provided with a white reflective layer which reflects light photons on the photocathode of the photomultiplier.
By simply placement a scintillation crystal above the photomultiplier window, part of scintillation photons would be lost by total reflection in the air layer between the two glasses, the crystal and the photomultiplier. The space between the scintillator outlet window and the photocathode is therefore filled with light guide material, silicone grease (with a refractive index approximately the same as that of glass) is most often applied, ensuring good optical contact of the photocathode with the crystal. If the photomultiplier and the scintillator are further apart, they are connected by a light guide, in special cases optical fibers are also used.

Photomultipliers
are special opto-electronic components for sensitive detection of low light fluxes and their conversion into electrical signals. Conventional photomultipliers are vacuum glass tubes containing a photocathode inside and several dynodes, to which a voltage of several hundred volts is applied. High sensitivity is achieved by the fact, that even a small number of electrons emitted by the impact of photons on the photocathode (due to the photoelectric effect) being multiplied by the repeated ejection and acceleration of the secondary electrons. The signal is thus amplified, so that even the impact of a single photon of light can cause a well-detectable electrical impulse. Photomultipliers are used not only in scintillation detectors, but also in spectrophotometry, luminescence detection (of physical, chemical or biological origin), detection of Cherenkov radiation, electron and mass spectrometry and in other technical applications.
Note1: The name "photomultiplier" is somewhat misleading, it does not multiply photons. Rather, it is an "electron multiplier" in which the secondary electrons released by the photoeffect from the photocathode are multiplied.
Note2: First we will deal with "classic" types of photomultipliers with photocathode and dynodes. Special photomultipliers, including semiconductors, will be mentioned below. Classic photomultipliers are special vacuum tubes in which electrons are generated by photoemission from a photocathode. Such a photomultiplier - PMT (PhotoMultiplier), consists of a glass flask equipped at one (front) end with an optical input window with a photocathode, inside it contains a series of electrodes - dynodes - connected to the terminals on the socket at the other end of the photomultiplier. Photomultipliers with a side input window are rarely used.
The photocathode
consists of a very thin layer (approx. 10^-7 cm thick, optically semi-transparent) vapor-deposited on the inside of a transparent input window, working in transmission mode (unlike the photocathode of a photon tube, which works in emission mode; the emission, or reflexion mode of the photocathode is only seldom used in photomultipliers). The photocathode must be sufficient thin so that the electrons released by the photoeffect can easily fly out and not be absorbed in the material. The material of the photocathode is substances with low electron output work for the photo effect. The most common are antimonides of alkaline elements, eg cesium and antimony Sb-Cs (SbCs₃ ), bialkaline materials Cs-K-Sb, Cs-Rb-Cs, Na-K-Sb, then Ag-O-Cs, or multialkaline Na -K-Sb-Cs. Photocathodes of p- type semiconductor materials with a suitable band structure have also been developed, the surface of which has a negative electron affinity, so that light-excited electrons penetrate the conductivity band very easily out into the vacuum. For example, a gallium-arsenide photocathode GaAs or InGaAs is used. An important parameter is the so-called quantum efficiency of the photocathode, which indicates the percentage ratio of the number of emitted electrons to the number of incident photons of light. This efficiency depends on the material of the photocathode, and also significantly on the wavelength l of light (photon energy h.n = h.c/l) - the spectral sensitivity *) of the photocathode. For optimal detection, it is desirable that the luminescent spectrum of the scintillator sufficiently overlap with the maximum spectral sensitivity of the photocathode. If part of the spectrum extends into the ultraviolet region (as is the case, for example, with Cherenkov radiation, see below), it is desirable to make the input window of the photomultiplier from quartz glass.
*)The spectral sensitivity of the photocathode is limited from below (for larger wavelengths l of light) by the condition that the energy h.n = h.c/l of the photon is higher than the output energy of the electrons from the photocathode material. From above (for shorter wavelengths - UV radiation) it can be limited by the optical transmittance of the input window; therefore, this window is sometimes made of quartz glass with better UV transmittance. For high photon energies (X and g ), the probability of a photoeffect in the thin film layer of the photocathode is very small - the photomultiplier is unusable for direct detection of this radiation. Using the conversion of hard radiation into flashes of light in scintillators, on the other hand, detection is very effective.
Dynodes
The weak electron flux from the photocathode is further amplified by the secondary emission of electrons on the dynodes. A thin layer of metal with a low electron output work (most often SbCs or BeO) and thus a high secondary emission factor S, like a photocathode material, is deposited on the surface of the dynodes. The mean number of ejected secondary electrons from a dynode is proportional to the energy of the incident electron. The current gain DI of one multiplication stage (one dynode) is thus DI = S. DU, where DU is the inter-dynode potential. At the usual value of the coefficient S » 0.04-0.06 and the voltage difference used between dynodes DU » 80-100 V, the gain of one stage is approx. DI » 3-6. By repeating the electron multiplication process between the dynodes, a large total gain G (up to 10⁸ ) of the initially very weak current from the photocathode can be achieved (for the number N of dynodes, the total gain G = DI ^N). The multiplication system, consisting of approx. 8-12 dynodes, is terminated by a collecting electrode - anode - with the highest positive potential, from where the output signal is taken via the working resistor R.
The electrical leads of the photocathode and dynode are not led "sideways" (with a few exceptions), as shown in Figures 2.4.1 and 2.4.2 for clarity, but are all led "down" (at the opposite end to the photocathode) in many pin socket. A high-voltage source (with a voltage of approx. 1000-2000V) and a resistive divider (exceptionally a diode cascade multiplier) are used to supply the dynodes and anodes of the photomultiplier. In the last three dynodes, the resistors in the divider are usually bridged by capacitors to ensure voltage stability in pulse operation. See also "Electronic power supply for photomultipliers ..." below for some electronic aspects .
The photomultiplier is drawn on the left in Fig.2.4.1 only schematically and simplified. The dynodes in a given arrangement actually have a concave curved shape (suitable shaping of the spatial distribution of the electric field potential), ensuring the focusing of electrons on the next dynode. Between the photocathode and the first dynode, a grid (diaphragm) is sometimes placed, the positive voltage of which accelerates the emitted electrons and directs them to the dynode. In addition to the linear arrangement of the dynodes (Fig.2.4.2.A), a compact circular arrangement of the dynodes (again in a focused shape) into a cylindrical surface (Fig.2.4.2.B) is sometimes used. Lamellar dynodes are often used in photomultipliers (in the shape of "blinds" - unfocused), are placed in layers on top of each other; through the gaps between the lamellae ("blinds") the ejected electrons pass to the next dynode with oppositely oriented lamellae and a higher positive voltage (Fig.2.4.2.C). Furthermore, dynodes in the shape of a wire mesh, coarser or finer. Rarely is used a linear arrangement of quarter-circle dynodes (somewhat similar to Fig.2.4.2.A), between which there are grids - sometimes referred to as a box-grid arrangement. The last dynode - the anode - is common to most photomultipliers. However, there are special multianode photomultipliers (Fig.2.4.2.D and partly also Fig.2.4.2.H), listed below in the section "Special types of photomultipliers".
Continuous channel dynodes
The above "classical" electron multiplier systems in photomultipliers consist of individual separate dynodes with secondary electron emission, supplied with voltage from a resistive divider. It can be said that it is an electron multiplier with discrete dynodes.
However, there is also a completely different design solution of the electron multiplier - a continuous dynode (Fig.2.4.2.H). It consists of a glass tube (channel), which is coated on the inside with a thin layer of semiconductor material, which has a high resistivity and good secondary electron emission properties. Between the input and output ends of the tube is connected high voltage, about 1000-3000 V, which along the inner wall it splits and creates a large voltage gradient. The functions of the secondary emission and the voltage divider are thus combined.
The photoelectrons emitted by the light from the photocathode enter the channel, where they cause the emission of secondary electrons when they hit the inner wall. These electrons are accelerated by a voltage gradient and, on further impact, more secondary electrons emerge from the wall. This process is repeated many times along the channel - the secondary electrons bombard the walls of the tube and produce more and more next electrons. The channel thus behaves as a "continuous-dynode" electron multiplier, the gain of which G is determined by the voltage on the tube (at a voltage of 3 kV the gain of approx. 10⁶ -10⁸ is achieved, comparable to classical dynod systems). Finally, a large number of electrons fly out of the output end of the channel, which impinges on the anode and create the resulting current signal.
This system of continuous channel electron muttiplier (CEM ) is sometimes called a channeltron. The channeltron tube is often initially wider and then narrowed and bent into the shape of a "ram's horn". Its advantage is small dimensions, when using a suitably shaped twisted channel, it can be just centimeters - Fig.2.4.2.H top right. Due to the high intensity of the electric field and the smaller transit distance of electrons, these photomultipliers have better resistance to magnetic fields. Channeltrons are used in optoelectronics, in electron and mass spectrometers. The complex combination of channel multipliers - multi-channel plate photomultipliers MCP, are listed below in the section "Special types of photomultipliers".

Fig.2.4.2. Design of various types of photomultipliers. In the upper part there is a photograph, in the middle and lower part of the picture there is a diagram of the construction and operation of the respective photomultiplier.

Special types of photomultipliers
imaging position-sensitive multianode photomultipliers PSPMT
For special purpposes of displaying the position of light sources, especially the position of scintillation in radiometric detectors, more complex photomultiplier systems, called PSPMT ( Position Sensitive photomultiplier ) - position sensitive photomultipliers are constructed. Such a photomultiplier consists of a photocathode with a larger area (approx. 5 x 5cm), an intricately configured system of dynodes (lamellar or channel design) and a larger number of anodes arranged on the other side of the evacuated flask (rectangular shape) into a matrix 4 x 4, 8 x 8, or 16 x 16 independent metal elements (Fig.2.4.2.D). At the location of the photocathode, where the detected light photon hits, a photoelectron is released, which is attracted and accelerated between the lamellar dynodes. Secondary electrons are released, which ultimately fall preferentially on the one of the anodes which lies opposite the point of emission of the original photoelectron - i.e. opposite the point of impact of the detected photon. By electronic evaluation of the amplitudes of signals from individual anodes, it is possible to determine the place of impact of the detected photon (or photon flash) on the photocathode - the photomultiplier has imaging properties. One such larger, position-sensitive photomultiplier can replace several separate smaller photomultipliers in some applications (such as special scintillation cameras or Cherenkov imaging detectors).
Microchannel plate photomultiplier
MCP (Multichannel Plate Photomultiplier) differs fundamentally from other types of photomultipliers in its shape and design. A plate (disk) is placed under the surface photocathode, in which a large number of glass capillaries (channels) with an inner diameter of about 5 - 100 mm are guided across. A semiconductor layer with a secondary emission property of a suitable considerably high electrical resistance is applied on their inner wall. High voltage is applied between both ends approx. 1000-3000V, which creates a large voltage gradient along the inner wall. The electrons emitted by the light from the photocathode enter the channels, where they cause the emission of secondary electrons when they hit the inner walls. These electrons are accelerated by a voltage gradient and further secondary electrons emerge on further impact. This process is repeated many times along the channels - secondary electrons bombard the walls of the channels and produce more and more next electrons. Thus, each channel behaves as a separate electron multiplier ("continuous-dynode"). Finally, a large number of electrons fly out of the output end of each channel, which impinges on the anode and creates the resulting current signal - Fig.2.4.2.H. In addition to photoelectronics, MCP detectors are used in electron and mass spectrometers. In multianode design can also have imaging properties, similar to the above PSPMT - Fig.2.4.2.H top center.
Hybrid Photon Detector HPD
An interesting type of sensitive "photomultiplier" is the so-called hybrid photon detector HPD (Hybrid Photon Detector). It combines the principle of a vacuum tube and a photocathode, with semiconductor detection of photoelectrons. It is again a vacuum tube with an optical input window, on the inner wall of which a thin layer of photocathode is applied. However, photoelectrons, released by the impact of detected light, do not fall on the dynodes, but are accelerated by a voltage of approx. +10 kV (a negative voltage of approx. -10 kV is connected to the photocathode, the anode is at zero ground potential). Accelerated electrons impinge on the semiconductor detector CCD (forming the anode), where they release electron-hole pairs, the sensing of which generates electrical impulses - in Fig.2.4.2.E. Each electron accelerated by a voltage of U produces about U/3.5 electrons and holes (at a voltage of 8 kV the "multiplication effect" is about 2500), which can be further multiplied 10-100 times by an avalanche effect when using an avalanche semiconductor diode APD (see below). Even the detection of one photon creates a relatively high output pulse, the level of several mV/1 photoelectron. The device has a high signal-to-noise ratio and is suitable for detecting weak light signals (single-photon measurement), such as Cherenkov radiation.
  The latest type of this technology is an imaging (position sensitive) pixel hybrid photon detector. The optical input window has larger dimensions and is provided on the inside with a highly homogeneous photocathode layer. The photoelectrons released by the impact of the detected light are accelerated by a voltage of 10-20kV applied to the ring electrodes. There are several of these electrodes (2-5), with a voltage gradually increasing from 0 at the anode to about -20kV at the photocathode. In addition to acceleration, these electrodes also serve as focusing "electron optics", projecting the surface of the photocathode to the anode equipped with a pixel detector (inverted reduced projection). Accelerated and directed electrons then impinge on the (silicon) pixel detector, formed by a matrix of a number of elementary detectors ( pixels) - about 32 x 32 = 1024 pixels. There are generate electron-hole pairs, the sensing of which generates electrical impulses from individual pixels, corresponding in position to the respective point of impact of light on the photocathode (Fig.2.4.2.F). The device therefore functions as a sensitive imaging light detector. Suitable especially for position-sensitive registration and display light signals such as Cherenkov radiation (RICH imaging detectors, see below).
SPM semiconductor photomultipliers
In addition to vacuum tube light detectors - photon tube, conventional photomultipliers and hybrid HPDs, pure semiconductor light detectors have also been developed. For higher luminous fluxes, where extremely high sensitivity is not required, photoresistors, photodiodes or phototransistors are commonly used, operating in (approximately) linear mode. At very low intensities, light already consists of individual separate photons. The detection of such light then consists in "counting" the individual photons. For "single-photon" detecting light (which is a standard task of photomultipliers) have been developed semiconductor so-called avalanche photodiodes APD (Avalanche PhotoDiode). They are silicon semiconductor diodes connected in the inverse direction to a suitable voltage (slightly higher than the breakdown voltage ) so that they work in the so-called Geiger mode . The photoelectron, released by the impact of light on a thin surface layer "P" (thickness <1 mm - serves as a "photocathode"), is accelerated in a strong electric field to cause further ionization, as well as the released secondary electrons, etc. - is initiated an avalanche of electron-hole pairs in the depleted layer " i " (thickness approx. 200-500 mm), impinging on the opposite layer "N" - temporary electrical breakdown of diode (fig.2.4.2.G below). This achieves a total electron gain of approx. 10⁵ -10⁶. A so-called quenching resistor R_Q (values of tens of kW) is connected in series with the diode, on which the resulting voltage drop causes a rapid interruption of the discharge in the diode. During an avalanche breakdown of a diode, a well-detectable electrical pulse is generated in the circuit, the height of which is constant, independent of the number of input photons that caused the avalanche detection; this property is analogous to a conventional gas-filled Geiger-Müller detector (see "G.-M. detectors" above).
For spectrometry, a certain disadvantage of photon detection by a single APD photodiode is the uniform magnitude of the output signal (which is given by the capacitances and resistances in the diode circuit), which does not allow to distinguish between the detection of one or more photons. This disadvantage has been overcome by using an entire array of multiple small APD elements, densely spaced on one small semiconductor wafer, including quench resistors for each element. The individual elements [APD + quenching resistor] are connected in parallel, so the output signal is the sum of the signals from the individual elements - the upper part of Fig.2.4.2.G. At low luminous flux, there is a low probability of simultaneous impact of multiple photons on a single cell, but the impact of multiple photons will result in the activation of multiple independent cells - so the output signal will be proportional to the number of photons incident on the detection field. The output signal is taken as standard from the working resistor R (approx. 100 W) via the isolating capacitor C (approx. 0.1 mF).
Optoelectric components of this type are sometimes called "silicon photomultipliers" and are abbreviated SiPM (Silicon Photomultiplier), or SPM (Semiconductor Photomultiplier), also SSPM ( Solid-state Photomultiplier), or MPPC ( Multi-pixel Photon Counter). Due to its small size and weight, mechanical and magnetic field resistance, ease of installation and wiring, it can be expected to replace conventional photomultipliers in a number of applications in the future, such as Cherenkov imaging detectors or hybrid PET + MRI imaging combinations.
Physical properties of photomultipliers
Basic parameter of photomultiplier is its overall sensitivity S, which is the product of sensitivity photocathodes S_F and multiplying dynod gain G :
      S = S _F . G .
In general optoelectronics, the total sensitivity of a photomultiplier is given in current units [Amperes /lumen], it is about 10 to 100 A/lm (however, the maximum permissible output currents of photomultipliers are only tens of mA - see below "Adverse effects with photomultipliers"). In radiometry, the sensitivity of a photocathode is expressed as [electrons / photon] - the number of electrons emitted per incident photon, or as the quantum efficiency, expressing this circumstance in [%]. The sensitivity of a photocathode significantly depends on the wavelength (energy of photons) of the incident radiation - we are talking about the spectral sensitivity of the photocathode, which is expressed graphically. Relative spectral sensitivity in [%] is often used, which is normalized to the maximum spectral sensitivity value.
Response linearity of photomultipliers are characterized the direct proportionality between the intensity of the incident light and the output current. Photomultipliers are usually linear over a wide range of radiant flux per photocathode, about 10² -10¹⁰ photons /sec. In the region of larger radiant fluxes, the linearity begins to decrease (the output signal is lower) due to the fatigue of the dynodes and due to the large spatial charge of the electron cluster at the last dynodes.
The time constant of the photomultiplier characterizes the duration (width) of the current pulse at the output of the photomultiplier at the impact of an instantaneous (almost infinitely short) light flash on the photocathode. The duration of the output current pulse from the anode is influenced mainly by the velocities (velocity distribution) of the secondary electrons and the different lengths of the electron paths from the photocathode between the dynodes. Due to the time scattering of the transit time, not all secondary electrons come from the instantaneous photoeffect to the anode at the same time, but their time distribution forms a pulse (approximately Gaussian) with a half-width of about 10^-8 sec. The time constant of the photomultiplier, the duration of scintillation in the crystal and the time constant of the electronics determine the speed of the scintillation radiometer - its dead time, or time resolution (analyzed above) "Dead time detectors").
The signal-to-noise ratio is manifested mainly when measuring very low luminous fluxes on the photocathode. Noise photomultiplier is caused by a "dark current"- output current that flows through the photomultipliers with unlit photocathode (see "Adverse effects with photomultipliers"). The dark current is formed mainly by thermal emission of electrons from the photocathode and dynod, leakage currents between electrodes and between the terminals in the socket photomultiplier. At room temperature, the dark current is of about 10^-15A, by cooling the photomultiplier it can be greatly reduced. The signal-to-noise ratio sometimes expressed by the so-called light equivalent of dark noise (ENI - Equivalent Noise Input ), which is the value of the luminous flux incident on the photocathode, that causes a signal equal to the dark current to be output at the photomultiplier.
Adverse effects of photomultipliers
Although photomultipliers are very sensitive and perfect light detectors, as with any more complex instrument, there may be several adverse effects that impair the detection properties.   One of the unfavorable phenomena in photomultipliers is the so-called dark current: it is an electric current flowing through a photomultiplier, even when the photocathode is not irradiated. The dark current is caused by the thermoemission of electrons from the photocathode (which occurs to a small extent even at normal temperatures), or thermoemission from the first dynodes participates in it; the multiplier effect on the other dynodes is then amplified. Statistical fluctuations of the dark current cause the detected noise pulses. The dark current of the photomultiplier is temperature dependent, by cooling the photocathode or the whole photomultiplier we will significantly reduce it.
Another problem affecting the energy resolution of the entire detection system is the inhomogeneity of photoelectron collection; especially from the peripheral parts of the photocathode, the efficiency of photoelectron collection on the first dynode of the multiplication system is reduced. Statistical fluctuations in quantum efficiency and dark current also contribute to the deterioration of energy resolution, which are superimposed on the useful signal and blur the amplitude of the output pulses.
The use of photomultipliers in the presence of a magnetic field , which deflects electrons in their path between dynodes by Lorentz force, is also problematic. In a stronger magnetic field, the photomultipliers stop working!
At stronger luminous fluxes, there may be a current overload of the photomultiplier - an enormous flux of electrons falls on the last dynodes, which causes "fatigue" of the dynodes, leading to a reduction in their emissivity. In the case of a short-term overload with a total current of several tens or hundreds of milliamperes, this is a reversible phenomenon, when after a certain period of "rest" the photomultiplier returns to its original state. However, in case of large or permanent overload, there is great fatigue or permanent damage to the last dynodes (in the case of large currents, also thermal damage - "burning" of the dynode surface) !
Note:These properties apply to "classic" photomultipliers with photocathode and dynodes. With appropriate modifications, these parameters and effects can also be applied to semiconductor photodetectors.

Scintillation probe
Scintillation crystal and photomultiplier with socket and resistive divider for powering dynodes, or with preamplifier, are housed in a light-tight housing *); this unit forms a so-called scintillation probe or scintillation detection unit, generally called a scintillation detector - Fig.2.4.1 on the right and Fig.2.4.3a. In the next we will deal with scintillation detectors with "classical" vacuum photomultipliers with discrete dynodes powered by a resistive divider - these are so far most often used for radiation detection and spectrometry.
*) Warning: Light tightness of scintillation detector is an essential condition for its function. The scintillation probe must not be disassembled in the light when the high voltage on the photomultiplier is connected, as a high luminous flux would cause such a strong current of electrons on the dynodes that it could be irreversibly damaged and destroy the photomultiplier ! - was discussed above in the section " Adverse effects of photomultipliers ".
In general purpose detectors, this housing is usually easy to disassemble, so that the crystal and photomultiplier can be replaced and assemble a scintillation probe with the desired properties for each application. Single-purpose scintillation probes are usually firmly assembled into a so-called scintiblock ( Fig.2.4.1 on the right). One of the tasks of the metal housing of the scintillation probe is the magnetic shielding of the photomultiplier (or the external magnetic field could affect the movement of electrons in the photomultiplier and thus change its amplification).
The basic scintillation probe consists of a "planar" cylindrical scintillation crystal in optical contact with a photomultiplier (Fig.2.4.3 a). The thickness of the crystal is chosen according to the gamma radiation energy used: for soft gamma and X it can be only 5 mm, for medium energy radiation of tens to hundreds of keV the thickness of the crystal is about 5-10 cm. By installing such a probe in a shielding case, equipped with a tube - collimator at the front, a collimated scintillation probe is created (Fig.2.4.3 b), which is used to selectively detect gamma radiation from a desired direction, defined by a collimator. Collimators are usually replaceable, the entire probe is mounted on a robust tripod with the possibility of vertical and horizontal displacement and angular rotation of the probe. Collimated detection probes are used in many applications of nuclear and radiation physics. In nuclear medicine, they have been used for the targeted detection of gamma radiation from examined organs to assess the accumulation of radiopharmaceuticals. In the 60.-80., pairs of collimated probes were widely used for radisotope nephrography (later it was displaced by far more perfect dynamic scintigraphy of the kidneys on a gamma camera - see §4.9.2 "Nephrological radionuclide diagnostics"). However, the collimated detection probe is still used to measure the accumulation of radioiodine in the thyroid gland (§4.9.1 "Thyrological radioisotope diagnostics") .
To measure radioactive samples in test tubes, a well scintillation crystal (Fig.2.4.3 c ) is used in the scintillation probe, into the opening of which is inserted a test tube for measurement in 4p -geometry (see below §2.7, Fig.2.7.1). This probe is built into a robust lead shield (Fig.2.4.3 d), it is mainly used for measuring low-activity samples in laboratory radiochemical analyzes, in nuclear medicine in in vitro methods (see below §2.7 "Measurement of radioactivity of samples (in vitro)"), mainly by radioimmunoassay. For the measurement of radioactive samples with larger volumes (approx. 250 ml.), the large-volume well crystals are used in the scintillation probe (Fig.2.4.3 e).

Fig.2.4.3 Some constructions of scintillation probes for measuring gamma radiation.
a) Basic scintillation probe with planar (cylindrical) scintillation crystal. b) Collimated scintillation probe for measuring radioiodine accumulation in the thyroid gland. c) Scintillation probe with well (cavity) scintillation crystal. d) NKG314 well scintillation detector for measuring radioactive samples in test tubes. e) High-volume well detector NKG315 (for illustration, the large sensitizing probe placed above, is actually located inside a robust lead shield - it is indicated by a white arrow).

A very special complex scintillation detector is a scintillation camera containing a thin large-area scintillation crystal equipped with many photomultipliers - see chapter 4 "Radionuclide scintigraphy", §4.2 "Scintillation cameras". For various detection and spectrometric purposes, very complex systems of many scintillation detectors are often constructed in various geometric arrangements, or in combination with other types of radiation or particle detectors. Extensive detection systems are being built for large accelerators, containing among many other detectors, several thousand individual scintillation detectors, connected in a coincidence or anticoincidence mode to complex electronic evaluation apparatus.(as mentioned above in the section "Arrangement and configuration of radiation detectors") .

Electrical supply of the photomultiplier and processing of output pulses from the scintillation detector
For the correct "multiplication" operation of the photomultiplier, it is necessary to apply a correspondingly high voltage to its individual electrodes - photocathode, dynodes, anode. The basic supply voltage of approx. 500¸1500 V, supplied from a high voltage (HV) source, is divided into gradually increasing voltages by a set of resistors (resistor divider) and led to individual dynodes (the last dynodes before the anode are sometimes blocked by capacitors to increase the pulse current did not cause voltage fluctuations on the divider, which would lead to changes in gain in the dynod system). As a rule, it is introduced between the photocathode and the first dynode a higher voltage than between other neighboring dynodes (the distance of the first dynode from the photocathode is also greater than between the other dynodes). A full voltage is connected between the photocathode and the anode via a working resistor (values of the order of MW), on which a current pulse generated by the passage of electrons through a photomultiplier causes a voltage pulse (by the effect of "voltage drop" according to Ohm's law). This output voltage pulse is fed via an separating capacitor to the amplifier for further electronic processing.
The simplest connection of a photomultiplier is a single-core power supply with positive polarity, where only one coaxial cable leads to the photomultiplier. Its "live" conductor supplies a positive voltage of 500¸1500 V both for the anode and through the resistive divider for the individual dynode. The cable is connected to the HV source via a working resistor (which is a part of the HV source), from which voltage pulses generated on this resistor during the passage of electrons through the photomultiplier are taken via a separating capacitor. This connection is simple and elegant, but it cannot take full advantage of the photomultiplier gain. It is suitable for the detection of higher energy radiation (from tens of keV), where the scintillations are sufficiently intense and the photomultiplier signal is relatively high.
For low energies, a more complex multicore connection with negative polarity is more suitable. A full negative voltage is applied to the photocathode ( -500 ¸ -1500 V), the resistive divider then gradually decreases the negative voltage to the individual dynodes; the anode is connected to zero ground potential via a working resistor. The output pulses from the working resistor are routed through a independent "signal" coaxial cable to the amplifier. A pulse preamplifier can then also be installed in the photomultiplier socket. Negative polarity with the anode at "zero" ground potential (in idle mode) is particularly advantageous when more complex low-current electronic processing of the output signals is performed and an excessive overall potential difference could be disruptive; this is the case, for example, with the above-mentioned hybrid photon detectors HPD.
When radiation is detected, a large amount of electrical impulses of various sizes appears at the output of the photomultiplier, which must be further processed and evaluated. The relevant electronic circuits are used for this, which amplify the pulses, sort them according to their size - they analyze, calculate, register, display. The processing of these pulses can be performed in two basic ways, according to the purpose of scintillation measurement - the upper and lower branch in the diagram in Fig.2.4.1 :

In special cases of multi-detector systems, further electronic analysis of signals is performed - coincidence, anticoincidence and comparison of signals from individual photomultipliers - in order to display, evaluate the position of sources, particle trajectories or angular correlations.

The technical development of radiometers and spectrometers
is closely connected with the development of low-current electronics and its component base. From an electronic point of view, radiometers and spectrometers can be divided into 3 generations :
1. Generation
Until the 1960s, radiometric instruments were equipped with electron tubes - they had larger dimensions and very limited possibilities of processing electrical signals from detectors, mostly single-channel measurements with one (lower) discriminant level - Fig.2.4.4 a. The display of the measured number of pulses was by means of analog hand gauges, or digitally by means of light bulbs or incandescent lamps placed vertically in columnar decatrons.
This display consisted of 10 light bulbs or incandescent lamps placed in a row (column) above each other, which illuminated the enclosed narrow glass rectangle with the numbers 0,1,2, ...., 9. These columns were placed side by side in several sets (4-6) according to the required number of decimal places. During the measurement, the numbers in the individual decatrons "ran" from bottom to top, and after the end of the preset measuring time, the respective digits remained lit in the individual decimal places (Fig.2.4.4a, left).
In the short transitional period of the late 1960s, circular glow decatrons were used to display the registered number of pulses. They were glow plugs with 10 wire circular electrodes, marked with the numbers 0,1,2, ..., 9. In addition to the display of the registered number of pulses used also as an electronic timer to tick pulses: When appropriate electronic participation of each incoming pulse switch lighting up the side of the electrode (1 or higher). And when the value "9" was exceeded, when the electrode "0" lit up, a pulse was sent to the neighboring decatron to increase the number there. During the measurement, the lighting electrodes "orbits" in a circle on decatrons at circularly arranged digits.. However, the reading of the measured number of pulses was difficult to see, the decatrons were soon replaced by digital digitrons.
2. Generation
of radiometric instruments (60s-70s) was already equipped with transistors (Fig.2.4.4 b). Multi-channel analysis could be performed, the display was using digital glow digitrons. The measured numbers of pulses could be printed on an electro-mechanical printer.
Digitrons are small circular or elliptical glow-neons, whose electrodes are thin wires shaped into the numbers 0,1,2, ...., 9. The electronic circuits of the pulse counter at each digit - a decimal place - light up and display the corresponding digit (Fig.2.4.4 b above). They were later replaced by semiconductor 7- segment LEDs. By lighting combinations of different segments, the necessary digits of the measured number of pulses are modeled (or other alphanumeric characters) - Fig.2.4.4 b down.
3. Generation
Great progress has been made since the 1980s with the development of digital electronics with a high density of integration and computer recording and control of measured pulses (Fig.2.4.4 c, d). They enable accurate complex processing of measured data and their mathematical analysis using special software. Including multichannel spectrometric analysis using an analog-to-digital converter (ADC).

Fig.2.4.4 Technical development of electronics of radiometers and spectrometers (examples of some instruments at our Nucl. department in Ostrava) .
a) Electron-tube radiometer NZG 319 (TESLA VÚPJT Pøemyšlení) with a columnar bulb display. b) Transistor spectrometer NZQ 717T (TESLA Pøemyšlení) with glow digitron display. c) Digital spectrometer MC1256 (TEMA) with 256-channel analyzer. d) Computer 4096-channel spectrometer Genie 2000 (Canberra Packard) for scintillation and semiconductor spectrometry.

All these generations of radiometric and spectrometric instruments have been gradually used at our Depertment of nuclear medicine in Ostrava since 1973. It is interesting that the electronic evaluation apparatus underwent significant technical changes, while the detectors themselves - ionization chambers, scintillators, photomultipliers, remained essentially the same for many decades. Only conventional vacuum photomultipliers have recently been seldom replaced by semiconductor photodetectors (they are described above in the section "SPM semiconductor photomultipliers").

Advantages of a scintillation detectors
If we compare the situation with G.-M. detector, we see that we achieved a similar result with the scintillation detector - again, the quantum of invisible ionizing radiation was detected by converting it into electrical pulses at the output of the photomultiplier. The question may arise: Why so complicated? The answer is: Scintillation detectors, compared to G.-M. detectors, have three important advantages (we will list them here for the most common case of gamma radiation detection) :

These three properties make the scintillation detector an almost ideal device for the detection and spectrometry of ionizing radiation, especially gamma radiation. High detection sensitivity allows its use for the detection of even very weak radiation or low activities. The short dead time, in turn, allows lossless measurement of even relatively higher radiation intensities or higher activities. *) The scintillation detector therefore has a very wide range of detectable intensities of ionizing radiation, with the possibility of spectrometric selection and analysis.
*) The same dependence applies to the dead time of the scintillation detector as shown in Fig.2.3.4 on the left in the paragraph about G.-M. detector, but the value of the dead time here being mostly t @ 1 ms. The same principles apply to the measurement of dead time and event. dead time correction.

Gamma radiation scintillation spectrum
Let's stop in more detail at point 3 - spectrometry. Scintillation detectors are by far the most commonly used for gamma radiation. Let us imagine initially that we irradiate a scintillation detector with mono-energy gamma radiation *) of energy Eg. The real ("physical") spectrum of this radiation will have a simple shape according to Fig.2.4.1 at the top right - the only narrow peak g₁ in the spectrum (we do not consider the other two lines yet). Photons of gamma radiation will interact with the scintillator either by a photo effect - then in a single interaction the photons are absorbed and give all their energy to the ionizing electron, or by Compton scattering, when they give up only a part of their energy to the electron (and then either escape or cause another interaction); at high energies also by the formation of electron-positron pairs (with a number of subsequent interactions including annihilation of the positron with the electron to produce additional radiation g). The generated secondary electrons then transfer their energy in the detector material in a series of collisions until they are completely braked (to thermal energy). The height of the pulse at the output of the photomultiplier will always be proportional to the energy that the gamma photon actually lost in the crystal.
*)Gamma-photons come from nuclear transitions between discrete levels with precisely given energies, so they are basically monoenergetic, their ideal physical spectrum represents a sharp line on the energy Eg. Very small fluctuations in energy values are caused by quantum uncertainty relations and backscatter of nuclei during gamma-photon emission. Furthermore, since these photons practically never come from free nuclei, but are emitted from radioactive atoms contained in a substance (in a certain material), some photons interact with the substance before leaving the sample. It can also blur their energy a bit. For e⁺ e^-annihilation radiation, the 511keV peak is somewhat blurred (by about 1.2keV) due to the Doppler broadering at different residual velocities of positron braking in the substance. However, the magnitude of these extensions is generally very small compared to the effects at self radiation detection. The real, physical, spectrum of gamma radiation can therefore be considered practically line (monoenergetic) - it is discussed in §1.2., passage "Spectrum of gamma radiation".
If we plot the magnitude of the amplitude A of the output pulses from the photomultiplier on the horizontal axis and the number of pulses n with this amplitude A on the vertical axis, we get the curve of the characteristic shape in Fig.2.4.1 at the bottom right - scintillation spectrum of gamma radiation. The horizontal axis of the amplitude can be calibrated so that the individual points correspond directly to the energy of the detected radiation in keV (see below). The energy scintillation spectrum of gamma radiation consists of two main parts - a relatively sharp photopeak and Compton's continuous spectrum. The structure of the scintillation spectrum is shown in more detail in Fig.2.4.5 on the left :

Fig.2.4.5. Scintillation gamma spectrum.
Left: Scintillation spectrum structure. Right: Dependence of the shape of the scintillation spectrum on the scattering medium.

Terminological note :
In the older literature we can find the terms "differential spectrum" and "integral spectrum". This comes from a time when amplitude analyzers were not yet as perfect, it was either just the lower discrimination level or two independent levels. The "integral spectrum" was created by measuring the integral pulse frequency as the lower discrimination level gradually shifted upwards; it was a descending curve with the largest gradient of decrease at the location of the photopeak. By derivation of this "integral spectrum" originated a actual spectrum, formerly called "differential". The term "integral spectrum" is no longer used for a long time, each spectrum is "differential" with a certain width of the window of the analyzer. The name spectrum or energy spectrum is used, possibly with the adjective "scintillation" or "semiconductor"...

Photopeak - energy resolution of scintillation detector
On the curve of scintillation spectrum is seeing a significant peak - the so-called photopeak or peak of total absorption, corresponding to photons g, which were completely absorbed in the crystal (especially by the photoeffect, or by multiple scattering or a combination of several interactions) and handed over all their energy.
The question arises, why the photopeak is relatively wide, when the actual spectrum of monoenergetic gamma radiation is very narrow - discrete, line? There are several reasons for this "blurring" of the photopeak :
1.The primary limitation on energy resolution is caused by statistical fluctuations in the number of scintillation photons released N . This gives a basic theoretical limit of what the best resolution can be obtained with a given crystal of known light yield - for the resolution R, defined below as the half-width of the photopeak in percent, it is R = (2.35/ÖN) .100%. In the NaI(T1) scintillator, an average of about 40 scintillation photons are released per 1keV; according to the laws of quantum statistics it will be 40 ± 6 photons, ie the relative statistical fluctuations in the number of photons emitted during scintillation will be about 16% for this energy 1keV and R @ 37%. Incomplete scintillation transfer to the photomultiplier and the imperfect efficiency of opto-electrical photon detection further reduce the number of detected photons and worsen the statistical fluctuations of the actually detected photons. These statistical fluctuations in the number of detected light photons blur the amplitude of the output pulses - and thus the photopeak.
2. Nonlinearitylight yield of the scintillator (disproportionate light output) - the number of photons of light emitted per unit of energy absorbed is not constant, but depends on the energy of the particles exciting the crystal *). Scintillation in the crystal occurs by cascades of secondary electrons of different energies, so if the light yield is disproportionate, the number of emitted photons will vary (according to different energy distributions of the primary detected quantum to a cascade of photons and electrons of different energies), although the total absorbed energy is the same. This also causes degradation of the energy resolution.
*)Violation of the proportionality of the scintillation yield is manifested mainly in the area of low energies (keV units). The main cause is the high concentration of charge carriers created by the interaction of ionizing radiation with scintillation material. As the kinetic energy of an electron moving in a matter of matter decreases (according to Bethe's relation), the linear energy transfer dE/dx increases and the ionization density increases along the path. This leads to higher non-radiation recombination of electrons with ions - there is a "quenching" of potentially scintillating electron contributions and thus a reduced scintillation yield in the field of low energy. However, some of the charge carriers may diffuse into the environment with a lower ionization density, where they may cause scintillation. This depends on the mobility of the charge carriers in the material. Significant changes in the effective cross section of the interaction in the areas of binding energies on the K and L shells of the scintillation material also contribute to the anomalies in proportionality (K- and L-edge effects).
The nonlinearity of the scintillation yield can be characterized as a function of the energy of photons or electrons. We recognize the photon disproportionality of the response, which affects the linearity of the energy calibration function of the detector. In terms of the effect on energy resolution, however, the nonlinearity of the response is more important as a function of electron energy - the electron disproportionate of response.
3.Imperfect (inhomogeneous) efficiency of scintillation photon collection on a photomultiplier photocathode. If scintillation occurs in the peripheral parts of the crystal remote from the photocathode, a slightly smaller number of photons strike the photocathode than when scintillation occurs in the middle and near the photocathode; the amplitude of the output pulses will differ even with the same delivered primary radiation energy. This effect is exacerbated if the scintillation crystal is not sufficiently optically transparent and homogeneous. The resolution therefore also depends on the perfect optical transparency of the scintillation material - so that, if possible, the same percentage of scintillation photons, regardless of the scintillation site, can fall on the photocathode of the photomultiplier.
4.Inhomogeneous photoelectric sensitivity of the photocathode - the impact of the same number of photons in different places of the photocathode can lead to the emission of a slightly different number of photoelectrons. There is also an inhomogeneity in the collection of photoelectrons; especially from the peripheral parts of the photocathode, the efficiency of photoelectron collection on the first dynode is reduced.
5.Statistical fluctuations of quantum efficiency and dark current of the photomultiplier, which are superimposed with the useful signal and blur the amplitude of the output pulses.
These effects cause "blurring" of the photopeak and deterioration of energy resolution of scintillation detector. From points 1.-3. it follows, that the best energy resolution can be expected for scintillators with high and energy proportional scintillation yield, high optical transparency and good optical contact with the photomultiplier.
By the energy resolution R of the detector we mean the smallest difference in the energies of the detected radiation, which still yet distinguish in the spectrum as two peaks, or equivalently so-called half-width of the photopeak D1/2 - its width at half height (FWHM). The resolution is expressed either absolutely in keV or relatively (percentage) as the ratio of the half-width D1/2 to the energy value Eg of the center of the photopeak: R = (D1/2 / Eg) .100 [%]. The measured value of energy resolution depends on the energy Eg; it is customary to state it for Eg = 662 keV of radionuclide ¹³⁷Cs (Fig.2.4.5 left).
For NaI(T1) scintillation detectors the energy resolution is around 6-10%. The best energy resolution of about 3% is provided by the lanthanum bromide scintillation crystal doped with cerium LaBr₃ (:Ce); this is due to its high light yield of 63,000 photons/MeV and good energy proportionality.
In Fig.2.4.1 on the right we see how the imperfect energy resolution of the scintillation detector causes the photopeaks of the two spectral lines of radiation g₂ and g₃ with close energies to partially merge into one peak; if the two energies were even closer, a single photopeak would be formed from which these energies could not be distinguished. In this case, a semiconductor detector must be used (see below §2.5 "Semiconductor detectors" , Fig.2.5.1) .
In our spectrometric measurement of the ¹³⁷ Cs radionuclide on a scintillation NaI(Tl) detector, the half-width FWHM of the gamma peak at 662keV was 55keV (8.3%), while with the semiconductor HPGe detector FWHM it was only 1.4keV (0.2%) - significantly better energy resolution !
Energy resolution and detection efficiency of different sizes of scintillation crystals
For the NaI(Tl) scintillator, the theoretical resolution limit, resulting purely from the statistics of the number of scintillation photons emitted, for an energy of 662keV would be about 1.4%. In reality, however, the resolution is much worse (this is due to the significant disproportionate light output in the low energy region, irregularities in photon collection and other influences discussed above at the beginning of this paragraph). For NaI(T1) scintillation detectors of conventional designs, the energy resolution is around 6-10 %; it is better for small thin scintillation crystals, while for large-volume and well detectors it deteriorates to about 15-17 %.
For NaI(Tl) scintillation detectors of several different sizes and designs used in our workplace, we measured the energy resolution FWHM in [%] and detection efficiency [%] for gamma radiation ¹³⁷Cs energy 662keV (measured spectra are normalized to the same height of the 662keV ¹³⁷Cs photopeak) according to the following table :

diameter 40 mm thickness 5 mm	diameter 40 mm thickness 25 mm	diameter 40 mm thickness 50 mm	diameter 127 mm thickness 60 mm	diameter 170 mm thickness 130 mm
FWHM : 5.7 %	7.2 %	8.3 %	11.8 %	17.1 %

Detection 4 % efficiency:	13 %	22 %	35 %	82 % (4p mode)

In the first 3 columns in the table, cylindrical NaI(T1) scintillation crystals of standard diameter 4 cm and thickness 5-50 mm were used. A very thin 5mm detector has good energy resolution, but it has a reasonable detection efficiency only for low-energy radiation of tens of keV (we used it to measure X-fluorescence), but for higher gamma energy it has a very low detection efficiency. Scintillation crystals 4 cm in diameter with thicknesses of 25 mm and 50 mm we use as standard in our radioisotope laboratory. The detector with a diameter of 127mm and a thickness of 60mm was used in a motion scintigraph, the large crystal with a diameter of 170mm and a thickness of 130mm of the well design is used for measuring large volume samples.
Specific values may vary slightly between different manufacturers of scintillation crystals and photomultipliers, but the overall trend is a deterioration in energy resolution with crystal thickness. The best energy resolution is for thin scintillators, the worst is for large-volume well detectors (last column in the table on the right), where there is a complex geometric situation for detection in different places of the crystal - see below §2.7 "Measurement of sample radioactivity", passage "Position dependence of the photopeak at the well scintillation detector", Fig.2.7.2 on the right.
Another trend is also seen from the measured spectra, that the relative proportion of the photopeak relative to the continuous Compton scattered component in the spectrum is higher for thicker crystals (this compton continuum is discussed below in the section "Continuous Compton scattered spectrum"). The main and obvious pattern is increasing the detection efficiency with the size (thickness, volume) of the scintillation detector, especially for high-energy radiation - bottom row of the table.
Continuous Compton scattered spectrum
Before of the photopeak, to the left to the beginning of the graph, stretches a continuous spectrum corresponding to photons, which have lost only part of their energy in the crystal by Compton scattering (Fig.2.4.5). The continuous Compton scattering spectrum has a characteristic shape resulting from the laws of Compton scattering (see §1.6 "Ionizing radiation", section "Interaction of gamma and X-rays", passage "Compton scattering"). Just before the photopeak, the Compton continuum ends with a relatively rapid decrease called the Compton edge - it corresponds to the maximum possible energy transferred to the electrons in one Compton scattering of a given gamma radiation (at a total reflection of 180°). With multiple Compton scattering of the photon g, the transmitted energy is higher - a part of the Compton scattering also extends into the photopeak region, which is disturbing in spectrometry. The shape and relative representation of the Compton spectrum with respect to the photopeak somewhat depends on the geometric conditions at detection.
The shape and relative proportions of the Compton spectrum with respect to the photopeak depend somewhat on the size of the scintillator and the geometric proportions of the detection. With a larger scintillation crystal volume, it is more likely that Compton-scattered photons will not escape from the scintillator, but will eventually be completely absorbed by the photoeffect or repeated Compton scattering, thus contributing to the photopeak. Thus, for larger scintillation crystals, there will be a lower representation of the Compton continuum and a larger representation of the photopeak (but the photopeak will be wider, with worse energy resolution...).
In the continuous Compton continuum is sometimes observed a low and wide backscattering peak, corresponding to photons that were scattered in the surrounding material and only then be detected. Since Compton scattering also occurs in the measured sample itself and in the material around the detector, it can be in the presence of a larger amount of scattering medium a substantially increased representation (height) of the continuous part of the spectrum, as can be seen in Fig.2.4.5 at the bottom right.
X-escape spectrum
Upon absorption of the primary photon g in the scintillator material by the photoeffect, a characteristic X-ray (K-series) is produced, which is usually absorbed and then contributes to the photopeak, but some of it can escape from the detector. If this occurs, then a response is generated reduced by the energy of this photon X. In the case of the NaI(T1) scintillator, it is a characteristic iodine X-ray with an energy of about 28keV. At energies g higher than about 200keV, when the photopeak is wide, the corresponding impulses fall into the photopeak and cause only some expansion of its leading part. However, at low energies (around 60-80keV, when the photopeak is narrower), a so-called escape peak may appear in the spectrum, lying about 28keV lower than the main photopeak.
Annihilation spectrum
When g radiation with an E_g energy higher than 1,022 MeV is detected, electron-positron pairs are produced when interacting with the detector material, while the positrons immediately annihilating with the electrons to form two gamma quanta of 511 keV. Therefore, an annihilation photopeak corresponding to this 511keV energy appears in the spectrum. If both annihilation photons are detected by complete absorption, they contribute to the primary photopeak. Furthermore, some of the 511 keV annihilation photons may escape from the detector, which will reduce the response by this energy - an escape peak corresponding to the energy E_g-511 keV appears in the spectrum. If both annihilation photons escape, this will result in a peak in the energy range 1022keV lower than the primary photopeak.
Summation (coincidence) peaks
are discussed in the following section "Gamma-ray spectrometry".
Pile-up effect
If two quanta of radiation fly into the scintillator almost simultaneously, the respective scintillations are not detected separately, but the light and electrical response from the two quanta is added (pile-up) and gives rise to a single the resulting pulse at the output of the photomultiplier, the amplitude of which corresponds to the sum of the amplitudes from booth scintillations. If one or both scintillations correspond to a photopeak, then the resulting summation pulse will be above the photopeak; when measuring in the analyzer window set to the photopeak, this pulse will fall outside the window and the corresponding pair of quanta will not be detected. This situation occurs mainly at high frequencies of radiation quanta - the pile-up effect contributes to the loss by dead time, it can simulate the so-called paralyzable component of dead time. However, if there is a pile-up effect on two simultaneous Compton scattered photons, the resulting pulse may fall into the photopeak with its amplitude. This situation can be adversely applied to scintigraphy at high pulse frequencies - see §4.2 "Scintillation cameras" section "Adverse effects in scintigraphy - Compton scattering g ".
Noise
At very beginning of spectrum appearing pulses of low amplitude (but unfortunately high frequency) corresponding to the noise - spontaneous thermal emission of the photocathode, noise in electronic circuits. Noise is a fundamental limiting factor and an obstacle in the detection and spectrometry of low-energy radiation. These noise pulses can, if necessary, be substantially reduced by cooling photomultiplier and the preamplifier, e.g. to the temperature of liquid nitrogen.

Gamma and X-ray spectrometry
Here we briefly analyze some methodological principles of spectrometric analysis, which are common to all types of spectrometric detectors, not only for scintillation but also semiconductor (described in the following §2.5 "Semiconductor detectors") and magnetic ("Magnetic spectrometers").
The basic task of gamma radiation spectrometry *) is to determine the energy and intensity of individual discrete groups of gamma radiation photons emitted by the investigated radionuclide or mixture of radionuclides, or photons of characteristic or braking X-rays arising in the electron shell of atoms as a result of nuclear or electrical processes.
*)Gamma radiation is by far the most common subject of spectrometric analysis. Beta spectrometry will be briefly discussed in the following paragraph. Spectrometry of other types of ionizing radiation is performed only sporadically; appropriate references to the methodology of such measurements are given in various parts of the text as appropriate.
In most spectrometers, the energy and flux of gamma photons are not determined directly, but by measuring the energy and current intensity of secondary charged particles, especially electrons, which are produced by the interaction of primary radiation with the substance - sensitive material of the detector. The only exception is crystal diffraction spectrometry, where the energy (wavelength) of X-ray or soft gamma radiation is determined directly - goniometrically according to the scattering angle (§3.3, section "X -ray diffraction analysis").
The individual energy groups of gamma photons (or characteristic X-rays) are displayed in the spectrum as respective peaks called photopeaks; the radiation energy determining the position of the photopeak on the horizontal axis of the spectrum and the intensity determining the height of the peak, resp. area (integral) under the photopeak. Braking X-rays and Compton-scattered gamma rays have a continuous spectrum. The energy and efficiency calibration of the detector must be performed to accurately determine the energies and intensities of the radiation g.
Calibration of the spectrometer
In order for the measured spectrum to objectively express the distribution of energies and intensities of photon radiation, must be performed an accurate calibration of energy responses and the dependence of the detection efficiency of the spectrometer on energy .
The energy calibration of a spectrometric detector consists in determining the correct scale on the horizontal axis, based on the fact that the amplitude of the output pulses is proportional to the energy of the radiation absorbed in the detector. For energy calibration, it would in principle be sufficient to measure the position of the photopeak for one known radiation energy g and to guide a straight line passing through the origin (direct proportionality) through this calibration point. However, the exact linearity of the entire electronic chain may not be ensured a priori; the calibration dependence also sometimes does not go through a "zero" origin (different voltage levels in electronic circuits play a role here). For reliable energy calibration, it is therefore advisable to use several radiation lines g of different known energies. The most common standard radionuclides for energy calibration of gamma spectrometers are: americium ²⁴¹ Am (g 26.3+ 59.6 keV + X 11.9 + 13.9 + 17.8 +20.8 keV), cobalt ⁵⁷ Co (g 122 +136 keV), cesium ¹³⁷ Cs (g 662 keV - the most important standard ever) , cobalt ⁶⁰ Co ( g 1173 +1322 keV) , europium ¹⁵² EU (g122, 245, 344, 779, 867, 964, 1086, 1112 and 1408 keV). The scintillation and semiconductor spectra of these radionuclides are given in §1.4, section "Properties of some of the most important radionuclides".
For energy calibration, we should therefore measure the spectrum of at least three radionuclides in the region of energies Eg of interest (or one radionuclide with a larger number of gamma radiation energies) and determine the positions of photopeaks Ag. Using the calibration points [Eg, Ag] obtained in this way, we interpolate the calibration line (or the curve with larger deviations from linearity) - least squares method, by projection of their values Eg we get the energy calibration of the horizontal axis - Fig.2.4.6 on the left :

Fig.2.4.6. Energy calibration dependence (left) and efficiency calibration dependence (right) of a gamma radiation scintillation spectrometer (a 10 mm thick NaI (Tl) scintillation crystal was used, an Al cover of 1 g /cm² ).

  Calibration of the detection efficiency of a spectrometric detector is much more complicated. This is because the detection efficiency is significantly dependent on the gamma radiation energy according to the curve shown in Fig.2.4.6 on the right: for low gamma radiation energies, the detection efficiency is low because these photons are absorbed through the input window and have difficulty penetrating in the sensitive detector volume. Therefore, first the detection efficiency increases with energy and reaches a maximum for energies of about 60-100 keV. Then, again, the detection efficiency slowly decreases with increasing energy, because at higher energies more an more part of the photons g flies through the sensitive volume of the detector without being absorbed by the photoeffect. The dependence of the detection efficiency on the energy can be roughly expressed by the biexponential function :
      h (Eg) = P. (1- e ^-R¹^.E^g) . e ^-R²^.E^g ,
where the coefficients R1 and R2 (> 0), indicating the rate of rise and decline, depend on the size and material of the detector and on the absorption properties of the input window.
For absolute calibration of the detection efficiency h is necessary to measure the spectra of several spectrometric standards of precisely known activity and thus the intensity Ig of gamma radiation of different energies Eg , by integration determine the area under the photopeaks Sg and vith thus created calibration points [Eg, Sg] then interpolate the efficiency calibration curve h(Eg), as shown in Fig.2.4.6 on the right. If only a relative calibration of the detection efficiency is sufficient, a suitable radionuclide with several g radiation lines (such as europium ¹⁵² Eu) can be used and the calibration curve can be interpolated based on the known intensity ratios of the individual peaks.
If we have already calibrated the spectrometer, the actual spectrometric analysis begins by preparing the sample and measuring its spectrum with a sufficiently high "statistic" - a sufficiently large number of n registered pulses to allow statistical fluctuations 1/Ön were low enough. The following is an analysis in which we find individual photopeaks in the spectrum, determine their energy and use the integral (area) under the peak to determine the intensity of the respective gamma radiation line. For this purpose, it is usually necessary to mathematically separate the actual photopeak curve from the continuous spectrum and event. decompose the composite photopeak into individual components - photopeaks of energetically close lines g. Photopeaks are usually approximated by Gaussian curves. This mathematical analysis of the spectra is now performed using special computer software, and on the basis of the measured energies and intensities of the gamma radiation lines, this spectrum is they assign the corresponding radionuclides - interpretation of the spectrum.
Scintillation and semiconductor gamma radiation spectra of a number of important radionuclides, together with decay schemes, description of their properties and applications, are shown in detail in §1.4 "Radionuclides", section "Properties of some of the most important radioactive isotopes".
Summation (coincidence) peaks
In gamma radiation spectrometry we can encounter an interesting phenomenon of false so-called summation peaks, which do not correspond to any of the actual energies of the emitted radiation g or X. This phenomenon occurs at the detection level, when the measured radionuclide emits two or more groups of radiation photons g or X at the same time (none of the respective levels is metastable). If both such photons g₁ and g₂ are detected simultaneously, the light or electrical responses from both quantums are summed in the detector to give a single resultant pulse whose amplitude corresponds to the sum of the energies E_g₁ + E_g₂. This resulting summation peak mimics gamma radiation of the sum energy, which does not actually exist.
The relative intensity of the summation peak crucially depends on the detection efficiency. With low detection efficiency, simultaneous detection of both quanta is unlikely, so when planar measurements in geometry 2p and lower, have a summation peak of negligible intensity and we usually do not even observe it. The higher the detection efficiency, the more pronounced the summation peak; with a detection efficiency of 100%, we would no longer observe the primary peaks of both real quanta, only a false summation peak would appear in the spectrum! - (provided, of course, 100% of radiation emission, without internal conversion, etc.). This dependence can even be used to determine the absolute detection efficiency of measuring a given radiation or activity of a sample. Under these simple circumstances, the detection efficiency h can be determined from the simple relation h = 4. I²_Sg₁₊_g₂ / (I_g+ I_g₂ + 2.I_Sg₁₊_g₂ )² , where I_g₁ and _g₂ are the intensities of the primary peaks and I_Sg₁₊_g₂ is the intensity of the summation peak.
  The summation peak often manifests itself in radionuclides decaying by electron K-capture (accompanied by the emission of characteristic X-rays when electrons jump from the L shell to the K shell) immediately followed by the emission of g from the excited level of the daughter nucleus. This is where coincidence g is detected and the characteristic X-rays (line Ka , Kb ), and form a summation peak corresponding to energy E_g + E_X. A typical example is the ¹²⁵I radionuclide, which is converted to ¹²⁵Te by K-capture, emitting g with an energy of 35 keV and X with an energy of 27 keV. With sufficient detection efficiency (¹²⁵I samples are often measured in tubes in a well scintillation detector), a significant summation peak corresponding to an energy of 62 keV is observed - see §1.4. "Radionuclides", passage "I-125". Summation peaks can also be observed in the gamma spectra of lutetium ¹⁷⁶ Lu or indium ¹¹¹In .
  The summation peak can occur even at a high flux of photons of radiation g, when two photons can fall into the detector at the same time and cause the resulting scintillation with the sum intensity - random coincidence.
Analysis, evaluation and interpretation of spectra
The analysis of the measured spectrum is used primarily to determine the energies and intensities of individual components of the detected radiation. The radiation energy is determined by finding the position of the peaks of the photopeaks in the measured spectrum, of course, assuming the correct energy calibration of the spectrometer (Fig.2.4.2 on the left). The intensity of the respective line g is determined from the integral of the photopeak (area under the photopeak curve), in the first approximation can also be easily determined using the height of the photopeak. This value then needs to be recalculated (corrected) according to the energy efficiency curve (Fig.2.4.2 on the right).
A significant problem in the analysis of spectra is the imperfect energy resolution of the spectrometer. Photopeaks of nearby energies then partially (or in the worst case even completely) merge, it is difficult to separate them from each other. Special "filtration or deconvolution" is sometimes used to additionally "improve" the energy resolution when evaluating spectra (eg application of Laplace filters, Metz or Wiener filters). However, these procedures are only applicable with a sufficient number of accumulated pulses (good "statistics"), as they are very sensitive to data fluctuations - their application significantly amplifies statistical fluctuations. The issue is largely similar to the spatial resolution of photographic or gammagraphic imaging (cf. the work "Filters and filtration" in scintigraphy).
In the mathematical analysis of spectra, the positions of the vertices are determined, the photo peaks are interspersed with suitable functions (mostly Gaussian curves), the background curves are also fitted, the photo peaks are separated from the background and from each other. The integrals of the resulting photopeaks are then determined and corrected for the energy dependence of the detection efficiency. This creates values of energies and intensities of individual components of the measured radiation, which is the final result from the point of view of spectrometry. Depending on the application used, these results are then further interpreted - for example, they are assigned the appropriate radionuclides (their type and quantity) contained in the analyzed sample. Spectrum analysis used to be done manually, which was a very laborious matter. Powerful spectrometry computer software is now available that allows instant online analysis of spectra, including evaluation and interpretation of results - such as assignment using a radionuclide spectrum database.
Adverse events with scintillation detectors
were discussed in more general terms in more detail in the conclusion of §2.1, passage "Aging and radiation wear of detectors" and "Nuclear reactions and induced radioactivity inside detectors". In addition, we will mention the risks of very intense radiation. Exposure to strong radiation can cause radiation-induced chemical reactions in the detector material, deteriorating the detector's properties - reducing detection efficiency and deteriorating resolution. Immediately after such overexposure, the detector may exhibit an increased intrinsic background, caused by deexcitation of metastable levels and chemiluminescence of molecules released in the detector during intense exposure. Extreme radiation intensity can irreversibly damage the detector ! - strong electron flux in the photomultiplier can damage the surface of the dynodes.

Scintillators and their properties
Mechanism of scintillation formation
Inorganic scintillators
Solid state physics describes the electrical and optical properties of these substances using the so-called band theory, according to which electrons in matter are combined into energy bands separated from each other by unoccupied bands of "forbidden" energies. Discrete energy states of electrons orbiting individual atoms in solids in orbits propagate into energy bands due to interaction with other atoms in the solid, but there are certain gaps between these bands - the so-called bands of forbidden energies, which electrons cannot acquire. The highest energetically occupied belt is the valence belt, followed by a forbidden strip and above it lies the conductivity strip, which is completely unoccupied in the equilibrium (basic) state of the insulators. However, this is only the case with an ideally formed crystal lattice. In reality, however, various changes and defects occur in the regularity of the crystal lattice (they occur both spontaneously and can be created by activation of ions of suitable elements), which lead to local discrete energy levels in the forbidden area between the energy bands. Electrons from other bands can jump into these new energy levels. This creates excitation centers, which are of three types according to the nature of the process in which the transition of electrons between energy levels occurs: luminescent centers, centers of metastable states and quenching centers - Fig.2.4.7 on the left (there is only one luminescent center marked).
If ionization occurs in the crystal by a charged particle or photon and the released electron has a sufficiently high energy, it jumps to an empty conduction band. During movement in this band, the electron can be captured by the luminescent center at a higher energy level (excited state). When switching from this higher level to a lower level, the emission of luminescent (fluorescent) radiation occurs. However, electrons from the conduction band can first be trapped in free metastable levels and only after returning to the conductive band will they cause light radiation to pass through the luminescent centers - delayed luminescence radiation, or phosphorescence, is emitted. The activated alkali metal halides, metastable energy levels also exist directly in the luminescent centers, so there occurs immediate fluorescence and delayed phosphorescence in the same spectrum as in direct luminescence (from the metastable state, the electrons first pass to the excited luminescent energy level after gaining energy, from which the transition to the ground state occurs as in direct luminescence). Finally, electrons can be trapped in the levels extinguishing center, where there is no emission of light, but non- radiative energy transfer by electromagnetic interaction with surrounding atoms.
In inorganic scintillators, the luminescent centers can be formed by the base material, and a large number of luminescent centers can be additionally formed by introducing activator ions - dopants *) into the crystal lattice - these ions cause said additional discrete levels in the band gap (Fig.2.4.7 left ). Silver ions in zinc sulfide crystals ZnS(Ag) or thallium ions (in an amount of 1-2%) in crystals of alkaline element iodides such as NaI(Tl) can serve as activators.
*) Activator labeling convention :
In the literature on ionizing radiation detection, it is customary to indicate the activator or doping element in parentheses after the chemical label of the main carrier - eg NaI (Tl), Lu₂ SiO₅ (Ce), etc. However, chemists prefer the convention of colon ":" labeling - eg NaI: Tl, Lu₂SiO₅: Ce, Al₂O₃: C and the like. The designation with parentheses in chemistry could be confused with indexed groups in chemical samples of compounds, eg SO₄(NH₄)₂. Here in our physical treatise, we mostly use designations with parentheses, sometimes compromise designations combined - Al₂O₃ (: C), CaF₂ (: Dy) etc.

Fig.2.4.7. Symbolic representation of the mechanism of scintillation formation in inorganic and organic substances.
Left: In inorganic scintillators, scintillation photons are formed by jumps of electron captured at higher levels of luminescent centers formed by perturbations in the scintillator crystal lattice (activator Tl in the NaI crystal lattice).
Right: In organic scintillators, the scintillation occurs by deexcitation of the excited molecules of the scintillator itself.
For both cases, the resulting scintillation consists of several hundred of these secondary photons, depending on the absorbed energy of the primary quantum detected (and thus the number of ionization electrons) and the conversion efficiency of the scintillator.

Organic scintillators
In organic scintillators, the mechanism of scintillation formation is different from that of inorganic substances - it is the excitation and deexcitation of the energy states of the scintillator molecules themselves. Organic molecules exhibiting scintillation properties are mainly benzene nuclei of cyclic "aromatic" compounds.
The energy states of a molecule, which are quantized, arise in three ways: by rotating the molecule as a whole, by oscillating motion (vibrations) of atoms in the molecule, and as a result of changes in its electronic configuration. Rotational states are separated only by very small energy intervals (approx. 10^-3 eV) and the radiation that arises during transitions between these states has a spectrum in the microwave region with wavelengths of 0.1-10 mm. The vibrational states are separated by slightly larger energy intervals (approx. 0.1 eV) and the vibrational spectra lie in the infrared region with wavelengths of approx. 1 mm-0.1 mm. The electronic states of the molecule have higher energies, the distances between adjacent energy levels of valence electrons are several electron volts, and the respective spectra are in the visible and ultraviolet regions. It is the excited electronic states that are important for the formation of scintillations; these are mostly excitations and deexcitation of electrons forming interatomic bonds in the aromatic molecule (p -electrons).
A molecule in an excited electronic state can lose energy and return to its ground state in various ways (if this energy is too high, the molecule may even dissociate and disappear). One possibility is simply a direct transition to the ground state with the emission of one photon (if the excitation occurred by irradiation with light, the emitted photon has the same energy as the absorbed photon). Another possibility is fluorescence: a molecule can give off part of its vibrational energy in collisions with other molecules, so that the radiant transition occurs from a lower sub-level of the electronic state (fluorescent radiation has a lower frequency than the radiation originally absorbed). Radiant transitions between some levels are "forbidden" by selection rules, so such transitions occur for a very long time - it arises phosphorescent radiation, which can be emitted for minutes or even hours after the molecules have been excited. Many transitions during collisions lead to non- radiative energy transfer. In general, however, the electron transitions are accompanied by radiation in the visible or ultraviolet part of the spectrum, with each transition having a fine structure - appearing as a series of closely spaced lines due to the presence of different rotational and vibrational states in each electronic state.
Thus, when energy is absorbed, the molecules transition from the ground state to a higher energy level, from which the molecule returns to the ground state by radiating thermal energy and the fluorescent quantum - Fig.2.4.7 on the right (again, only the luminescent deexcitation of the scintillator molecule is marked there). Fluorescence molecules appear mainly in aromatic hydrocarbon molecules with double or multiple benzene nuclei (specific species will be mentioned below).

Different formation of scintillation in inorganic and organic scintillators
It is appropriate to emphasize the different mechanism of scintillation in organic and inorganic scintillators :
¨ In inorganic scintillators, the scintillation effect is a property of a suitably arranged crystal lattice with luminescent centers - they are always solid -based detectors. When the inorganic detection substance is dissolved (eg in water), the crystal lattice decompose and the scintillation effect disappears.
¨ In organic scintillators, the scintillation is formed by deexcitation of its own molecules of suitable organic compounds. When dissolving such a scintillator in a suitable organic solvent, the organic molecules remain unchanged and the scintillation effect is usually preserved - a liquid scintillator is formed (the properties of liquid scintillators and their use will be discussed in more detail below in §2.6, section "Detection of beta radiation by liquid scintillators") .

Properties of scintillators
We will now introduce some physical parameters that can characterize scintillation materials and which are important for their practical applications.
¨ Conversion efficiency
The basic parameter of the scintillation material is the conversion efficiency, which is the ratio of [%] of the total energy of the emitted light and the absorbed energy of the primary incoming quantum of ionizing radiation. In practice, more often than the conversion efficiency is used so-called light yield, given as the number of emitted light photons per 1 MeV of absorbed energy of the detected quantum of primary radiation.
¨ Luminescence spectrum
describes the spectral composition (wavelengths) of the emitted light. It is important to align this luminescence spectrum with the maximum spectral sensitivity of the photocathode, which in most photomultipliers is in the blue region of the spectrum about 600-700nm.
¨ Scintillation afterglow
Another important characteristic, describing the temporal properties, is the duration of scintillation, or so-called scintillation afterglow - the time during which the scintillation photon flux drops to 1/e. This parameter co-determines the speed of the whole scintillation detection process - the dead time of the detector and the time resolution when coincidently using two or more scintillation detectors.
¨ Density
and the proton (atomic) number of the scintillation material is particularly important for the detection of gamma radiation. It determines the degree of absorption of radiation g in the scintillator and thus the resulting detection efficiency. For light materials, most of the g- radiation passes through without absorption by the photoeffect (or multiple Compton scattering). Scintillators with a density of about 3-9 g/cm³ are suitable for the effective detection of especially harder radiation g (with energies of hundreds of keV up to MeV units).
¨ Mechanical, chemical and optical properties
of scintillator material are important for practical implementation and construction of scintillation detectors. Of particular importance is how big single crystals can be grown from a given material, while maintaining good homogeneity and optical transparency (see next point). This is especially crucial for applications in scintillation cameras (see §4.2 "Scintillation cameras"). Some scintillation materials, especially NaI(Tl), are hygroscopic, so they must be hermetically encapsulated. Some larger inorganic single crystals can be quite brittle, so they need to be protected from mechanical pressure and also from larger temperature gradients (different thermal expansion can cause mechanical stress inside the crystal and lead to its cracking). For organic scintillators is important solubility in organic solvents and other chemical properties, important for the application of liquid scintillators (see below).
¨ Energy resolution
characterized by the ability to distinguish two photons of gamma radiation with close energy values. The resulting resolution depends on several factors, discussed above in the "Scintillation Spectrum" section. The internal resolution of a scintillation crystal depends on the light yield of the scintillator and the nonlinearity of the scintillation response for different electron energies. Furthermore, also on the perfect optical transparency of the scintillation material - so that, if possible, the same percentage of scintillation photons, regardless of the scintillation site, can fall on the photocathode of the photomultiplier.

Scintillation materials
There are a number of substances that exhibit scintillation properties. It can even be said, that almost every optically transparent substance, when interacting with ionizing radiation, emits a certain amount of photons of visible light; but the light yield is usually small, the wavelength of this light may not correspond to the spectral sensitivity of the photomultiplier photocathode and scintillation time may not be short enough. Therefore, only substances that have optimized these properties, are designated as true scintillators.
Inorganic scintillators
First we will mention inorganic scintillation materials. As already mentioned, the longest known scintillator is zinc sulfide activated by silver atoms ZnS(Ag). However, the most used inorganic scintillator is a crystal :
¨ NaI (Tl) - sodium iodide, activated with 1-2% thallium. It is suitable for the detection of low and medium energies of gamma radiation (see the curve of energy dependence of the detection efficiency in the right part of Fig.2.4.6). Its disadvantage is that it is hygroscopic. It must therefore be mounted in airtight housings with a glass outlet window, the inner walls of the housing are provided with a reflective coating such as magnesium oxide to increase the light yield. If the case is not perfectly hermetic, the crystal absorbs moisture from the air, it is hydrolyzed (manifested by yellowing - dissociation of NaI), loses perfect transparency, deteriorates energy resolution and conversion efficiency (Fig.2.4.8 b, c) :

Fig.2.4.8. Influence of encapsulation hermeticity on NaI(Tl) scintillator properties.
a) Perfectly hermetic encapsulation of the crystal ensures its long-term transparency and good spectrometric properties.
b) The NaI(T1 ) crystal, yellowed due to imperfect hermeticity, shows impaired resolution and reduced conversion and detection efficiency.
c) A more serious violation of the hermeticity leads to a browning of the NaI(Tl) crystal, which not only completely loses its spectrometric properties, but to a large extent also loses its simple detection properties!
Note: All three scintillation detectors have the same dimensions (diameter 45 mm, height 25 mm) and their age from production is 43 years.

For the detection of higher energies of gamma radiation, scintillators with a higher density are more suitable from the point of view of detection efficiency :
¨ Bi₄ Ge₃ O₁₂ (bismuth-germanium oxide, abbreviated BGO );
¨ Lu₂ SiO₅ (: Ce) (cerium-activated lutetium orthosilicate - LSO );
¨ Lu_1.9 Y_0.1 SiO₅ (lutetium yttrium silicate LYSO );
¨ Y₂ SiO₅ (: Ce) (cerium-activated yttrium orthosilicate - YSO);
¨ Gd₂ SiO₅ (: Ce) (cerium activated gadolinium orthosilicate - GdSO);
¨ further LuAlO₃ (Ce) (LAO).
¨Based on LSO, the LFS (Lutetium Fine Silicate) scintillator was further developed, which has a finer crystal structure and, in addition to basic lutetium, silicon and oxygen (LSO) with doping Ce, also contains carefully tested small impurities of some other elements such as Ca, Gd, Sc, Y, La, Eu, or Tb. Depending on the type and content of alloying elements, there are several types of numbered LSF scintillators, such as LFS-3. This results in slightly better energy resolution and shorter scintillation afterglow.
These high-density scintillators are mainly used for the detection of 511keV energy annihilation e^-e⁺ gamma radiation in positron emission tomography (PET) cameras, where it is necessary to achieve high detection efficiency with not too large crystal thickness (in order to achieve high spatial resolution of scintillation localization by a system of photomultipliers) - see §4.3 "Tomographic cameras", section "PET cameras".
¨ The heaviest scintillators, such as PbWO₄, are used as part of complex detection systems that register high-energy radiation
from the targets of large accelerators of elementary particles (eg the new "Large Hadron Collider" at CERN uses almost 80,000 PbWO₄ crystals in the detection part) - see §1.5 "Elementary particles", section "Charged particle accelerators".
For some special purposes, such as the detection of harder X-rays in CT, other scintillation materials such as Lu_1.9Y_0.1SiO₅ (LYSO), CdWO₄ are used . Scintillators based on ceramic materials (silicon oxides), doped with rare earths (such as gadolinium or yttrium) and possibly and other elements, sometimes referred to as UFC (Ultra Fast Ceramic) - ultra-fast ceramic detectors. Scintillation flashes are detected by either photomultipliers or phototransistors (significantly simpler and cheaper phototransistors or photodiodes are sufficient if it is only a simple detection, not spectrometry; another advantage is the miniature size) - see §3.2 "X-ray diagnostics", section "Transmission X-ray tmography (CT)". The use of so-called silicon semiconductor photomultipliers described above is promising (section "Photomultipliers", Fig.2.4.2g ).
The following table lists several inorganic scintillation materials used in scintillation detectors. They are sorted by increasing density (which increases the detection efficiency for higher energy gamma radiation) :

Scintillator:	NaI (Tl)	CsI ??(Tl)	Y ₂ SiO ₅ (Ce)	BaF ₂	LaBr ₃ (Ce)	Gd ₂ SiO ₅ (Ce)	Bi ₄ Ge ₃ O ₁₂	Lu ₂ SiO ₅ (Ce)	CdWO₄	PbWO₄
Density [g/cm³]	3.67	4.51	4.53	4.89	5.1	6.71	7.13	7.41	7.9	8.23
l max [ nm ]	415	400/565	420	220/310	360	440	480	420	470/540	410/500
scint. afterglow [ms]	0.23	0.6 / 3.4	0.07	0.008	0.016	0.06	0.3	0.04	20/5
h [photon/MeV]	4.10⁴	5.10⁴	4.6.10⁴	1.8.10³	6.3.10⁴	1.10⁴	8.10³	3.10⁴	5.10³	3.10²

Note: In terms of spectrometric properties, it is worth noting the lanthanum bromide crystal doped with cerium LaBr₃(:Ce 5%), which thanks to its high light yield of 63000 photons/MeV and good energy proportionality, in the scintillation detector provides very good energy resolution (approx. 4% at 137-Cs). It also has a very short scintillation afterglow of 16ns, which makes it promising for the coincidence detection of annihilation photons in PET positron emission tomography (§4.3 "PET cameras", TOF analysis).
Internal radioactivity of LSO scintillators
A certain disadvantage of lutetium -based scintillators (such as LSO or LYSO) is their relatively high background due to the internal radioactivity contained in the scintillator. In addition to the basic stable isotope ¹⁷⁵Lu (97.4%), natural lutetium also contains an irremovable admixture of the long-term radioisotope ¹⁷⁶Lu (2.6% - a natural radionuclide of primary origin), which decays with a half-life of 3.8.10¹⁰ years b^- converted to a stable hafnium ¹⁷⁶Hf, emitting beta radiation with max energy E_b_max = 596 keV (99.6%) and a prompt cascade of gamma radiation with energies E_g88keV (15%), 202 keV (78%), 307keV (94%) and 401keV (0.4%) - see §1.4, passage "Lutetium".
The mass specific activity of ¹⁷⁶Lu in the LSO material is about 39 Bq/1gram LSO *) and the resulting internal radiation background (due to the 100% efficiency of internal detection) reaches values of about 250 imp./s./cm³ LSO; medium large scintillation detector 100cm³ of the LSO would therefore have an internal radiation background of about 25,000 imp./s.! Therefore, LSO scintillators are not suitable for measuring weak radiation fluxes and low activities. However, when used in medical positron tomography PET, for which they are primarily intended, this disadvantage does not apply in practice. On the one hand, coincidence measurements are performed, and on the other hand, the internal background of LSO/LYSO scintillators is negligibly small compared to the fluxes of the measured annihilation radiation of about 10⁶ photons/s in clinical scintigraphy. However, certain problems may arise in experimental studies of PET with low activities and long measurement times (animal PET) - it is discussed in more detail in §4.3 "Tomographic cameras", section "PET cameras".
*)Mass specific activity can be determined using the formula derived in §1.2. "General laws of atomic nucleus transformation", passage "Relationship between half-life and activity": A_1g @ (6.10²³/N).ln2/T_1/2 @ 4.16.10²³/ (N.T_1/2). Substituting the mass number N and half-life T_1/2 [s] for ¹⁷⁶Lu is 51.23 Bq /1 g of pure ¹⁷⁶Lu and after conversion to a content of 2.6% ¹⁷⁶Lu in lutetium and a lutetium content of 76% in LSO we get a final value of about 39 Bq /1 gram LSO.
Just a small interesting thing is that the above-mentioned lanthanum bromide LaBr₃ (: Ce) scintillator has also an internal natural radioactivity: natural lanthanum, in addition to the stable basic isotope ¹³⁹La, also contains 0.09% of the long- lived radioisotope ¹³⁸La, which is converted to barium-138 by electron capture (70%) with a half-life of 1.12.10¹¹ years, or b^- radioactivity (30%) at cer-138; it is accompanied by the emission of gamma photons 1426 and 790 keV. However, the volume specific activity here is only about 1 Bq/cm³ LaBr₃.
How did lutetium ¹⁷⁶Lu form?
The answer is given by nuclear astrophysics - a fascinating scenario of cosmic nucleogenesis (see "Cosmic alchemy" or "We are the descendants of the stars!"). ¹⁷⁶Lu was nuclear- synthetized, along with a stable¹⁷⁵Lu and all the heavier elements, more than 5 bilion years ago during a supernova explosion, the ejected gases of which formed the solar system, including the planet Earth ...

Organic scintillators
There are also a number of organic substances that have scintillation properties (see Fig.2.4.7 on the right for the mechanism). It is mainly naphthalene, which emits scintillation radiation with a very short flash time of 0.08 ms and a wavelength of around 345 nm (this wavelength is shorter compared to the maximum spectral sensitivity of the photocathodes of most photomultipliers, so a "spectrum shifter" is sometimes used - see § 2.6). An important organic scintillator is anthracene, which is used as a standard to compare the properties of all other organic scintillators. Anthracene emits scintillation with a flash time of 0.03 ms and wavelength of 450 nm, its conversion efficiency is about half that of NaI(Tl). Other organic substances include stilbene, which emits scintillation with a duration of 0.08 ms and a wavelength of 380-410 nm; its advantage is the ability to form large crystals. Organic scintillators have too low a density to detect gamma radiation, so the detection efficiency would be low. However, they are very suitable for the detection of beta electrons, alpha particles, protons, deuterons and also fast neutrons (neutrons eject protons from the molecules of organic matter, which cause scintillation and are thus registered).
Organic scintillants usually retain their scintillation properties even when dissolvedin suitable organic solvents *) (toluene, xylene, benzene, dioxane, phenylcyclohexane, phenyl ether, etc.) - liquid scintillators are formed. Liquid scintillators have the advantage that they can be adjusted to a suitable shape even by a simple filling into a suitable container, even to a size which is not achievable with solid (crystalline) scintillators; they are therefore used, for example, in the detection of cosmic rays. However, the main use of liquid scintillators is in the method of detecting beta emitters directly in solution with these scintillators (§2.6, section "Liquid scintillators"). The use of organic and liquid scintillators will be described below in §2.6 in connection with the beta and alpha detection methodology.
*) This is due to the mechanism of scintillation formation (which was outlined above - Fig.2.4.7). In inorganic scintillation crystals, where scintillations occur during deexcitation of energy levels in the luminescent centers of the crystal lattice, when the scintillator dissolves, the crystal lattice disappears and the scintillation effect also disappears. In contrast, in organic scintillators, where scintillation occurs during excitations and deexcitation of the energy levels of the molecules themselves of organic substance, the scintillation effect persists even after the scintillator is dissolved.

Cherenkov detectors
In addition to the scintillation mechanisms described above, there is another process of light formation during the interaction of ionizing radiation with matter: Cherenkov radiation. As stated in §1.6 "Ionizing radiation", the passage "Cherenkov radiation", a charged particle that flies through an optically transparent medium with a refractive index n at a speed higher than the speed of light c' = c/n in this medium, produces "shock" electromagnetic waves - visible light called Cherenkov radiation. The physical mechanism of this radiation was clarified in the mentioned §1.6, passage "Cherenkov radiation", where the table also shows the threshold energies for the generation of this radiation for different types of particles in different media environments. This radiation can be used to detect charged high-energy particles, event. also hard gamma radiation (which ejects fast electrons when interacting with matter).
The Cherenkov detector, in its simplest configuration, consists of a transparent dielectric with a high refractive index (eg plexiglass), in which the fast-flying charged particles excite Cherenkov radiation, which impinges on the photocathode of photomultiplier, where it is converted into electrical impulses, similar to scintillation detectors. Different sizes and shapes of dielectric are used, the detection medium is sometimes liquid (eg water) or air, lens or mirror optical systems are sometimes used to concentrate Cherenkov radiation on the photocathode of one or more photomultipliers. Since the number of emitted photons and the angle of the direction of their emission with respect to the direction of motion of the primary particle depend on its energy (superluminal velocity), the energy of the detected charged particle and the direction of its motion can be determined.
When detecting Cherenkov radiation, the problem of a small number of emerging photons is encountered. According to the relations given in §1.6, the passage "Cherenkov radiation", about 200 photons per centimeter of ultrarelativistic electron trajectory are produced in water, under less optimal conditions it is less. Therefore, high demands are placed on the properties of photomultipliers - high quantum efficiency of the photocathode for the spectral range of Cherenkov radiation, low noise, good optical contact of the photomultiplier with the environment, as well as low absorption of radiation in the environment. This problematics is somewhat similar to the detection of low energy b -radiation of tritium ³H in liquid scintillators (see below §2.6 passage "Liquid scintillators").
The ring imaging Cherenkov detectors - RICH
For special purposes of directional detection of high-energy particles, more complex detection systems have been developed, using the properties of Cherenkov radiation. They are called RICH (Ring Imaging Chrenkov detector). They consist of a system of mirrors (spherical and planar) that reflect light photons of Cherenkov radiation, created along the path of a particle in an optical medium (eg CF₄, C₄F₁₀, ....), and direct them to a system of a large number of imaging photomultipliers. Electronic analysis of impulses from these photomultipliers can reconstruct the trajectory of the particle and determine its energy. The device therefore works as imaging detector-spectrometer of fast charged particles.
Cherenkov detectors have their main use for the detection of high-energy particles - they are used in large accelerators and in the detection of cosmic radiation (see also the passage "Neutrinos - "ghosts" between particles" in §1.2 "Radioactivity" or "Cosmic radiation" in §1.6).

2.5. Semiconductor detectors
By the mechanism of direct electrical use of ionizing radiation effects, the semiconductor detector is somewhat similar in principle to the ionization chamber, wherein the sensitive medium is of course not gas, but a suitable semiconductor material. From an electronic point of view, the semiconductor detector is basically a diode connected in a high voltage electrical circuit (approx. 1000-2000 V) via a large ohmic resistor in the closing (non-conductive) direction (Fig.2.5.1), so that no current flows through the circuit at rest.

Fig.2.5.1. Diagram of a semiconductor detector. On the right is an example comparing the semiconductor spectrum of gamma radiation with the scintillation spectrum.

If a quantum of ionizing radiation enters the active layer of the detector (it is a "depleted" layer or volume region without free charge carriers), the ionizing energy causes in the semiconductor to jump a proportionate number of electrons into the conductive band and form electron-hole pairs. These electrons immediately start moving in the electric field to the positive electrode (and the holes to the negative) - a short current pulse passes through the electric circuit, a voltage drop occurs on the working resistor R and through the capacitor C the electric pulse leads to a charge-sensitive preamplifier. The amplitude (or time integral) of the pulse at the output of the amplifier is directly proportional to the total charge colected, and thus the energy of the detected radiation (more precisely, the energy that was absorbed when the quantum of radiation passed through the active detector layer). Thus, by amplitude analysis of the output pulses, we can perform a spectrometric analysis of the energy of the detected radiation, similarly to scintillation detectors. The amplified pulses are fed to an analog-to-digital converter and from there to the memory of a "multichannel analyzer", now realized in a computer, in the memory of which the resulting spectrum is stored.
Semiconductor g radiation detectors have a very good energy resolution(usually better than 1 keV), about 30 times better than scintillation detectors - see comparison of spectra in Fig.2.5.1 on the right. Two basic factors in particular contribute to this :
1. Thecollection of the charge created in the semiconductor by ionization is relatively perfect from the entire sensitive volume.
2. Thesmall width of the band gap leads to the low energy required to form one electron-hole pair. The number of these charge pairs generated by the detection of a quantum of a given energy is therefore high (more than 10 times higher than with gas or scintillation detectors) and thus the relative quantum-statistical fluctuations in their number are low.
Semiconductor detectors also have a high ratio of photopeak to continuous Compton background. However, compared to scintillation detectors, they usually have somewhat lower detection efficiency for gamma radiation and also longer dead time (dead time is given by the capacity of the detector + preamplifier system and the value of the working resistance). Semiconductor detectors are used wherever we need the best possible energy resolution, eg in nuclear physics, neutron activation analysis, X-ray fluorescence analysis, detection of radionuclides in ecology or measurement of radionuclide purity of preparations. Otherwise, all the principles and principles of gamma-ray spectrometry (§2.4, section "Scintillation spectrum"), including energy and efficiency calibration, which have been discussed in the scintillation detector, also apply also to the semiconductor detector.
In some applications, the great advantage of semiconductor detectors is their independence from the magnetic field (unlike photomultipliers used in scintillation detectors).
Differences in scintillation and semiconductor gamma spectra
If we look at the example of gamma spectrum in Fig.2.5.1 on the right (enlarged section from the spectrum of radionuclide ¹²³I), we can see at first glance two significant differences between the spectra measured by scintillation and semiconductor detector :
¨The photo peaks on the scintillation spectrum are round and gradual, as if "blured" - the energy resolution is relatively imperfect here (approx. 10% for the 662keV test line¹³⁷Cs), the nearby gamma lines merge into one wider photopeak. The semiconductor spectrum, on the other hand, consists of very sharp and narrow peaks - the energy resolution is about 30 times better. Some compact ("overlapped") peaks of scintillation spectra on a semiconductor spectrum are decomposed in two or several discrete g-lines (Fig.2.5.1 right) ...
¨In the scintillation spectrum is seen distinctly represented continuous component of Compton scattered radiation, especially in lower energy areas. This continuous background is disturbing (especially in the "peak" area of the backscatter, which can interfere with the actual gamma peak of the measured radionuclide). In semiconductor spectra, the continuous component is strongly suppressed because better energy resolution leads to narrow and high peaks (while maintaining the same area under the peak , which automatically leads to a reduction in the relative height of the continuous background in the spectrum - graphical drawing of the spectrum is normalized to the top of peak.
Germanium and silicon semiconductor detectors
Semiconductor detectors are mostly made of germanium single crystals, either with a trace amount of lithium, so-called drift - Ge(Li) detectors, or more recently of superpure germanium HPGe (High Purity Ge), or from silicon Si *). Germanium detectors are constructed either in a coaxial arrangement of n-i-p layers (for the detection of higher gamma energies) or in a planar shape with a thin input window (for the detection of soft gamma and X). Silicon detectors Si(Li) are mainly intended for the detection of soft gamma and X radiation with high resolution, planar shape, often a beryllium input window with low absorption of soft gamma and X radiation is used.
*) Other semiconductor materials are also used, such as Ga(As), Cd (Te), .... For the detection of gamma and X-rays, detectors based on CdZnTe (CZT) are also used, which have a high detection efficiency for photons of energy of tens of keV and work even at room temperatures, see below.
Upon absorption of a gamma photon of energy 1MeV in germanium HPGe, approximately 3x10⁵ electron-hole pairs is formed. Compared to silicon, germanium is more effective for detection than silicon because its atomic number is much larger. The average energy for electron-hole pair formation is 2.9 eV for silicon and 3.6 eV for germanium. Due to its higher atomic number, germanium has a significantly higher absorption coefficient for gamma radiation, so it is suitable for the detection of gamma radiation of higher energies up to several MeV. Silicon detectors with a thickness of several millimeters, on the other hand, are suitable for low energy spectrometry of gamma and X photons, keV units, with high resolution.

Scintillation and semiconductor detector when used in gamma-spectrometry of radionuclides.
Left: Scintillation probe - a scintillation crystal NaI(Tl) + photomultiplier, with shielding. Middle: Analog-to-digital converter (ADC) and computerized (CPU) multichannel analyzer. Right: Semiconductor Ge(Li) / HPGe detector with preamplifier and Dewar vessel with cooling liquid nitrogen.

Semiconductor spectrometric detectors usually need to be cooled to liquid nitrogen (LN₂ - Liquid Nitrogen) *) to function properly to reduce the closing current and electronic noise. In low-energy detectors, also the preamplifier is often cooled, the input element (field-effect transistor) of which is located in the cryostat together with the detector in order to minimize the preamplifier noise. For some new types of semiconductor spectrometers with HPGe, it is no longer necessary to use liquid nitrogen added to the Dewar for cooling, as an electronic cooling system is used, working on the basis of Joule-Thomson expansion of compressed gas (in addition to nitrogen, helium or other suitable cryogenic gases are also used), with a miniaturized compressor with a Stirling cycle and possibly also with Peltier thermocouple.
*) Ge(Li) detectors even have to be cooled permanently also during storage; interruption of cooling leads to diffusion of Li drift and destruction of the detector! The advantage of detectors made of very pure germanium HPGe is the possibility of thermal cycling - during the measurement it is cooled to the temperature of liquid nitrogen, but they can be stored at room temperature.
However, semiconductor detectors have been developed that operate at room temperature, using semiconductors with a large bandwidth, such as alloys of two (GaAs, CdTe, InP) or three (CdZnTe, InAlP) different semiconductor materials. Although these detectors do not achieve such a perfect energy resolution, they have a higher detection efficiency against photon radiation (see CZT detectors below).
Semiconductor detectors with a surface barrier are used to detect corpuscular radiation (alpha, beta, protons - see below), which has a short range in substances. They are designed so that a very thin metal layer of eg gold (thickness of only a few atoms - less than 1 micrometer) is applied to the front side of the polished silicon wafer of the "n" type semiconductor, which serves both as an electrode and an input window of the detector; the back wall is nickel-plated and serves as the second electrode. A voltage of approx. 100-200V is connected to such a detection diode with a p-n junction via a working resistor, pulses generated by particle detection are taken from the working resistor for amplification and further processing.

Diamond detectors
Crystalline carbon - diamond can also serve as a suitable material for electronic detection of low-energy radiation. Here, the carbon atoms are bonded to each other by a strong covalent bond and are arranged in a cubic crystal lattice. The width of the band gap is 5.45 eV. Pure diamond is electrically non-conductive (dielectric, high resistivity »10¹⁶ W cm). A small amount of defects or dirt causes the diamond to discolor; such a diamond also behaves like a semiconductor. Diamond detectors are somewhat similar to silicon detectors.
The diamond crystal is placed between two electrodes to which voltage is applied - the connection is the same as in Fig.2.5.1. An ionizing particle or photon of electromagnetic radiation releases electrons (and positive ions - "holes") in the crystal lattice upon their impact and passage, which move under the influence of an electric field in the conduction band in the crystal and cause an electric impulse at the electrodes. The principle is very similar to a classic gas ionization chamber - a diamond detector is a kind of "solid ionization chamber".
As with other semiconductor detectors, diamond detectors can be made either as single single crystals or as layers formed by chemical Vapor Deposition technology (CVD, lat.. vapor = steam ). With this CVD technology, even more complex structures of a larger number of detection elements can be created - multi -detector systems or polycrystalline active surfaces in the strip-detector mode.
Diamond detectors have some advantageous properties :
× Mechanical resistance and good thermal conductivity.
× Insensitivity to visible light (they are sensitive only from harder UV radiation).
× They work at room temperature, no cooling is required.
× High signal-to-noise ratio.
× Fast signal response. Diamond detectors are very fast, have a time resolution in the order of tens of picoseconds. They are able to work even at high intensity particle flow. They are therefore used as internal "trigger" detectors, which define the exact moment of interaction in complex detection systems at accelerators ("Arrangement and configuration of radiation detectors").
× High radiation resistance to damage in strong radiation beams.
They are used, or are promising, in a number of areas :
- detection of high energy particles, detection of neutrons and a-particles;
- monitoring and dosimetry of photon and particle beams for radiotherapy;
- measurements on cyclotrons and synchrotrons;
- trackers for complex detection systems examining the interactions of high - energy particles in accelerators ("Arrangement and configuration of radiation detectors").

Cadmium-Zinc-Teluride (CZT) detectors
Spectrometric germanium and silicon semiconductor detectors provide excellent energy resolution, so they play an irreplaceable role in the precise analysis of gamma radiation from natural samples and laboratory preparations. However, their technical disadvantage is the need to cool to liquid nitrogen temperature. This is a serious, often insurmountable, obstacle in many laboratory and all practical technical applications of radiation. Therefore, there is a need to develop semiconductor detectors that have at least "slightly good" spectrometric properties, but could operate at the usual room temperature (in the laboratory, natural terrain).
From this point of view, some compounds of tellurium (tellurides) with metals such as zinc and cadmium (used in photovoltaic cells of solar panels) have proved successful. For detection and gamma spectrometry is used in particular cadmium telluride and zinc CZT (Cadmium -Zinc-Tellurium) - Cd_xZn_(1-x)Te in different ratios, usually x = 0.1-0.15. Sometimes small admixtures of other elements are added to improve the crystalline-electrical properties of the alloy (usually 0.05-0.07 selenium).
This alloy acts as a semiconductor detector operating at room temperature, which converts gamma and X radiation into electrical impulses with high efficiency. Semiconductor CZT detectors can in most applications serve as a (better) replacement for conventional scintillation NaI(Tl) detectors, with significantly smaller dimensions.
The comparison of the basic parameters of the semiconductor detectors HPGe, CZT and scintillation detector NaI(Tl) is in the table (approximate practical - average, typical - values are given) :

Detector type	Energy resolution (FWHM at 662keV ¹³⁷Cs)	Density	Detection efficiency	Pulse reverberation time	Max. pulse frequency / s .
HPGe	1.4 keV (0.2%)	5.32 g / cm ³	%	... [ns]	1.5 . 10 ⁵ cps
CZT	33 keV ( 5% )	5.82 g / cm ³		...	2 . 10 ⁶ cps
NaI (Tl)	55 keV (8%)	3.67 g / cm ³		230 ns	2 . 10 ⁵ cps

Compared to spectrometric germanium GeHP detectors, CZT detectors have poorer energy resolution (which is sufficient for many applications), but higher detection efficiency and shorter dead time.
Semiconductor CZT detectors are often mounted on printed circuit boards, which on the opposite side have connected integrated circuits containing amplifiers, analyzers and other electronics for processing the detected pulses. This creates miniaturized compact integrated modules - detection blocks (analogous to scintiblocks), which can be fitted to more complex detection systems. The use of suitably arranged pixel CZT detectors for semiconductor gammagraphy is particularly interesting and beneficial (planar and SPECT "scintigraphy" - §4.2, part "Alternative physical principles of scintillation cameras", passage "Semiconductor multidetector gamma cameras").

Multidetector semiconductor systems
Advantageous electro-mechanical properties of semiconductor detectors enable their miniaturization and integration of individual semiconductor elements into multidetector systems. These multidetector systems can provide information both on the energy of the registered radiation and on the point of impact of the individual ionizing quanta, or on the paths of the flying particles - they can therefore have imaging properties. The most commonly used semiconductor multidetector systems are of three types :
¨ Array of semiconductor detectors arranged on a suitable surface, usually at regular intervals. Allows by a single measurement chart e.g. geometric progression of the intensity of radiation beams (........
¨ Pixel semiconductor detectors (SPD - Semiconductor Pixel Detector). On a thin semiconductor wafer (most often silicon, type N) electrodes (P) are applied, which in the form of an output electrical signal dissipate the charge created by the passage of an ionizing particle. The electrodes are distributed in a dense regular grid, forming cells - pixels - with dimensions of a few micrometers to tenths of a mm. Electronic circuitry for evaluation can also be integrated on the board - preamplifiers, discriminators, multiplexers, counters, analog-to-digital converters (ADC - allow to evaluate the energy of particles absorbed in individual pixels). By processing the pulses from such a detector, we get a planar image of the distribution of the positions of the incoming particles and possibly also their energies. Such imaging detectors are used, among others, in radiography, especially X-rays - so-called flat panels with direct conversion, §3.2, part "Electronic X-ray imaging". Detectors of this type are also beginning to be used in gamma cameras of nuclear medicine - §4.2, part "Alternative physical principles scintillation camera" passage "Semiconductor multidetector gamma camera".
Pixel detectors can be spatially stacked in many layers, in blocks or other units, allowing spatial display tracks the passing particles - this is called tracker (tracking of path of particles). Systems of these detectors are used in complex analyzers of high energy particle interactions, the typical arrangement of which is given above in §2.1, section "Arrangement and configuration of radiation detectors", Fig.2.1.3 below - forms the innermost part of the detection system, the tracker.
A simpler variant of the position-sensitive semiconductor detectors are called strip detectors (tape-strip-shaped), which also consist in systems constituting trackers ...
¨Semiconductor Drift detectors (SDD)
On the surface of the N-type silicon wafer with a high resistivity, regions P are implanted, forming P-N transitions. Anodes are placed on the edge of the plate, collecting charge from the detector. During the passage of the ionizing particle, electron-hole pairs are released, after which the electrons are moved in a drift motion to the region of the anodes, where they are captured and generate an output electrical signal. If we know the rate of electron diffusion, we can determine the position of the place where the particle flew through the detector from the time of the pulse at the anode (from the time of the drift motion).

LBSD detectors
A uniquely used type of semiconductor detector is the so-called long base silicon diodes (LBSD - Long Base Silicon Diode), designed to measure the radiation dose (kerma) from heavy particles, especially fast neutrons. As a result of irradiation and ionization, the crystal lattice of silicon is damaged, which changes the lifetime of the minor charge carriers and thus the conductivity of the diode. The voltage drop across the diode is measured in the forward direction before and after irradiation, the change in voltage drop after irradiation relative to the initial value being an approximately linear function of the radiation dose (kerma).

Microcalorimetric detectors
During the interactions of radiation with a substance, a certain part of its energy is converted into heat (the thermal effects of radiation have already been mentioned in §1.2 "Radioactivity" and in §1.6 "Ionizing radiation", section "Thermal and electrical effects of radiation). Based on this fenomenon, detectors were developed that use the thermal effects of energy transferred to the substance at absorb quantum radiation. These detectors can to some extent be classified as semiconductor detectors, either in terms of the primary sensor, or for semiconductor technology used in the electronic processing of measured signals. The methodology for measuring physical quantities through heat is generally called calorimetry; in a figurative sense, all detectors measuring the energy of radiation quanta are sometimes referred to as calorimeters.
Calorimeter (lat. Calor = heat )
is generally an arrangement or device that in thermodynamics is used to measure heat quantities based on heat exchange between test specimens located in an insulated system, where the law of conservation of heat-energy applies. Heat, temperature, heat capacity, heat of reaction, heat conversion to other types of energy, etc. are measured. For simple calorimeters, the temperature of the examined environment is measured with a conventional mercury thermometer. With modern calorimeters, the temperature is registered electronically using thermistors - electronic components whose resistance is strongly temperature dependent.
The so-called isothermal calorimeters, operating at normal temperature, are sometimes used for absolute measurement of the radioactivity of high-activity preparations - bridge temperature thermistors are used to compare the temperature difference between a reference sample and a sample containing radioactive material (in which radioactivity causes the material to heat).
Bolometer (from the Greek bole = incident, beam )
is generally a device or element that measures radiation based on its thermal effects. These thermal effects are mostly measured thermoelectrically, using the pyroelectric effect - the ability of some materials to generate a temporary electrical potential when the temperature changes. Depending on the heating, the electrical resistance of the detector changes. The basic principle of the bolometer is simple: the absorber converts the radiation into heat and the thermistor converts this heat into an electrical signal. In modern bolometers, the absorber and the thermistor are usually combined into one element - the detector.
The detector consists of a suitably shaped thin metal strip or semiconductor or superconducting material - thermoresistor, with electrical outlets to the evaluation circuit. By absorbing the incident radiation, the temperature increases and the resistance of the thermoresistor changes, on the basis of which the evaluation apparatus determines the amount of absorbed energy. Bolometers are sensitive to radiation of any frequency, they respond to different types of radiation.
An interesting special type of microcalorimeter is the bolometer on the edge of superconductivity TES (Transition Edge Sensor). It uses a very steep course ("edges") of the dependence of the resistance of a suitable material on the temperature around the phase transition between normal conductivity and superconductivity (Fig.2.5.2 on the right). The bolometer sensor itself consists of a small, suitably shaped thin metal strip (eg a tungsten film several tens of nanometers thick, deposited on a silicon substrate) - Fig.2.5.2 on the left, cooled just below the superconductivity temperature, so that its resistance is practically zero. The impact of a quantum of radiation (photon) slightly heats the tape material beyond the edge of the superconductivity, thus transitioning to the normal conductivity mode, the resistance rises sharply (Fig.2.5.2 on the right) and in the electrical circuit it causes a fast voltage pulse, which is amplified (Fig.2.5.2 in the middle) and registered in the evaluation device. After detection, the sensor cools down quickly to superconducting temperature and is ready to detect another quantum. The current pulse in the bolometer circuit (its integral value) is proportional to the change in temperature and thus the energy absorbed of detected quantum. Instead of a metal film, superconducting nanofibers with a thickness of about 100 nm are sometimes used in the TES bolometer.

Fig.2.5.2. Highly sensitive bolometer working on the edge of superconductivity TES (Transition Edge Sensor) - principle diagram.
Left: Cooled superconducting sensor. Middle: Electronic signal acquisition. Right: Steep curve dependence of TES resistance on temperature.

In the most demanding applications, to achieve the highest possible sensitivity, the signal in the electrical circuit of the TES bolometer is sensed and amplified first using the so-called SQUID magnetic detector *), magnetically connected via a coil L connected in the bolometer circuit (Fig.2.5.2 in the middle). The magnetic flux F from the coil L sensitively modulates the current through both branches of the SQUID ring. Only thus pre-amplified signal is fed to a standard electronic amplifier and then to evaluation.
*) SQUID ( superconducting quantum interference device )
is a highly sensitive magnetometer used for measuring very weak magnetic fields. Is based on Josephson junction, in which an electric current passes between two superconductors separated by a thin layer of insulator. This is due to the quantum tunneling of electron Cooper pairs across this seemingly impermeable barrier. The most commonly used superconducting material is niobium, or an alloy of lead with 10% gold or indium. The insulating layer is usually made of aluminium oxide. Two types of SQUID elements are used in low-current electronics :
- Radio frequency RF SQUID consists of one Josephson junction connected to a superconducting ring. It is used in the circuit of a high-frequency oscillator, where the measured external magnetic flux modulates the frequency of the signal ...
- Direct current DC SQUID consists of two Josephson junctions arranged in a superconducting ring. It is much more sensitive to weak magnetic fields:
The highly sensitive quantum magnetometer DC SQUID consists of a small superconducting ring interrupted by two Josephson tunnel layers (contacts). The input current I is divided into two parallel branches in the ring. The wave properties of electrons are manifested here. In the SQUID ring, the electron waves split into two, passing through the tunnel effect through the insulating layers, and then the two meet again. In the absence of an external magnetic field, the two waves meet without a phase difference. In the presence of a magnetic field, it will interact with the electric current in the ring and a phase difference will occurin the wave functions of the electrons between the two tunnel transitions. The electrons will show quantum interferences depending on the strength of the magnetic field (magnetic flux F through the SQUID ring). The current through the superconducting ring with tunnel layers then very sensitively depends on the intensity of the magnetic field (the electrical resistance of the DC SQUID shows a response even to very small changes in the magnetic field). Using a suitable electronic circuit (Fig.2.5.2 in the middle), this can be used to detect very small changes in the magnetic field.
Small note:The current I through DC SQUID is a periodic function of the magnitude of the magnetic flux F (with the period given by the elementary quantum of the magnetic flux F _o= h /2e). However, for our purposes of detecting slight changes in the magnetic field, this periodic course is not important.
Cryogenic microcalorimeters
are bolometers made up of elements of a suitable thermoelectric material that electronically register a slight increase in temperature caused by the absorption of quantum radiation in the material. The element then cools down again and is ready to detect another quantum. The smaller the working element of the microcalorimeter, the smaller its heat capacity and the faster it is enough to cool to the initial temperature - the shorter the dead detection time. Microcalorimetric detectors are therefore formed by a larger number of individual small bolometric elements - microchips FET ( field-effect transistor) or SET (single-electron tunneling transistor), or the above-mentioned highly sensitive TES bolometers. The whole system is cooled by liquid helium, additional active cooling to an operating temperature of the order of 0.1 °K is achieved by the method of adiabatic demagnetization (the most commonly used paramagnetic magnetocaloric material are gadolinium alloys).
The great advantage of microcalorimetric bolometers is their extremely wide spectral range sensitivity - in the electromagnetic field it ranges from millimeter radio waves to high-energy gamma radiation. It reacts similarly to particles of various energies. Cryogenic microcalorimeters are used experimentally to detect soft radiation b and X, and are used in some unique sensitive experiments such as energy analysis of radiation b to determine the mass of neutrinos (§1.1, part "Neutrinos"). Interesting is their use in astronomy for measuring the intensity and polarization of microwave relic radiation (see §5.4, passage "Microwave relic radiation - messenger of early space news", in the monograph "Gravity, black holes and space - time physics").

Scintillation and semiconductor gamma-spectrometry
The basic criterion for the choice of scintillation or semiconductor detection and spectrometry of gamma radiation is the required detection efficiency and especially energy resolution. Where an energy resolution of about 10% is sufficient, scintillation spectrometry is more advantageous, due to the somewhat higher detection efficiency. For accurate energy measurement and resolution of nearby gamma lines, spectrometry on a semiconductor detector with about 30 times better energy resolution, is required. These differences can be seen in §1.4 "Radionuclides", section "The most important radionuclides", on a series of radionuclide spectra measured simultaneously by a scintillation and semiconductor detector.

2.6. Detection and spectrometry of a, b, protons and neutrons. Magnetic spectrometers. Liquid scintillators.

Detection of charged particles - alpha, beta, protons - radiation
Detection and spectrometry of alpha and beta radiation is more difficult than with gamma radiation, because this radiation is less penetrating, easy to absorb and difficult to penetrate into the sensitive area of the detector. Detectors for such radiation must have very thin entrance windows, or are "windowless".
Otherwise, essentially the same types of detectors as described above are used to detect charged particles of corpuscular radiation. The simplest are ionization chambers, G.-M. or proportional detectors with appropriately adjusted thin windows (eg mica), or flow ionization detectors (without window). Scintillation detectors for radiation a and b are usually plastic (high density is not required as for radiation g) with or without a thin metal window (insulating against light) - such windowless scintillation detectors must be operated in light-tight chambers. Furthermore, the semiconductor detectors described in the previous paragraph are used, for higher energies Cherenkov detectors can also be used. The use of liquid scintillators is very common and effective, as described in more detail below in a separate paragraph.
Detection and Spectrometry of cosmic rays
Within this our category falls partly detection of cosmic rays (see §1.5, section "Cosmic radiation"), consisting primarily of high-energy protons, particles a, heavier nuclei. Secondary cosmic radiation, created by interactions in the atmosphere, also contains electrons + positrons, muons, gamma radiation, often in large sprays. However, the detection of cosmic radiation has some significant specifics, so we have already discussed it in the treatise on cosmic rays - §1.5, section "Detection and spectrometry of cosmic radiation".

Magnetic spectrometers
The most advanced instruments for accurate measurement of the energy of charged particles are magnetic spectrometers *). The magnetic spectrometer is based on the force of a magnetic field on moving charged particles. Permeating particles of charge q moving with velocity v in the magnetic field intensity (induction) B , it will be (perpendicular to the direction of movement) to act Lorentz force F = q. [v x B] , causing bending the particle pathway. When moving perpendicular to the direction of the homogeneous magnetic field B , the charged particles are acted upon by a radial Lorentz force, which is in equilibrium with the centrifugal force: B.q.v = m.v² /R. The particles will therefore move around the circle of radius R = m.v /(q.B) = Ö(2E_v .m) / (q.B) wherein p = m.v is the momentum of the particles, q charge and E_v= ¹/₂ m.v² is the kinetic particle energy. By measuring the radius R of curvature of the path of a particle of known mass and charge in a magnetic field of a given intensity B, we can determine the energy of the particle E_k . ...? ... give a formula for the relativistic case ...? ...
*) Electrostatic spectrometers
For accurate radiation spectrometry of electrons b in the field of low energies, the electrostatic spectrometers based on the curvature of the particle path in an electric field are sometimes advantageous; or combined spectrometers (e.g. an electrostatic spectrometer with a magnetic collimation).

Spectrometer with a transverse magnetic field
Magnetic spectrometer with transverse magnetic field is formed by a strong electromagnet, between whose pole pieces forming an almost homogeneous magnetic field *), a vacuum measuring chamber is placed. Particles fly into the chamber through the inlet orifice, move along a path curved in a magnetic field and fall through another orifice onto the detector, where they are registered by conversion into electrical impulses - Fig.2.6.1. This detector does not have to have spectrometric properties - the spectrometry is "taken care of" by the magnetic field + geometric arrangement. Only good detection efficiency is required for the analyzed charged particles in a sufficiently wide range of energies.
*) Focusing: To achieve better detection efficiency, or "luminosity" of the spectrometer, special shapes of pole pieces are sometimes used, creating in the main homogeneous magnetic field certain additional gradients causing, by effect of a magnetic lens, to focus an otherwise diverging beam of charged particles...
For a given geometric configuration of the input window, apertures and detector and a certain specific value of magnetic induction B, only particles of a certain energy E_k = E_foc can fall into the detector, which is curved in the magnetic field so that it "hits" the detector location of position R_foc. By increasing the excitation current I in winding the electromagnet, we increase the magnetic induction B and thus the energy of the particles that selectively impinge on the detector and are registered.

Fig.2.6.1. Schematic representation of the operation of a magnetic spectrometer with a transverse magnetic field (left) and a longitudinal magnetic field (middle). On the right is the use of a magnetic spectrometer for gamma radiation spectrometry.

Each value of current I through the coil of the electromagnet thus corresponds to a certain energy E_kof charged particles, which will be registered in the detector. The magnetic spectrometer operates cyclically in a dynamic mode, during which the current I in the electromagnet increases continuously, while the pulses from the detector are registered. Particles of different energies gradually fall into the detector, depending on the instantaneous intensity of the magnetic field. In the next cycle, the electric current increases again from zero to the set maximum value. If we plot the appropriate calibration multiple of the square root current ÖI on the horizontal axis and the registered number of pulses for each value I on the vertical axis, we obtain a graph of the energy distribution of the measured charged particles, ie. the energy spectrum of corpuscular radiation. Magnetic spectrometers have a very good resolution, usually better than 1%, but their detection efficiency is relatively low (the energy resolution and "luminosity" of the spatial detection angle compete with each other).

Magnetic lens spectrometers
In addition to transverse magnetic field spectrometers, smaller longitudinal magnetic field spectrometers are also used, especially for radiation spectrometry b. The focusing effects of the axial magnetic field are used here, which, according to the laws of electron optics, create an image of the source similar to a converging lens. The principle of operation of such a spectrometer is shown in Fig.2.6.1 in the middle. The spectrometer consists of a coil *) through which a current I passes and excites in the vacuum chamber inside the coil a longitudinal magnetic field with a vector B directed along the axis of the coil. Source of analyzed radiation, eg radiation b, is located on the axis of the magnetic field. Particles (electrons) emitted by this source in the direction of the coil at an angle J to the axis, move under the influence of magnetic forces for spatial spiral paths whose projection into a plane perpendicular to the axis is a circle with radius of curvature R = (m.v.sin J) /(q.B), and are focused to one point on the axis, which is from the source at a distance F = (2p.p/q.B) .cos J, where p = m.v is the momentum of the particle. At a constant angle J, which is defined by the aperture of the spectrometer, we can focus particles with different momentum and thus different energy by focusing the magnetic field B to one point on the coil axis and register particles of respective energies with a detector located at this point on the coil axis. Thus, depending on the current I through the coil winding, the particles passing through the annular orifices are focused to the location of the detector according to their energies - this dependence, after appropriate calibration, creates an energy spectrum.
*) It is either a long coil - a solenoid, creating a homogeneous magnetic field inside, or a short coil, creating an inhomogeneous axially symmetric magnetic field, limited to a short space between the source of measured radiation and the detector. If current I flows a coil with n turns, for particles with momentum p and charge q, this coil behaves in the direction of its axis as a magnetic lens with a focal length f = k.(p /q.n.I)², where the coefficient k depends on the dimensions and construction of the coil.

Mass spectrometers and separators
Mass spectrometers and separators used in physical chemistry and radiochemistry also work in a similar arrangement as the charged particle magnetic spectrometer according to Fig. 2.6.1 on the left. The analyte is ionized in an ionization tube, the formed cations are accelerated by an electric field, and ions with a constant velocity v are selected in a velocity filter (consisting of, for example, a crossed electric and magnetic field). These then fly through the entrance slit into the magnetic field, in which they describe a circle of radius R = (v/e.B).m, proportional to the mass m . Ions of different masses describe different paths and thus fall on different places of the base - so the device separates from each other ions of different masses (given by the weight of the nucleus). By changing the magnetic field, ions of corresponding masses are gradually focused into the detector - a mass spectrum is created .
In the mass separator, instead of the detector, a suitable target is installed on the base, on which the incident ions of the selected mass are absorbed. This method allows isotopic enrichment of the target, or the creation of an isotopically pure preparation, but only in small amounts.

Magnetic gamma spectrometers
An important use of magnetic spectrometers is also for accurate gamma spectrometry. A thin foil called a radiator (not very apt name, a converter would be better...) is placed in the input window of the magnetic spectrometer, from which the incident photons g eject electrons, whose energy is measured from the curvature of the path in a magnetic field, as with a magnetic beta spectrometer (Fig.2.6.1 right). If the radiator is made of a substance with a low atomic number, the secondary electrons are generated mainly by Compton scattering, in the case of using a heavy substance (lead, tungsten) the secondary electrons will be produced mainly by a photoeffect (at lower energies of quantum gamma). High-energy gamma radiation (Eg > 1.02 MeV) also produces electron-positron pairs; in this case, paired gamma spectrometry can be used by simultaneously measuring the energy of electrons and positrons using two detectors located on opposite sides of the base.

Magnetic spectrometers have played a very important role in the accurate measurement of the spectra of b, g, a, protons, conversion and Auger electrons in radioactivity and nuclear reactions; they thus contributed to the specification of physical ideas about the structure of atomic nuclei as well as about the interactions of elementary particles. Most of the data in the nuclear tables (eg in the detailed tables of isotopes from Lederer, Hollander, Perlman) were obtained by measurements using magnetic spectrometers.

Spectrometric analysis of radiation b
While the analysis of radiation spectra g, containing clearly expressed photopeaks of discrete energy lines, is in principle relatively easy, the analysis of radiation spectra b is quite difficult. On the appearance of the continuous spectrum of radiation b, we often do not even know visually whether the radiation belongs to one maximum energy, or is composed of several groups of radiation. The so-called Fermi-Kurie graphs are sometimes used for detailed spectrometric analysis of radiation b.
The exact shape of the curve of the radiation spectrum b follows from the analysis of the energy distribution of the emitted electrons within Fermi's theory of weak interaction. It follows from this theory that the intensity N(p) of radiation b on momentum p a energy E_b is given by N(p) = (E_b_max-E_b)².p².F(Z,p), where E_b_max is the maximum decay energy b and the constant F in itself includes the relevant constants, including the proton number Z. From this relation, for the spectrum b follows the equation E_b_max-E_b = Ö[N(p)/p².F(Z,p)]. If we plot the function Ö[N(p)/p².F(Z,p)] on the vertical axis depending on the energy E_b on the horizontal axis, we get a linear dependence called the Fermi-Kurie graph. It is a descending line that intersects the horizontal (energy) axis at the point indicating the maximum decay energy b. If the studied radiation b is composed of two or more energy groups, we get a graph composed of two or more linear segments. By interpolating and extrapolating these linear segments, we can determine the energies and relative intensities of individual groups of radiation b. Analyzes of this kind can now be performed by computer using special spectrometric software.

Magnetic "cyclotron" radio-frequency spectrometry
The spectra of low-energy beta radiation can in principle be measured using coherent so-called cyclotron radiation emitted by individual electrons b in a spiral motion in a magnetic field. The evacuated detection chamber, located in a strong homogeneous magnetic field, is equipped with microwave antennas that register this "cyclotron" radiation and the electronic apparatus evaluates its frequency. In the classical approach the Larmor frequency f cyclotron radiation f = e.B /(2p.m_e) with the electron charge e and rest mass m_e is given only by the intensity of the magnetic field B and does not depend on the velocity v the electron, and thus on its kinetic energy E _b. However, due to the effects of the special theory of relativity, in reality the Larmor frequency will slightly depend on the velocity of the electron v and thus on its kinetic energy E_b: f = [e.B/2p.m_e] .Ö(1-v²/c²) = (e.B/2pm_e)/[1+E_b/(m_e.c²)]. By accurately measuring the frequency, we can determine the energy of the electron - perform beta spectrometry. For a 1T magnetic field, the emitted radiation will have a frequency of around 27GHz.
This method is not suitable for higher electron energies in the relativistic region, because cyclotron radiation changes into synchrotron radiation , which has a continuous spectrum and no longer carries direct information about the energy of the electron. The origin and properties of cyclotron and synchrotron radiation are briefly discussed in §1.6, section "Interaction of charged particles", passage "Cyclotron and synchrotron radiation".
This method is not yet standard used. The prototype of this detector was assembled in 2009-2012 by J.A.Formaggio and B.Monreal.

Detection of beta radiation by liquid scintillators
The difficulties encountered in detecting beta radiation on the detector side, mainly associated with radiation absorption, were mentioned above. However, even bigger problems occur on the side of the measured sample! Significant (self) absorption of beta radiation occurs directly in the sample itself - beta electrons from the inner parts of the sample usually do not penetrate out at all, this radiation also does not penetrate trought any packaging of the radioactive sample (e.g. a vials). To measure beta radiation from such samples, it is necessary to make a relatively damanding treatment of the sample into a very thin layer (evaporated) and then try to measure it in a geometry of 2p using window GM tubes or plastic scintillators.
Accurate activity measurement b-radioactive preparation, especially low-energy beta radiation, is therefore not possible (due to the absorption of beta radiation in the sample itself) even with the use of very perfect radiation detectors b. However, there is an interesting and well-functioning method of accurately and with high efficiency (approaching even 100%) to detect the radiation of b- radioactive preparations: it is a method of liquid scintillators.
A liquid scintillator is a substance in the liquid state which, upon interaction with ionizing radiation, converts part of the absorbed energy into flashes of light (scintillation), similar to the solid state scintillators described above. These are suitable cyclic hydrocarbons in organic solvents (specific compositions and properties of some types of liquid scintillators will be given below). The use of liquid scintillators for measuring beta-radioactive samples is as follows (Fig.2.6.2) :

Fig.2.6.2. Left: Schematic representation of the principle of beta radiation detection by a liquid scintillator. Right: Mark II instrument (Nuclear Chicago) with a sample exchanger for measuring beta-samples in a liquid scintillator (at Department of Nuclear medicine in Ostrava).

In principle, one photomultiplier would be sufficient to capture light flashes from a liquid scintillator. The reason for using two photomultipliers in a coincidence circuit according to Fig.2.6.2 is, in addition to increasing the detection efficiency, to suppress unwanted impulses coming from photomultiplier noise and chemiluminescence. Some chemical reactions between the sample material and the scintillator can lead to light emission - chemiluminescence (see below), which in the photomultiplier produces false pulses not originating in the detected beta radiation. In contrast to scintillation, chemiluminescence is characterized by the fact that only one photon (or a few photons) is emitted in one act, while true scintillation is a flash of several hundred or a thousand photons. Therefore, if we use two photomultipliers according to Fig.2.6.2 to detect light from a liquid scintillator, then noises and photons from chemiluminescence always generate an impulse independently in only one of the photomultipliers, while from a large number of simultaneously emitted photons during true scintillation, a certain part always falls into both photomultipliers at the same time. Thus, at the output of the coincidence circuit, we receive pulses only when beta-induced scintillation is detected, while noise and chemiluminescent pulses are not transmitted. This suppression of unwanted pulses is particularly important when measuring tritium samples, where the noise pulses from the photomultiplier have an amplitude comparable to the signal pulses coming from the detection of low-energy beta radiation from 3H.
When measuring low-energy radiation b in liquid scintillators, we encounter the problem of a small number of emitted photons, which can be only tens of photons per scintillation. Therefore, high demands are placed on the properties of photomultipliers - high quantum efficiency of the photocathode for a given spectral range (see below for spectrum shifters), low noise (in co-production with coincident photomultiplier connection), good optical contact of photomultipliers with scintillator (incl. reflectors), also low absorption of radiation in the scintillator itself.
The entire detection system with photomultipliers is of course enclosed in a light-tight shielded box, where the cuvette with the measured sample, mixed with the liquid scintillator, is lowered through a light curtain by means of an elevator and is extended back after the measurement has taken place. Laboratory instruments of this type for measuring series of a larger number of samples are equipped with an electro-mechanical system of a sample transducer with a capacity of several tens to hundreds of vials, which gradually inserts individual cuvettes, after a preset measuring time extends, moves and inserts another vial (Fig.2.6.2 right - the principle is similar to the one below in Fig.2.7.3 on the left ). Some devices have the entire space of the detection system and the sample converter tank cooled to a temperature of about 4 °C, which contributes to the reduction of noise, chemiluminescence and possibly evaporation of samples.
In Fig.2.6.2 on the right is the deviceMark II (Nuclear Chicago) with a cooled sample exchanger for measuring beta samples in a liquid scintillator. For many years (1974-1990), we have successfully used this state-of-the-art instrument at our nuclear medicine department in Ostrava to measure b- radioactive samples of radiocarbon ¹⁴C, tritium ³H, ³²P and others. It was later replaced by a newer RackBeta (LKB) device.
Measurement of beta-radioactive samples using Cherenkov radiation
We present this possibility as rather of curiosity. If the radionuclide in the measured sample emits beta radiation of sufficiently high energy (higher than about 300keV for water samples), we can use the described instruments according to Fig.2.6.2 in principle to measure without the use of liquid scintillator - using the emission of Cherenkov radiation (§1.6., passage "Cherenkov radiation") in the sample material. It is applicable, for example, to ³²P or yttrium ⁹⁰Y samples. The conversion efficiency of Cherenkov radiation production is significantly lower than for scintillation radiation, so the method is not suitable for samples of very low activities.

Use of liquid scintillators for the detection of external radiation
In addition to the internal measurement of radioactive samples mixed directly into the scintillator described above, the liquid scintillators can in some cases also be used for the detection of external radiation. We simply pour the liquid scintillator into a container of suitable shape and size, so that we can obtain a detector of a size not achievable with solid (crystalline) scintillators; they are therefore used, for example, in the detection of cosmic rays or neutrinos (.....).
Make the invisible visible
At our department, we used a liquid scintillator (in a very unconventional way) for mapping and visualization of irradiation beams - electron, photon, proton - used in radiotherapy. We filled a glass measuring cylinder with a diameter of 6 cm and a height of 44 cm with 1 liter of liquid scintillator (we used a dioxane scintillator with a density of 0.95 g/ml) and placed it under the irradiation head of the appropriate accelerator - electron, photon CyberKnife, proton. From the side, we observed and photographed the scintillation radiation generated in the scintillator along the passage of the irradiation beam - Fig.2.6.3 :

Fig.2.6.3 Scintillation radiation generated in a cylinder (diameter 6 cm and height 44 cm) filled with a liquid scintillator during irradiation with electron, photon and proton radiation beams.
a), b): A cylindrical phantom filled with a liquid scintillator was irradiated with a wide electron beam of 6 MeV and 18 MeV from a linear accelerator.
c), d): When irradiating the same phantom with a beam of photon radiation - max. energy 6MeV, beam with a diameter of 1.5 cm and 3.5 cm - they form secondary electrons along g beam scintillation radiation - with a deep decrease in intensity as the primary photon beam attenuates as it passes through the liquid.
e), f), g): When irradiated with narrow ("pencil beam") proton beams of energy 100, 170 and 226 MeV, the protons penetrate to different depths depending on the energy, with a significant Bragg maximum.

Liquid scintillators - composition and properties
The liquid scintillator consists of two main components: the solvent and the scintillator itself dissolved in it . The most commonly used solvents are toluene and 1,4-dioxane. The actual scintillator is some organic compound characterized by fluorescence. In particular, 2,5-diphenyl 1,3-oxazole (PPO) and 1,3,4-oxadiazole (PBD) are used in concentrations of about 5 g/liter, and naphthalene in dioxane-based scintillators.
The energy of the beta radiation is first transmitted to the solvent molecules. The excitation energy of these molecules is then transferred to the molecules of the scintillator itself, which emit photons of visible light during deexcitation. However, the spectrum of this emitted light is distributed in the region of shorter wavelengths than the maximum spectral sensitivity of the photocathode of conventional photomultipliers. To increase the detection efficiency, therefore, a spectrum shifter *) is added to the scintillation solution, the molecules of which absorb the primary energy of the scintillation and emit subsequent light photons of lower energy, corresponding to the spectral region of maximum photomultiplier sensitivity. The most commonly used spectrum shifter is 1,4-bis- (5-p-tolyl-2-oxazolyl) -benzene (POPOP) and its modifications, in concentrations of tenths of grams/liter.
*) The spectrum shifter also provides another positive effect. In one-component scintillators, the optical emission and absorption spectra are identical, so that the radiated scintillation photons in the surrounding scintillator molecules self - absorb back . The scintillator is thus not very transparent for the emitted scintillation photons, from a greater depth many photons do not penetrate the photomultiplier. This reduces the conversion efficiency of the scintillator. The addition of a spectrum shifter leads to the absorption of the original scintillation energy and the emission of lower energy photons, for which the environment of the organic scintillator is already well transparent.
For better miscibility of the solvent and the sample, secondary solvents, tissue solubilizers, are sometimes added to the scintillation solution or gelling agents. A dioxane scintillator that is up to about 10% miscible with water is suitable for measuring samples in aqueous solutions. Sometimes different heterogeneous mixtures of liquid scintillator and measured sample are also used. E.g. the microfilter film with the captured beta sample soaks up when immersed in the scintillator and becomes transparent, so that the resulting scintillations can also be measured similarly to a conventional homogeneous arrangement. In all these non-standard methods, due to the geometry of measurement, absorption and increased quenching, the detection efficiency is significantly lower than in homogeneous unquenched samples, but in many cases it is fully sufficient and is sometimes the only applicable method.

Quenching and chemiluminescence
Based on the principle of detection by liquid scintillators, it can be expected that practically every electron b emitted by the measured sample inside the scintillator (except for a thin layer at the surface and walls of the measuring cuvette) will cause scintillation and be registered - this is true "4p -geometry", detection efficiency should be close to 100% *). However, there are two adverse events that can reduce detection efficiency, increase background, and overall impair the accuracy and reproducibility of liquid scintillator sample measurements: quenching and chemiluminescence.
*) Radiation spectrum b it is continuous and contains a significant proportion of low-energy particles (the rest is carried away by neutrinos - §1.2), whose scintillations cause low signal pulses of the same magnitude in the photomultiplier as the noise pulses generated by the thermoemission of the photocathode. These pulses then do not pass through the lower discriminatory level of the analyzer - a certain initial part of the spectrum is therefore often lost for detection. Therefore, for soft beta radiation from ³H, it is generally not possible to achieve a better detection efficiency than 50% in practice.
Quenching
A side effect of mixing the measured sample into the scintillator is a series of chemical reactions that can cause a reduction in the light yield (conversion efficiency) of the scintillator and thus a corresponding reduction in the amplitude of the pulses from the photomultiplier. These reduced pulses may fall outside the discriminant levels on the analyzer and are not registered. This phenomenon is called quenching. We distinguish two types of quenching, which usually occur in the samples at the same time :
Chemical quenching is caused by the fact that the molecules or atoms of the measured sample, by their chemical action, partially prevent the transfer of excitation energy between the molecules of the solvent and the scintillator, so that only weaker scintillation occurs.
Color quenching then it causes part of the photons emitted during scintillation to be absorbed by the substances contained in the sample. The designation "colored" refers to the fact that these non-fluorescent substances have a discrete absorption spectrum and absorb photons in a certain energy (= color) range.
Some chlorinated hydrocarbons, such as chloroform or tetrachloro CCl₄, peroxides, as well as water and oxygen dissolved in the scintillator, have strong quenching effects .
The consequence of quenching is that two samples containing the same activity, but showing different quenching, give different numbers of pulses.
Quenching correction
Because quenching can vary the detection efficiency differently for different samples, quenching correction is required for accurate and reproducible measurements. The quenching correction is based on the analysis of the measured radiation spectrum b in the amplitude analyzer. In Fig.2.6.2 on in the middle, the radiation spectra b of the same radionuclide (eg ¹⁴C) measured by a liquid scintillator at low quench and at high quench are plotted. Extinguishing significantly affects the shape of the spectrum b - the spectrum shortens and shifts to lower energies. Thus, by analyzing the shape of the spectrum, we can determine the degree of quenching. The analysis of the shape of the spectrum is simply performed here by determining the ratio of the number of pulses in the two analyzer windows suitably set to the spectrum b. Calibration or standardization is required to correct for quenching. We will prepare several identical samples of the given radionuclide b in a liquid scintillator. Gradually add an increasing amount of quencher (eg chloroform) to each of them and perform their spectrometric analysis on the instrument according to Fig.2.6.2. The ratio of the number of pulses in two suitable windows of the amplitude analyzer is plotted on the horizontal axis, on the vertical axis efficiency (all samples have the same activity). This gives the so-called quenching curve (usually in the form of a parabola or hyperbola), which can then be used to correct for quenching in unknown measured samples: from the ratio of the number of pulses in the two analyzer windows on the quenching curve we determine the correction coefficient by which we must multiply the measured number of pulses to compensate for loss by quenching. This is the so-called internal standardization of quenching.
Some devices also have a built-in so-called external quenching standardization. It consists in that the measured sample with a liquid scintillator, inserted in the measuring position between the photomultipliers, is irradiated for a moment with gamma radiation from an external source and the correction coefficient is determined by analyzing the shape of the spectrum thus obtained (ratio of two parts of the spectrum). The external standard uses radionuclides (mixed emitters b+ g or a + g ) ¹³⁷Cs, ¹³³Ba, ²⁴¹Am, ²²⁶Ra, sometimes a pair of radionuclides, with an activity of tens of kBq. The external standard is placed in a lead shield, from where is automatically extended into close of the measuring cuvette with a liquid scintillator, and pushed back again after standardization.
Chemiluminescence
Chemiluminescence is an event in which light is emitted as a result of chemical reactions. Some chemical reactions between the sample material and the scintillator can lead to this chemiluminescence, which in the photomultiplier produces spurious pulses not originating in the detected beta radiation. Fortunately, however, chemiluminescence is limited in time and expires exponentially within about 30 minutes of placing the finished samples in the sample exchanger container, where they are not exposed to light.

Neutron detection
Because neutrons have no electrical charge and can not themselves directly ionize the electron shells of atoms, for their detection is necessary to use the processes of interaction which produce secondary charged particles which already have an ionization effect, and can be detected. The following methods are mainly used for neutron detection :

In principle, neutrons can be detected using conventional g or charged particle detectors (b, a, p), event. provided with a suitable converting material. This converting material absorbs neutrons, creating secondary radiation that can already be easily detected. For slow neutrons, layers containing lithium ⁶Li or boron ¹⁰B are often used, in which neutrons are converted into charged particles and g. For fast neutrons, for example, a polyethylene film is suitable, from which fast protons are emitted by interaction. In general, it should be noted that the layer of converting material is depleted during interactions. Another negative phenomenon in neutron detection may be internal radioactive contamination of detector materials, induced by nuclear reactions with neutrons inside the detector (see §2.1, section "Nuclear reactions and induced radioactivity inside detectors").
Neutron spectrometry
Energy measurement, or neutron spectrometry, is more difficult than with gamma or beta radiation. To measure the spectrum of slow neutrons, so-called mechanical selector is used. They consist of two disks made of a highly neutron-absorbing matter (cadmium) mounted on a rotating shaft. The discs have a series of identical radial slots around the circumference, the position of which is shifted at the second disc by a very small angle relative to the first disc. The measured neutron beam passes parallel to the shaft axis through the slit of the first disk and is absorbed by the second disk, except for those neutrons whose velocity is such that they reach the second disk at a time when they can pass freely through the shifted slit of the second disk. For a given shaft speed, disk distance and angular displacement, neutrons are only transmitted in a narrow speed range. By changing the speed of the shaft speed, neutrons of different speeds are gradually transmitted, their count rate is measured by a neutron detector and thus their velocity spectrum is measured, from which the energy spectrum is derived. In this way, the spectra of only slow neutrons, of the order of eV, can be measured.
The spectrum of slightly faster neutrons can be measured by their Bragg scattering on the crystal lattice. Due to corpuscular-wave dualism, the neutron of mass m_n and kinetic energy E behaves as a wave of wavelength l = h/(2m_nE)^1/2. For slow neutrons, the wavelength corresponds to the order of magnitude of the distance of the atoms in the crystals. On such a grating, neutrons can be scattered by Bragg reflection (similar to X-rays): neutrons of only one energy are reflected to a certain angle between the plane of the lattice and the direction of the incident beam. By continuously changing the angle between the neutron beam and the crystal on the goniometer, the measured frequencies in the neutron detector give us an angular distribution curve from which the spectrum is determined. Crystal neutron spectrometers are suitable for energies in the range of about 0.1-100 eV.
To measure fast neutron spectra, reflected protons can be used, whose energy is measured by a proportional or scintillation detector, event. by measuring the length of the proton trace in the nuclear emulsion. It is also possible to use the already mentioned scintillation detector ⁶LiI (Eu), where neutrons in the reaction (n, a) transfer to the scintillator released energy 4.78MeV + energy of the arriving neutron, which can be determined by amplitude analysis of output pulses from a photomultiplier with a resolution of about 10% (at an energy of 5MeV).

2.7. Measurement of radioactivity of samples (in vitro)
One of the most common types of radiation measurements is the measurement of radioactivity of samples - whether they are samples in medicine and biology, samples from the environment, or samples taken from various places in industrial systems. The specific methodology for measuring the radioactivity of samples depends on several circumstances - the type and energy of radiation, the activity of samples, the size and shape of samples, the required accuracy, whether it is a relative or absolute measurement, etc. The questions of the choice of detectors according to the type of radiation were discussed above in §2.1-2.6, the most frequently used detectors for gamma-samples in the passage "Scintillation probes", Fig.2.4.3. Here we will mention some practical aspects of measurement geometry, on specific methods for measuring series of samples and radiochromatographic methods for analyzing samples.

Measurement geometry - 2 p , 4 p
The overall measurement efficiency is given not only by the detector's own detection efficiency, but also by the mutual arrangement of the measured sample and the detector - the so-called measurement geometry. By measurement geometry we generally understand all aspects of the spatial relationship and configuration of the measured sample or beam of radiation with respect to the detector. Fig. 2.7.1 shows typical geometric configurations when measuring samples using gamma radiation :

Fig.2.7.1. Geometry of sample measurement. Planar detector for geometry max. 2p and two types of well scintillation detectors for measuring the activity of samples in geometry close to 4p .

¨ Geometry 2p
The simplest configuration arises when the measured sample is simply placed tightly to the detector (Fig.2.7.1 on the left). If we neglect the absorption and the effect of the final size of the sample and the detector, ideally all radiation is detected that from the sample is directed to the half-plane in which the detector is located, ie half of all radiation emitted by the sample - we say that we measure in geometry 2p (full spatial the 360° angle expressed in radians is 4p, its half 180° then 2p). The total detection efficiency for the attached sample here can reach a maximum of 50%. Detectors for this type of measurement are sometimes referred to as planar.
¨ Geometry less than 2p
If the sample is placed at a greater distance from the detector, it is a measurement at a spatial angle w < 2p, with a correspondingly lower detection efficiency (0-50%).
¨ 4p geometry
If we want to increase the detection efficiency and measure all radiation emitted by the sample to a full spatial angle of 360° - ie in 4p geometry, we use the so-called well detector (see Fig.2.4.3b in §2.4, passage "Scintillation probes") in the arrangement shown in the middle and right part of Fig.2.7.1. A well detector for measuring higher activities in the design of the ionization chamber is shown in Fig.2.3.3 on the right in §2.3 dedicated to ionization detectors. However, for sensitive measurements of low activities sample, well scintillation detectors are used with a hole drilled in the crystal either longitudinally to a certain depth (middle part of Fig.2.7.1 - well crystal), or with a hole drilled transversely through the whole crystal (Fig.2.7.1 on the right). The vial with the measured sample is inserted into this hole, so that almost all the radiation emitted by the sample (except the narrow cone in the direction of the hole) must pass through the sensitive volume of the detector and can be detected - a geometry close to 4p. In the 4p geometry, the detection efficiency can theoretically approach up to 100%, in practice it reaches approx. 80-90% for well scintillation detectors.
Note: The real 4p -geometry is the above measurement of beta samples dissolved in a liquid scintillator, where we can sometimes approach up to 100% efficiency ("Detection of beta radiation by liquid scintillators").

Detection efficiency
The most important parameter at the measurement of radioactive samples is the detection efficiency of the measurement - the ratio between the measured number of pulses in the detector and the number of radiation quantum emitted by the sample during radioactive transformations. The general detection efficiency of a radiometer depends on a number of physical factors of the interaction of radiation with the detector material, absorption and geometric conditions - it was discussed above in the section "Detection efficiency and sensitivity". There are some specific influences and circumstances in the measurement of samples, which we will mention here.
Positional and volume dependence of the detection efficiency
When measuring radioactive samples, the detection efficiency depends crucially primarily on the geometric configuration of the sample relative to the detector. Each sample emits radiation isotropically in all directions *), but only a certain part of this radiation enters the sensitive volume of the detector and can be registered. In the basic geometry of the planar detector according to Fig.2.7.1 on the left, the detection efficiency depends mainly on the distance of the sample from the detector - it decreases approximately with the square of the distance, reaching the highest values (but max. 50%) close to the detector, as discussed above.
*)Angular (directional) correlations of gamma photons
For some radionuclides, in one and the same transformation event cascaded emits two or more gamma quanta occurs. In such a case, angular correlations may occur between the emission direction of these photons (see §1.2, section "Gamma radioactivity", section "Angular (directional) correlations of gamma radiation"). This relative "anisotropy" can have some effect on the geometric dependence detection efficiency. If the sample is close to the detector, the effect of angular correlation is averaged over a wide range of angles (close to 180°) and is practically not manifested. If the sample is at a greater distance from the detector, the detection angle is smaller and the effect of angular correlation on the different efficiency of gamma photon detection from cascade deexcitation is slightly increased. In some accurate measurements, even this small dependence is corrected.
With a well detector, the highest detection efficiency is when the small sample lies at the "bottom" of the well detector - then most of the radiation passes through the sensitive volume of the detector and the smallest part comes out in the cone through the hole without registration. The higher the sample is placed in the well hole, the more radiation comes out "useless" - the well detector has a significant positional dependence of the detection efficiency. Closely related to this position dependence is the volume dependence of the detection efficiency: the larger the volume of the sample in the vial inserted into the hole of the well detector, the larger part of the sample is near the hole, where the detection efficiency is lower - Fig.2.7.2 left. The self-absorption of radiation in the sample also contributes to the volume dependence of the detection efficiency.
In addition to geometric influences, the detection efficiency can also be reduced by radiation absorption, both in the sample itself (self-absorption) and in the input window of the detector. When measuring samples, different glass thicknesses of test tubes and ampoules can also have an effect, especially when measuring low-energy gamma radiation (eg for ¹²⁵I the plastic test-tubes are recommended here).

Fig.2.7.2. Left: Volume dependence of the detection efficiency of a well scintillation detector. Right: Positional dependence of the photopeak on the location of the sample in a well of scintillation detector.

Positional dependence of the photopeak in a well scintillation detector
In well scintillation detectors, we encounter an strange typical phenomenon: the broadening or doubling of the photopeak and the dependence of its position on the location of the sample inside the well. Gamma radiation from a sample placed inside a well passes through two areas of the scintillator :
1. Bottom of well - usually a smaller portion of gamma-photons passes through the well bottom, but scintillations from this area of the scintillator, closest to the photomultiplier photocathode, are registered with higher efficiency, ie with higher amplitude output pulses.
2. The walls of the well passes the larger part of gamma photons, wherein the scintillations from those regions farther away from the photocathode being registered with less efficiency, i.e. with a lower amplitude of the output pulses.
In the resulting spectrum, the photopeak consists of two parts. The main, dominant peak of the photopeak, shifted to the left to lower amplitudes (energies), corresponds to the majority detection of gamma radiation in the massive side walls of the well crystal. Right (descending) part photopeak is towards higher energies expanded a sort of bump - "second photopeak", corresponding to the detection of a smaller fraction of gamma radiation passing through the bottom of the well crystal - Fig.2.7.2 on the right. This effect is most pronounced for a point source located at the bottom of the well, where a significant part of the radiation passes through the bottom of the well (a partial photopeak shifted to the right - resulting in a "double photopeak"); for higher positions of the source in the well, the effect diminishes and ceases to be noticeable, with large-volume samples or sources outside the wells, we see only one overall extended photopeak.
This complex geometric situation during detection at different locations of the scintillation crystal leads to a worsened energy resolution of the well detectors compared to planar detectors (the effects affecting the resolution were analyzed above in the section "Photopeak - energy resolution of a scintillation detector"). For large-volume well detectors (as in Fig. 2.7.2 on the right), the energy resolution is around 17%.
Spectrometric setting of detection apparatus
On the detection efficiency has a significant influence also spectrometric setting of detection device. The highest detection efficiency would formally achieved in integral mode when we measure all impulses coming from the detector. We cannot use the integral mode if we want to distinguish more radionuclides with different energies in the measured samples - then we have to use differential measurement with the analyzer window set to the photopeak of the required gamma radiation. However, even when the samples contain only one type of radionuclide, photopeak measurement is advantageous because we achieve the best signal/background ratio, which is especially important when measuring samples with low activities, background-comparable. For accurate measurements of the content of radionuclides in samples, mostly calibrated semiconductor detectors with a multichannel analyzer are used, on which careful spectrometric analysis is performed measured gamma photopeaks.

Measuring series of samples
Measuring large series of samples, numbering tens, hundreds or thousands of samples, would be very laborious and time-consuming when measured manually with one detector. Therefore, special instruments are used that allow automatic measurement of series of samples - sample changers and multi-detector instruments.

Automatic sample changers
Sample changers, often also called gamma automates (usually gamma radiation are measured *), are detection apparatus equipped with an electro-mechanical device for exchanging samples. Prior to measurement, the samples we they stack in a tray (cartridge) with a capacity of about 100-500 samples, which has either a chain or cassette arrangement. The electro-mechanical drive unit uses an small electric motor to move the individual samples to the location of the detector, where a motor-operated elevator inserts the given sample into the cavity of the well or drilled detector. The measurement is then performed for a preset time, the measured number of pulses is registered (printed out, sent to computer), the elevator extends the sample, the next sample moves and another measurement takes place - Fig.2.7.3 on the left.
*) The same principle of electro-mechanical displacement of samples in the cartridge is used by sample changers for measuring beta radiation in liquid scintillators.

Fig.2.7.3. Measurement of larger series of samples. Left: Gamma-automat with electromechanical sample changer. Right: 20-detector gamma sample meter.

Multi-detector systems
Sampler changers with one detector allow automatic measurement without the need for manual manipulation, but measuring large series of samples is time consuming - the total measurement time N samples is T = N.(t + t_m), where t is the average measurement time of one sample and t_m is the sample exchange handling time. E.g. the measurement of 300 samples with a measuring time of 100 s. takes about 8.5 hours. With such a long time (sometimes measured overnight), there is also a certain risk of power failure, instability or other malfunction.
The most powerful and fastest instruments for measuring large series of samples are multi-detector systems. They consist of 10, 12, 16 or 20 independent well scintillation detectors placed right next to each other, possibly in two rows (Fig.2.7.3 on the right). Each scintillation detector has its own photomultiplier, usually firmly connected to a crystal in a so-called scintiblock. The samples are stored in trays (casets), which fit exactly into the holes of the detectors. After the insertion of such a set of samples, the measurement of each of them takes place simultaneously (but independently) in well scintillation detectors, the measured pulses being registered in the memory of the instrument. At the end of the measuring time, insert the container with another set of samples, etc. The above example of measuring 300 samples after 100 s. takes only less than 30 minutes here when using a 20-detector device!
In addition to the high measurement speed of large series of samples, the great advantage of multi-detector instruments is that they have no mechanical parts (they are purely electronic), so they do not require maintenance and have a minimum failure rate.
The basic requirement for multi-detector instruments is the same detection efficiency of all detectors - the result must not depend on which detector the sample was measured. This is achieved by careful selection of scintillation crystals and photomultipliers, the remaining differences are compensated by numerical correction of detection efficiency - results from detectors with slightly reduced sensitivity are multiplied by an appropriate correction factor greater than 1, pulse counts from detectors with increased efficiency by a factor of less than 1. The matrix of correction coefficients is obtained by either measuring one sample sequentially on all detectors and calculating the respective ratios to the mean value, or by measuring a set of samples - standards - with the same activity. The correction factor for each detector is then stored in the instrument's memory and the measured pulse counts are automatically corrected.
Another requirement for multi-detector measurement is that radiation from a sample inserted in one detector does not penetrate to the surrounding detectors and does not affect the measurement results. Due to the low energies of gamma radiation (devices of this type are most often used for ¹²⁵I), this radiation is prevented by the lead shielding in which the individual detectors are embedded. For higher energies, where panetration can be actually applied, the devices are equipped with radiation penetration correction: the numbers of pulses registered in the other (surrounding) detectors, multiplied by certain weight transmission factors, are subtracted from the measured number of pulses in the given detector . The matrix of these transmission factors is obtained by measuring the sample of a given radionuclide gradually in individual detectors, registering not only the number of pulses in the detector, but also the response of other (empty) detectors and dividing it by the number of pulses in the detector. The obtained factors are again stored in the device's memory and the correction takes place automatically during the measurement.
Hybrid sample changers
In addition to single-detector sample changers and multi-detector systems, sample changers with several detectors - approx. 3-5 detectors - are also rarely used. The electro-mechanical device gradually moves the sample cartridges and the elevators periodically insert 3-5 samples into the detectors for the duration of the measurement. These instruments, sometimes called "hybrid" instruments, measure faster than single-detector sample transducers (as many times faster as there are detectors), but generally do not achieve the performance of multi-detector systems and are mechanically very complicated...

The category "Measurement of radioactive samples" can also include two complex chemical-analytical methods using ionizing radiation - radiochromatography and radioelectrophoresis. We will describe here both these methods in terms of physico-chemical principles and laboratory procedures, as well as radiodetection measurement of the obtained distribution of analyzed radioactive substances.

Radiochromatography
Chromatography
is a physico-chemical separation method that spatially separates the molecules of the analyte from each other on the basis of their different mobility in the carrier media. This is due to their different physical or chemical properties, especially sizes - molecular weights and shape, as well as polarity and chemical bonding. This separation is performed primarily for the purpose of analyzing the molecular representation in the test substance (occasionally also for the purpose of isolating the required substances).
Terminological note:The somewhat misleading name "chromatography" (formed by combining Greek words chroma = color, graphein = write, draw) comes from the first experiments with this separation method, which were performed with plant pigments chlorophyll, carotene, xanthophyll (M.S.Cvjet, 1903). Their separation was observed visually according to different colors - green, red, yellow. Now analyzed substances are usually not colored.
The separation process takes place in a chromatographic system, which contains two phases: mobile and stationary. The mobile phase (eluent, solvent) - liquid, gas or plasma, containing a sample of the analyte, moves - flows, seeps - through the system and entrains carry the sample through the stationary phase (immobile, anchored in place), which leads to separation of the various molecular components. This creates a certain spatial distribution of the analyzed substances along the chromatographic system - chromatogram. The analyte is applied ("drip") to a site called the "start". The places where the individual molecular fractions of the analyzed sample penetrate at a given time form more or less sharp local concentration maxima - chromatogram peaks.
The mobile phase itself (eg solvent) passes through the system the fastest - it forms "forehead" of chromatogram (we stop the chromatography when the forehead arrives near the end of the chromatographic system). Passage of analyzed sample components are then various ways slowed down - retarded according to the size or other characteristics of the molecules. For quantification of the different speeds of the passage of analytes in a sample is introduced so-called retardation factor R_F - the ratio of the distance of the forehead from the start, to the distance of the center of the peak ("spots") of the substance from the start, is in the range of values <0,1>. For substances that are not carried by the mobile phase (heavy poorly soluble macromolecules), is R_F= 0 - remain detained at the start; for substances that the stationary phase does not slow down at all and are freely entrained together with the forehead, R_F= 1.
For systems where a chemical chromatogram is not formed (such as liquid and gas chromatography) the so-called retention time is introduced - the time from the start of flow so that the sample fraction reaches the detector at the end of the chromatographic column.
A number of types of chromatographic methods have been developed, depending on the arrangement of the separation system, the mobile and stationary phase used, instrumental techniques (column chromatography, liquid, gas, plasma chromatography, gel, paper, thin layer chromatography). Three methods are more often used :
- Gel chromatography takes place in a gel, which is placed in a vertical column. The gel contains small holes (pores) inside, which act as a "molecular sieve". However, the gel is most often used in the Electrophoresis described below.
- Thin layer chromatography uses a plate covered with a thin layer of sorbent - silica gel, to which the analyte is applied to one starting point with a thin capillary in a suitable organic solvent. The end of the plate in front of the starting point is then placed in ascending order in a solvent which begins to rise with silica gel and entrains the analyte with it, at a rate depending on the size of the molecules..
- Paper chromatographyis the most common method, using as a fixed phase "absorbent" - non-glued chromatographic paper (thickness about 0.2-0.6 mm), consisting of a compressed layer of cellulose fibers, between which there is a large number of gaps and pores; in them, the solvent seeps through by capillary forces. The analyzed sample is applied to the paper strip at a certain "starting" point near one end and before this point the strip is immersed in the mobile phase - solvent (the starting line must be above the surface!). Depending on the type (solubility) of the analyte, the mobile phase may be water or aqueous salt solutions, but often organic solvents ethanol or methanol, acetone, methyl ethyl ketone, ethyl acetate, acetonitrile, tetrahydrofuran, dichloromethane and the like. Chromatography is performed in a vessel with saturated solvent vapors to prevent the chromatographic strip from drying out during the process.
Depending on the direction of movement - leakage - of the mobile phase (solvent) in the chromatographic strip, two embodiments are used, "descending" or "ascending". In the descending design, a small dish with solvent is attached in the upper part of the analytical vessel, into which the upper end of the chromatographic strip is immersed, which then hangs and the solvent seeps downwards - Fig.2.7.4a above (second dish with solvent, built on the bottom, ensures a saturated atmosphere of vapors). In the ascending design, a layer of solvent (approx. 5 mm) is poured at the bottom of the vessel and the chromatographic strip is suspended so that its lower end is immersed in the solvent, which then capillaries rises upwards and carries fractions of the analyte with it from the starting point - Fig.2.7.4a bottom. In this ascending position, a plate with a thin silicagel foil can be used instead of a paper tape.
The mobile phase flows or rises through a layer of paper or thin film due to capillary forces and carries with it the individual molecular components of the sample, which are divided according to their solubility and mobility. The low-molecular, well-soluble and mobile components travel the furthest, larger molecules remain near the starting point. When the front of the chromatogram approaches the end of the paper tape, we end the process by breaking the contact of the tape with the solvent (pull out the tape). After the mobile phase has dried, the chromatogram is detected and evaluated.
Upon completion of the motion of mobile phase, the separated molecular components remain temporarily fixed at the sites of the stationary phase where they have reached *). This creates a basic chemical chromatogram, which is mostly latent (except for the analysis of color substances) and it is necessary to "make it visible" - "evoke" - detect -evaluate. Several methods can be used for this. In the chemical method of development, a suitable indicator substance is sprayed onto the chromatogram, which causes a color reaction with the distributed molecules. Physical - radiation - methods of detection use irradiation of the chromatogram with visible or ultraviolet radiation, which elicits a fluorescent optical response on distributed substances. From the point of view of our field of nuclear and radiation physics, we will describe the method of radiochromatography below.
* ) This is especially true for paper and thin layer chromatography. For some other methods (such as gas chromatography) no chromatogram is created, but at the end of the column there is one fixed detector, which gradually registers the arrival of individual molecular fractions and evaluates the time of their arrival - retention time....

Fig.2.7.4. Paper chromatography and radiochromatogram evaluation.
a) Descending (top) and ascending (bottom) chromatography on paper tape (in the ascending version, a plate with a thin silica gel foil can be also used instead of chromatographic paper). b) Simple method of radiochromatogram evaluation by measuring cut strips (with scissors) in a scintillation detector. c) Automatic radiochromatograph measuring the radiation profile of the chromatogram by moving the collimated detector along the strip.
Note: Spots or stripes on the chromatographic tape are drawn only symbolically, they are not directly visible (- only after evaluation) ...

Radiochromatography
is a method of chromatographic separation of radioactive substances with subsequent use of ionizing radiation detection for chromatogram evaluation. These are either primarily radioactive substances (such as radiopharmaceuticals) or substances labeled with radionuclides specifically only for the purpose of their analysis.
Detection of the distribution of analyzed radioactive substances on the chromatogram is performed by radiometric methods - using suitable electronic radiation detectors (alpha, beta, gamma) along the chromatographic strip or column. The simplest (especially previously used) procedure consists in cutting (with scissors) dried chromatographic tape into narrow strips (width approx. 5 mm), which are then measured separately with a scintillation detector (usually in test tubes in a well detector); their radioactivity - the measured number of pulses - is plotted graphically, resulting in a final chromatogram (Fig.2.7.4b). It is a relatively lengthy and laborious procedure, suitable only for occasional chromatography of simple samples.
Therefore, detection devices have been developed for frequent routine use, which perform automatic profilographic measurements and evaluation of radiochromatograms. The collimated scintillation detector passes just above the chromatographic strip or thin layer, registers the local intensity of the emitted radiation - the count rate of detected pulses - and outputs chromatographic curve (Fig.2.7.4c), with event. quantitative computer evaluation. In the graphical record, the individual chromatographically separated fractions of the analyzed substance form "bell-shaped" curves - peaks. The positions of the peaks are given by the specific chemical properties of the fractions - molecular weight, polarity, solubility. The area (integral) under the curves of these peaks is proportional to the relative proportion of the respective fractions in the separated mixture from the analyzed sample.
Radiochromatography is very often used to measure the radiochemical purity of radiopharmaceuticals - §4.8 "Radionuclides and radiopharmaceuticals for scintigraphy", section "Radiochemical purity".
A special method of chromatogram evaluation is autoradiography, based on the action of emitted radiation on a photographic emulsion (or on an electronic imaging detector) - §2.2, passage "Autoradiography".

Radio-electrophoresis
Electrophoresis (from the Greek electro foresis - to be carried by electrons; - transmission by electricity ) is a physico-chemical separation method that spatially separates the molecules of the analyte on the basis of different mobility of charged particles - molecules - ions *) - by the action of an external electrical field in a liquid, gel or porous medium. This mobility of particles depends on the value of the charge, the size, shape and weight of the particle (molecular weight), the properties of the environment and, of course, the strength (gradient) of the electric field. It is performed primarily for the purpose of molecular composition analysis of the analytes (rarely used for preparatory purposes). It is an alternative (often more sophisticated) analytical method to the chromatography described above.
*) Generation of electric charge of analyzed molecules
Molecules of analyzed substances acquire electric charge by interaction with the carrier medium. Conventional neutral molecules within contain both positive and negative charges in different parts of the molecule, wherein the total charge is equal to zero. By interacting with the environment, the molecule can gain or lose hydrogen ions (H⁺ - protons) and thus become more positive or negative. This property depends on the pH value (acidity or alkalinity) of the environment. In an acidic environment (pH <7) there is an excess of hydroxide cations H₃O⁽⁺⁾, so molecules will generally tend to acquire protons and become cations, while in a basic environment (pH> 7) there is an excess of hydroxide anions OH⁽^-⁾ and molecules they will more often lose protons and act as anions. The isoelectric point pH(I) (often abbreviated as pI) is that pH of the medium, at which the molecules of a given substance are electrically neutral (on a statistical average). If the pH value of the environment is lower than pH(I), the molecules acquire an overall positive electric charge, for pH values higher than pH(I) the given molecules have a resulting negative charge.
E.g. for proteins, pH(I) = 7.3 and NH3 groups have a charge of "+" and COO^(-) groups have a charge of "-", the molecules are generally neutral. At lower pH values, eg around 6, positive values prevail for NH3⁽⁺⁾, COOH are without charge, the resulting charge is positive. At a higher pH, around 8, the NH2 groups are uncharged and a negative charge predominates in COO⁽^-⁾. Therefore, at the recommended pH = 8.6, the proteins travel from the cathode (-) towards the anode (+).
The movement of charged particles at electrophoresis
During electrophoresis, two forces act on a charged particle with charge Q in an electric field of intensity E :
1.The electrostatic force F_E = E . Q, which tries to accelerate the motion of a particle. The intensity E of electric field is given by the voltage U [V] on the electrodes and their distances L [m] (the length of the chromatographic column) : E = U/L [V/m] , so that F_E = E . Q/L.
2.Resistance of environment (viscosity, shocs in the "molecular network" - Fig.2.7.5a), which tries to slow down the speed of particle motion: force F_r = k.R_m.s, where k is the material coefficient, R_m is the effective diameter of the molecule and s is the intrinsic resistance of the medium.
At the starting moment, when the velocity of the particle is zero (except for thermal movements), the particle is set in motion by the electric force F_e. With increasing velocity, the force F_r of the environmental resistance increases (in fact it is a slight moment, microseconds) until both forces acting on the particle equalize F_e= F_r. Now is the stationary state, in which the particles will move at a constant speed v = Q . U / (k . L . R_m. s). The speed of particle movement - electrophoretic mobility - is therefore directly proportional to the charge of the particles and the electrical voltage at the electrodes and indirectly proportional to the distance of the electrodes, particle size and resistance (viscosity) of the environment.
(Electrophoretic mobility is usually normalized to 1V voltage.)
The carrier, environment or medium in which the electrokinetic movement of the substances of the analyzed sample takes place, can be either a free liquid - an electrolyte (not commonly used, except for capillary electrophoresis), a porous support such as chromatographic paper or cellulose acetate film (the channels of which can serve as a "molecular sieve"), but it is usually a gel (agarose, polyacrylamide, starch). In terms of hydromechanical properties, the gel is a kind of transition form between solid and liquid state. More than 90% is made up of water, but in which a dense three-dimensional network is formed from polymerized sugar or acrylic chains connected by transverse hydrogen bonds. The size and density of the "mesh" of this network depends on the concentration and method of gel polymerization - the gel concentration determines the size and density of pores through which the analyzed molecules pass (typically around 100-300 nm, for selected gel species it is comparable to nucleic acid molecules and proteins). The concentration of the gel can therefore influence the separation rate and the size resolution of molecular fractions (proteins, DNA fragments). Usually a concentration of around 1-2% is used (up to 4% gel is used for finer resolution of short DNA fragments).
The pores of this network function as a "molecular sieve" for the movement of molecules under the influence of an electric field, through which larger molecules pass more slowly than smaller molecules - Fig.2.7.5a. Analyzed molecules is thereby progressively separated according to their size (molecular weight) over a distance of several millimeters to centimeters; individual fractions are arranged according to the size of molecules. The places, where the individual molecular fractions of the analyzed sample penetrate at a given time, form more or less sharp local concentration maxima - peaks of the electrophoreogram.
This resulting graph of the electrophoreogram is already used for chemical analysis of the measured sample: the positions of the peaks determine the type of substances contained (molecular weight), their intensities - peak heights (or areas - integrals - below the peak curves) determine the representation of relevant substances. Quantitative analysis can also be performed with the appropriate calibration.

Fig.2.7.5. Gel electrophoresis and evaluation the density and radio-electrophoresis.
a) Principle of separation of molecular fractions by electric field through a "molecular sieve". b) Basic arrangement of electrophoresis in a gel environment. c) Stained electrophoreogram. d) Optical - photoelectric - evaluation of electrophoresis fractions. e) Radiometric evaluation of the electrophoreogram of the radioactive analyte.

A small amount (drop - a few microliters) of the analyzed sample - analyte - is applied with a micropipette to the starting point in the gel (it is a well in the gel, usually several wells next to each other, extruded by a special "comb"). Then an electrical voltage of the order of tens to hundreds of volts (approx. 1-10 V/cm) is applied to the electrodes between which the column is inserted *) --> electrophoresis begins - Fig.2.7.5b. After a preset time, or when the fastest molecular component approaches the end of the column, the electrophoresis process is terminated by disconnecting the electrodes from the high voltage.
*) Electrical conductivity of the environment, pH, buffer
The electrical conductivity (resistivity) of the environment - the gel - affects the passing current and the mobility of molecules during electrophoresis. It is regulated by the composition and concentration of the electrophoretic buffer in the gel. Buffer is an agent regulating the alkalinity or acidity of the environment - the pH value. The fundamental importance of the pH environment for obtaining the electric charge and thus the mobility of the analyzed molecules was discussed above in the note "Origin of the electric charge of the analyzed molecules". Without the presence of buffer salts, the electrical conductivity is minimal and the molecules move and separate hardly and very slowly. However, if the salt content in the buffer is too high, undesired heating of the gel may occur during electrophoresis. Typical parameters used for conventional columns are: pH 8.6, voltage 200-250 V, current about 10mA per 1cm of gel width, separation time about 10 minutes.
pH gradient, isoelectric "focusing"
Depending on the pH value of the environment, many important analyzed molecules (amino acids, peptides, proteins) acquire a positive or negative electric charge. This is decided by their so-called isoelectric point pH(I) - the pH value at which they are uncharged (discussed above in the section "The formation of an electric charge of the analyzed molecules"). This regularity can be used for a certain "trick" to improve the resolution of separating capability of electrophoresis.
There are certain chemicals called ampholites which, when an electric current passes through the electrolyte (in gel) creates a stable linear pH gradient , with the lowest pH at the anode and the highest at the cathode. In this situation, the assayed molecules, e.g., proteins applied to the gel, will move with a pH gradient only to the place, where the pH of the medium be equal to their isoelectric point pH(I). Here is stopped, because the molecule here becomes electrically neutral; and it will remain stand firmly there, because if it is deflected towards the anode or cathode, it would gain a positive or negative charge and the electric force would immediately return it. The result is very narrow and sharp streaks - zones - peaks in the gel, where the molecules are precisely concentrated (focused), with a high-resolution of separation. The method is called isoelectric focusation (ISS).
Electrophoreogram
After switching off the electric voltage, the movement of the molecules stops and the separated molecular components remain temporarily fixed in the places of the gel where they reached. After electrophoresis, the gel must be dried or fixed with a suitable reagent (such as acetic acid) to immobilize the separated molecules in the support medium and prevent their diffusion. This creates a basic chemical electrophoreogram, which is usually latent and needs to be "made visible" - detected - evaluated. This can be achieved mainly by two methods :
- Optical detection methods
make use of colored or luminescent labeling of the analyzed molecules - gel is stained in order to visualize individual molecular fractions (sometimes the dye is added to the sample before analysis) . Special organic dyes are used (blue, red, green, similar to microscopic observation of specimens). Subsequent irradiation of the stained column with visible or ultraviolet radiation will elicit a fluorescent optical response on the distributed substances (Fig. 2.7.5c). It can be evaluated visually or electronically by photodetectors. In the density method, the electrophoreogram is shifted evenly over the slit of the photometer through which light of the respective color passes (wavelengths, approx. 400-700 nm). In the place of higher concentrations of individual fractions there is a partial absorption of radiation, which is registered by a photodetector - densitometry recording the changing value of light absorption according to intensity - density - color, Fig.2.7.5d. In fluorescence mode, the photodetector directly measures the intensity of the emitted fluorescent light.
In the graphical record of the absorbance or fluorescence of the individual electrophoretically separated fraction of the analyte, they form "bell-shaped" curves - peaks. The read positions and intensities of the individual fragments are compared with the standard sample, analyzed in parallel. The positions of the peaks determine the molecular weight of the fractions, the area (integral) under the curves of these peaks is proportional to the relative representation of the respective fractions in the electrophoretically separated mixture from the analyzed sample - it allows quantitative analysis.
Into one of the wells in the gel (in Fig.2.7.5b it is the last well on the right) a standard sample with a known representation of analyzed substances, eg various types of proteins, is applied. By comparing the positions of the peaks in the chromatograms of the analyzed samples in other columns, it is possible to identify the type and representation of the sought types of substances (molecules). The position coordinate on the chromatogram (Fig. 2.7.5d, e) - the distance of the peak from the start in [cm] - is thus calibrated to the molecular weight axis in [kDa].
- Nuclear radiation methods
use the detection of ionizing radiation emitted by radiolabelled sample molecules and its fragments. From the point of view of our field of nuclear and radiation physics, we will briefly present the method radio electrophoresis below.
The above-described method of electrophoresis in "plate" gel columns according to Fig. 2.7.5b,c is suitable for the analysis of a smaller number of samples and their molecular fractions. Current laboratory electrophoreographs have the option of about 12-60 sample routes in the gel column. They are used in biochemical analyzes of eg amino acids, peptides, proteins, nucleic acids.
Serum protein electrophoresis is most commonly performed. These proteins are here divided into about 6 protein fractions. The width of the zones shown depends on the number of individual types of proteins with similar mobility (molecular weight) that are present in the fraction. Albumin is the most common here, which also travels furthest towards the anode. By decreasing electrophoretic mobilities follow a1, a2, b1, b2 - globulins, b lipoproteins, the transferrin.... Gammaglobulins (G, A, M, D, E) form a wide "blurred" strip near the start. The electrophoreogram of blood serum proteins (unspecified example) was used above as an illustrative example in Fig.2.7.5c.
Electrophoresis of proteins in urine is also used (proteins of glomerular and tubular origin differ here) and cerebrospinal fluid proteins (an increased proportion of different types of proteins is found due to the increased permeability of the blood-brain barrier or the inflammatory process in the CNS).
However, for analyzes of a large number (hundreds or thousands) of samples, this standard method is somewhat complicated and time consuming. Here can be advantageously used a capillary electrophoresis :
Capillary electrophoresis
uses the electrokinetic effect of electrophoresis (and electroosmosis) to the separation process of materials within a thin capillary. A quartz glass (silicon-oxide) capillary is used with an inner diameter of approx. 20-200 micrometers and a length of min. 20cm to 1 meter. It is connected to high voltage of approx. 20-30 kV via tubes with buffer. Such a high voltage (causing a higher current density and thus Joule heat) can be used due to the efficient heat dissipation from the capillary to the surroundings. High voltage leads to increased separation efficiency and shortened analysis time to units of minutes.
This capillary serves as an electrophoretic chamber, in the end part of which a photoelectric fraction detector is located. No "chemical electrophoreogram" is created along the capillary (which would have to be subsequently evaluated), but the detection of fractions takes place continuously - "on line". The detector continuously evaluates the intensity and retention time arrival of a given molecular fraction - the time from the beginning of the flow, necessary for the given fraction of the sample to reach the detector at the end of the capillary chamber. This directly creates electrophoreogram peaks.
Current routine biochemical methods of DNA sequencing use fluorescently labeled nucleotides, which are analyzed by capillary electrophoresis in a large number (tens or hundreds) of parallel capillary sequencers, wherein the fluorescent light is registered by a sensitive opto-electronic detector. These new sequencing techniques allow very fast and relatively inexpensive "reading" of entire genomes. A huge amount of sequence data obtained in this way is processed by computer - it becomes the subject of bioinformatics.
The development of advanced very fast, highly parallel (approx. 10⁶) sequencing techniques continues, using fragmentation into short section, sequencing synthesis of complementary strands to the analyzed fragment using DNA polymerase, implementation of chemical luminescent labels signaling incorporation of new bases into the DNA strand. Completely new possibilities of electronic detection are also tested, during sequencing, based on electrical signals from a change in conductivity in the "molecular sieve" environment, in which DNA fragments are translocated ...
However, all these methods completely go beyond the scope of our treatises on nuclear and radiation physics (as well as the professional orientation of the author...).
Radioelectrophoresis
is a method of electrophoretic separation of radioactive substances with subsequent use of ionizing radiation detection to evaluate the distribution of radioactive molecular fractions in columns. These are either primarily radioactive substances (such as radiopharmaceuticals), or substances labeled with radionuclides only for the purpose of their analysis.
Detection of the distribution of analyzed radioactive substances on the electrophoregram is performed by radiometric methods - using suitable electronic radiation detectors (alpha, beta, gamma) along the electrophoretic tape or column (it is analogous to the radiochromogram in Fig.2.7.4c). The collimated scintillation detector passes just above the radioactive electrophoretic column, registers the local intensity of the emitted radiation from individual places - the frequency (count rate) of detected pulses - and outputs the electrophoretic curve (Fig.2.7.4e), with event. quantitative computer evaluation. In the graphical record, the individual separated fractions of the analyte form "bell-shaped" curves - peaks. The area (integral) under the curves of these peaks is proportional to the relative proportion of the respective fractions in the electrophoretically separated mixture from the analyzed sample.
Radioelectrophoresis is sometimes used - in addition to the more frequently used radiochromatography - to measure the radiochemical purity of radiopharmaceuticals - §4.8 "Radionuclides and radiopharmaceuticals for scintigraphy", section "Radiochemical purity".
A special method of radioelectrophoresis evaluation is the above-mentioned autoradiography, based on the effect of radiation emitted from radioactive fractions on a photographic emulsion (or on an electronic imaging detector) attached closely to the electrophoretic column - §2.2, passage "Autoradiography".

Chromatography <- versus -> electrophoresis
Both of the above analytical methods of chromatography and electrophoresis have much in common. They differ mainly in two aspects :
1. Chromatography is a passive method, where the molecules of the carrier and the analyzed substances move and separate due to natural thermal motion and intermolecular forces, manifested, for example, by capillary forces.
2. Electrophoresis is an active method, where the molecules of the carrier and the analyzed substances move and separate under the influence of an artificial electric field and current. This controlled method provides wider possibilities of optimized analysis of a large range of substances, especially proteins, nucleic acids, DNA fragments.
Therefore, the technical design and the course of the analytical process also differ. However, the evaluation of the result - chromatogram and electrophoreogram - is largely similar, including the possibility of using radiometric methods - cf. Figures 2.7.4 and 2.7.5.

2.8. Absolute measurement of radioactivity and radiation intensity
Like measuring methods in general, radiometric measuring methods can be divided into absolute and relative. For relative measurements, we are concerned with determining the ratios of activities or radiation intensities of individual samples either with each other or with respect to a suitable standard; in most applications of ionizing radiation, such relative measurements are sufficient for us. For absolute methods, we need to determine by direct measurement under precisely defined conditions, from the measured of ionization current or pulse frequency, the absolute value of activity in [Bq] or the absolute intensity of the radiation beam in [number of quant /cm²] (fluence) or in units of dose [Gy] or dose rate [Gy/s]. Absolute measurement of radiometric quantities encounters a number of fundamental and technical difficulties, which will be briefly discussed below. Methods of absolute measurement of radiometric quantities can be divided into two categories :

Absolute measurement of radioactivity
For the primary absolute measurement of the activity of radioactive emitters and preparations can be used several methods utilizing the physical and chemical manifestations of radioactivity.
Absolute counting of emitted particles
The activity A of a certain radioactive emitter (ie the number of nuclei that is converted per unit time) can be measured directly using the frequency of particles (quantum of radiation) that a given sample emits. Using a suitable detector, measure the number of pulses N for a certain time t , subtract the background pulses N_b and multiply the result by the correction factor F :
A [ Bq ] = F. (N - N_b) / t .
The total correction factor F includes all circunstances affecting the detection of radiation from a given sample; is the product of several partial coefficients: F = f_g . f_d . f_a . Here f_g = 4p/w is a geometric factor given by the ratio between the full spatial angle 4p (into which isotropic radiation from each source takes place) and the actual angle w, in which the quantums emitted from the source fall into the sensitive space of the detector (Fig.2.8. 1 top left). f_d is the correction factor for the detection efficiency, which depends on the type and size of the detector, the type and energy of the detected radiation, or on the dead time of the detector. f_a is the radiation absorption correction factor, which is the product of the self-absorption factors in the sample, the radiation absorption in the detector window and possibly radiation absorption in the environment between the source and the detector. These correction factors must be determined by independent measurement for each specific method.
For detecting the radiation quanta are used GM tubes (earlier), scintillation and semiconductor detectors, proportional detectors. A special group consists of methods with a measurement geometry of 4p, when the active space of the detector completely surrounds the radiation source. The measured sample is stored either inside the ionization chamber - GM or proportional detector, or the radioactive atoms are evenly dispersed in the gas charge, or the radioactive preparation is dissolved in a liquid scintillator. This measurement geometry is almost completely 4p, only at the edges and walls of the detection volume there is a reduction in detection efficiency.

Absolute coincidence methods
In certain special cases, it is possible to circumvented the chalenging and difficult determination of the above correction factors F. The elegant possibility of determining the absolute detection efficiency (ie h = 1/F), and thus automatically the possibility of measuring the absolute activity of a radioactive preparation, is offered for such radionuclides that emit two quanta of ionizing radiation simultaneously (or more quanta simultaneously). Here we can use methods of simultaneous - coincidence - detection of these two quanta of radiation emitted by a radionuclide.
Method of b-g coincidences
This method is suitable where the radionuclide emits beta radiation accompanied by gamma photons (decay scheme in the left part of Fig.2.8.1 above). In this case, we place a measured sample of (sought) activity A between two detectors, equipped with independent evaluation circuits (detection "channels") and a coincidence circuit. Detector D_b is sensitive only to beta radiation and will measure the pulse frequency n_b = A.F_b, where F_b is the geometric-efficiency factor for detecting radiation b from the sample. Detector D_g, sensitive only to gamma radiation, will measure the pulse frequency n_g = A.F_g, where F_g analogously characterizes the efficiency of g radiation detection from the sample. A pulse will appear at the output of the coincidence circuit only if pulses occur at both its inputs at the same time. The probability that a particle b and a quantum g emitted during one radioactive transformation will be registered at the same time is F_b.F_g , so the frequency of coincidences will be n_coin = A.F_b.F_g. From these three relations we can exclude the unknown factors F_b and F_g, thus obtaining the resulting relation: A_[Bq] = (n_b.n_g)/n_coin, according to which the absolute activity A can be determined by the coincidence method only on the basis of measuring the pulse frequencies n_b and n_g in both beta and gamma detectors.

Fig.2.8.1. Coincidence measurement of absolute activity and detection efficiency.
Left: Coincidence detection of radiation b and g by two separate detectors b and g. Right: Coincidence analysis of measuring pairs of photon radiation g .

Method of g-g coincidences
This method can be used if the investigated radionuclide emits two photons simultaneously during each transformation - either during deexcitation of nuclear levels in a cascade (eg ⁶⁰Co), or in electron capture accompanied by simultaneous emission of a characteristic X-ray photon from envelope and photon g from the excited daughter nucleus (eg at ¹²⁵I) - Fig.2.8.1 at the top right. If both of these photons enter the detector and are registered, the detector will not distinguish them from each other in time - they will coincide and the transmitted pulse will be equal to the sum of the pulses from both quanta. In the spectrum thus appears summation peak n_S corresponding to the sum of energies of both quanta (Fig.2.8.1 on the right).
If we measured in the geometry 4p and the detection efficiency was 100%, all pairs of coincidence photons would be detected simultaneously and only the summation peak would be present in the spectrum. If the detection efficiency is lower than 100% (which is practically always), in a part of the coincident gamma-pair only one from this twoo photons is detected, and in addition to the summation peak, the actual peaks of both quanta with respective energies appear in the spectrum. The lower the detection efficiency (whether by deviation from the geometry of 4p, or the lower the efficiency of the detector itself), the lower the probability of simultaneous detecting of coincidence photons and the lower the summation peak with respect to the separate peaks of the individual photons from the coincidence pair. By evaluating the ratio between the areas (integrals) of the summation peak n_S and the peaks of individual coincidence photons n₁, n₂ it is possible to determine the total detection efficiency in a given measurement arrangement, which includes all partial factors (geometric, absorption, detector efficiency), and thus determine the absolute activity of the measured sample: A_[Bq] = (n₁+n₂+2.n_S)²/4.n_S. This method works well in a geometries close to 4p and with not too low detection efficiency, when the summation peak n_S is well expressed (accuracy of absolute activity determination may be better than 1%). With a geometry of 2p or lower, the summation peak in the spectrum almost disappears - the method is subject to a large error or is not applicable at all.

Calorimetric measurement of absolute activity
In principle, the thermal effects of the energy released during radioactive transformationscan also be used for the absolute measurement of radioactivity. Since the amount of heat generated is relatively very small from a macroscopic point of view, this method can only be used for preparations with relatively higher activity, of the order of hundreds of MBq, GBq, TBq. The so-called isothermal calorimeters, operating at normal temperature, are sometimes used for the absolute measurement of the radioactivity of high-activity preparations - bridge temperature thermistors are used to compare the temperature difference between a reference sample and a sample containing the radioactive material. ...

Electrostatic measurement of absolute activity
can be used to measure the activity of radionuclides emitting charged particles - a or b. When a charged particle is emitted from a radionuclide (originally electrically neutral), this radionuclide acquires an equally large charge of the opposite sign. From the change in the total charge of the sample over a certain time interval, the activity can in principle be determined. As this creates very small charge values, it is necessary to use sensitive electrometers. There are a number of disturbing influences, coming from secondary electrons released during ionization by radiation and from the absorption of charged particles in the source itself ...

Measurement of activity by well ionization chamber
For approximate measurement of radioactivity, especially in the field of medical applications of open radionuclides, ionization chambers in well design are preferably used as activity meters of radioactive preparations (these meters are sometimes incorrectly called "dose calibrators") - was mentioned above in §2.3 "Ionization detectors", Fig.2.3.1 on the right. The vial or syringe with the radioactive substance is inserted into the opening of the well ionization chamber, which in the geometry close to 4p registers the emitting radiation g. The electrical signal I from this chamber is proportional to the activity of preparations A and G-constant of the given radionuclide: I ~ A. G; the G- constant is different for each radionuclide. The electronic circuits of the activity meter are calibrated so that for the selected radionuclide the display shows its activity directly in MBq.

Measurement of radiation intensity and dose rate
The intensity or fluence of radiation can be measured directly using suitable detectors, sensitive to the given type of radiation and located at the desired location of the beam. The measured frequency (count rate) of pulses N per unit area of the detector must again be corrected by the factor F of the detection efficiency. In the case of stronger beams of radiation, used for example in radiotherapy, the intensity of radiation is characterized by a dosimetric quantity of radiation dose rate at a given location of the substance that is exposed to radiation. Normalized and calibrated ionization chambers, and more recently semiconductor detectors, are most often used for these measurements.
For measuring doses and dose rates inside irradiated materials, eg inside tissue in radiotherapy, the so-called Bragg-Gray method of ionization chamber is used, located in a cavity inside the material (or this chamber itself is the cavity). This measurement is objective, assuming that the radiation intensity in the surrounding material and in the chamber is the same, the dimensions of the chamber cavity are much smaller than the range of secondary electrons in the gas and the dimensions of the surrounding material layer are much greater than the range of secondary electrons in this material. Then the electron equilibrium occurs in the system, the presence of the cavity - the ionization chamber - does not disturb the electron balance in the surrounding material. Then the ionization of the gas in the chamber cavity is caused almost exclusively by electrons coming from outside their walls (the contribution from the interaction of primary radiation in the chamber cavity is negligible) and these electrons lose only a small part of their kinetic energy as they pass through the chamber cavity. The transmitted energy at the location of the chamber and its surroundings is practically equal to the kinetic energy of the released electrons ( dose = kerma ). In this situation, the number of ion pairs formed in the chamber cavity is proportional to the dose of primary radiation in the material that surrounds the chamber cavity. Thus the dose rate D´ is proportional to the current I through the ionization chamber: D´ = L.w.I/(r.V), where L is the ratio of the linear ionization of the irradiated material and the chamber gas during electron motion, w is the energy required to form one ion pair in the chamber gas, r is the density (specific gravity) of the gas, V is the volume of the chamber cavity. In practical measurements, the ionization chambers are placed in the appropriate sites of the phantoms, either aqueous or tissue equivalent (which, by their composition, mimic the irradiated tissue).

2.9. Measurement of radioactivity in the organism (in vivo)
A specific area of radiometric measurements is the detection of radiation from radioactive substances deposited within the organism - in vivo measurements. Let us first ask the question: Under what circumstances can radioactivity enter the body? There are basically two options :

In both of these different situations, there may generally be a need to measure the amount or distribution of radioactivity in an organism.

Whole-body measurement of radioactivity
Absolute measurement of the total amount of radioactivity in the organism may be important in the mentioned case No. 2 - internal contamination of radiation workers.
We determine radioactivity in the organism on the basis of external detection of outgoing gamma radiation. In order to achieve approximately the same detection efficiency for all parts of the body during whole-body measurement, several scintillation detectors of larger dimensions are used, distributed around the patient's body in the arrangement of the so-called whole-body detector. In some types, the body passes evenly between the detector system. When evaluating the number of measured pulses from individual detectors, a number of corrections for absorption and geometric conditions are used, as well as multiplication by calibration coefficients expressing the relationship between the measured pulse frequency and the activity of the monitored radionuclide in the body.
To detect internal contamination by an unknown radionuclide, or a mixture of different radionuclides, high-energy spectrometric semiconductor detectors are also rarely used in the whole-body detector, while the spectra are measured and evaluated using a multichannel analyzer.
In diagnostic applications of radioactivity, in the 1970s and 1980s, whole-body measurements were performed only very rarely in determining the resorption of certain substances (eg vitamin B12 labeled with ⁵⁷Co); now this method is abandonded and by whole body measurements in nuclear medicine we usually mean whole body scintigraphy - chapter 4 "Radioisotope scintigraphy".

Local measurement of the distribution of radioactivity
In diagnostic and therapeutic applications of radioisotopes to the body, we do not need to measure the absolute value of radioactivity in the body (this was measured in a bottle or syringe before application). Rather, we need to determine the distribution of radioactivity in individual places and organs in the body - this has direct diagnostic or therapeutic significance. It is therefore a relative local measurement of radioactivity in certain places of the organism on the basis of external detection of the outgoing gamma radiation, which penetrates trough the tissues out of the organism.
This local measurement of the intensity of the emitted radiation can in principle be performed by simply placing the scintillation detector to the individual locations. However, a free detector (without shielding) would register g radiation not only from the desired location, but also from other locations in the body, with only slightly lower efficiency (given the greater distance of these locations from the detector). In order to achieve selective detection of radiation only from the desired place (direction) in the body, it is necessary to shielding radiation g coming from other (undesirable) directions and measure only radiation from a narrow cone in the desired direction - to equip the detector with a collimator. By gradually stoking such a collimated detection probe to individual parts of the body we can "map" the distribution of the radioindicator in individual organs within the organism. Or, with a collimated detection probe aimed at a specific organ, we can monitor the time course of distribution of the radioindicator in this organ after the application of a radioactive substance to the organism. But all this only very inaccurately !

Nuclear medicine
These detection methods have played an important role in the relevant early stage of development of nuclear medicine - a field dealing with diagnostics and therapy using open radionuclides (Chapter 4). The simplest method is to determine the accumulation of ¹³¹I in the thyroid gland, where after application of a known amount of radioiodine, the radiation g from the thyroid gland is measured with a collimated probe g and the percentage of radioiodine taken up by the thyroid gland is determined by comparison with the standard value; repeated measurements for several days further determine the half-life of iodine from the thyroid gland.
The most used measuring method in nuclear medicine in the 60s-80s was radioisotope nephrography: Two collimated scintillation probes were directed from behind into the right and left kidney, radioactive ¹³¹I-hippuran was applied, which was taken up in the kidneys, and the detection probes registered the amount of radiation from the left and right kidneys. The impulses from the nephrographic probes were fed via integrators to the recorders, whose pens gradually plotted the so-called nephrographic curves, showing the accumulation of ¹³¹I-hippuran in the left and right kidney and its gradual excretion into the urinary tract. From the shapes of nephrographic curves (steepness of increases, times of peaks and steepness of decreases) it is possible to deduce the functional ability of the kidneys and their drainage.
Occasionally, g- registration methods have been used collimated detection probes from the heart or brain - the method of so-called radiocirculation in order to examine the dynamics of heart activity or blood flow through the cerebral hemispheres. However, these and similar methods were already debatable at the time of their creation (due to large errors and inaccuracies in the detection of "blind" radiation) and were soon abandoned. All these methods, including nephrography, have been replaced by significantly more perfect and complex scintigraphic methods.
Radiation-guided surgery - sentinel nodes
Local radiation measurements with a closely collimated miniature gamma ray detection probe find important application in radiation-guided surgery in the detection of so-called sentinel nodes. In the surgical treatment of cancer, it is important to remove not only the primary tumor, but also, if possible, other tissues into which the tumor cells could be infiltrated. These tumor cells spread from the primary site mainly through the lymphatic pathways, so that the lymph nodes around the tumor site are the first to be affected. If we apply a suitable radioindicator of colloidal state to the peripheral part of the tumor lesion (most often ^99mTc nanocolloid, particle size approx. 50-600 nm, activity approx. 40-150 MBq), it will spread through the lymphatic pathways and capture and accumulate in those nodes that are lymphatically associated with the tumor site. The first such node in the lymphatic "basin" of a tumor foci is called the sentinel node. The accumulation of the radio indicator in the nodes can be displayed scintigraphically.
However, the most important thing is to monitor the radioindicator during the actual surgical procedure, when using a collimated detection probe the surgeon can find a sentinel node containing the radioindicator directly in the operating field, and also to make sure that the operated node contains a radioindicator. After application of the radioindicator, scintigraphic imaging is first performed with the imaging nodes drawn, then the patient goes to his own surgery, during which a detection gamma probe is used.
*) Along with the radioindicator, a blue dye (patentblue) is applied at the same time, which also penetrates the nodes, so that the surgeon can recognize the sentinel node even by its blue color.
Scintigraphy
The only viable and promising methods of analysis of the distribution of radioactivity in the organism (apart from the above-mentioned method of sentinel node detection) are methods of scintigraphic imaging of static or dynamic distribution of the radioindicator. These methods provide detailed mapping and a clear view of distribution of the radio indicator, including all peculiarities and anomalies within the organism, with the possibility of visual evaluation and detailed mathematical analysis and quantification of the parameters of the investigated processes within the organism. Methods of radioisotope scintigraphy are described in detail in Chapter 4 "Radioisotope scintigraphy".

2.10. Calibration and inspection of detection instruments
In order to ensure accurate and reproducible results of radiometric measurements, it is necessary to ensure the correct setting and calibration of detection instruments and to check these parameters regularly - thus ensuring their stability.

Calibration of radiometric instruments
The basic adjustment and calibration of these measuring instruments is usually performed by the manufacturer upon delivery of the equipment, it is a "company calibration". The need for self-calibration of the instrument arises for the user when he intends to use it for a different purpose than the one for which it was calibrated. Possibly, it is a device for general use, the final response of which is individual pulses, voltage or current signal. Some methods of absolute calibration have been mentioned above in §2.8. For the normal user, usually only the method of relative calibration is available - calibration of the instrument using etalons, or by comparing it with another ("standard") device. For instruments that are subject to high requirements for accuracy and reproducibility of results, metrological calibration or verification of the instrument is performed using standards with the participation of an authorized laboratory (metrological institute).

Stability of the measuring instrument and its control
The instability of radiometric instruments can be caused by various influences, depending on the type of detection instrument. In simple devices based on ionization chambers, instability is often caused by a change in pressure and the composition of the gas filling in the chamber due to a leak (filling leakage) - it usually leads to a reduction in detection efficiency.
In the case of spectrometric instruments, the instability of the detector and the electronic circuits of the evaluation apparatus is manifested by a shift of the spectrum and thus also by a change in the position of the photopeak; if the analyzer window is correctly set symmetrically to the photopeak, due to the instability, the photopeak will "travels away" from the window and the number of registered pulses will decrease significantly. For multi-channel analyzers, instability can lead to shifts and blurring of photopeaks. The cause of the spectrum shift is a change in the height of the signal pulses at the output of the detector, or a change in the electronic gain evaluation apparatus. These changes can be caused by high voltage fluctuations at the photomultiplier dynodes (this is very sensitive!), amplifier gain fluctuations, changes in electrical values of electrical circuit components either by temperature fluctuations or "fatigue" and aging, photomultiplier "fatigue", changes in scintillation crystal properties (such as yellowing due to water absorption) or a semiconductor detector (drift diffusion, etc.).
To eliminate the effect of supply voltage fluctuations, modern devices are equipped with voltage stabilizers. In order to achieve high stability of the detection devices and to reduce or eliminate the influence of temperature on the response of the device, it is recommended to ensure temperature stabilization the environment or room in which the device operates (eg air conditioning). Another rule to ensure accurate and stable measurement results is that we never measure on the instrument immediately after it is turned on. The amplification and other parameters of the electronic apparatus, as well as the detector itself, may change slightly after switching on the device and only in a few minutes the device enters a steady mode, in which it remains for a long time (unless there is instability due to another cause or failure). Some devices do not turn off at all to ensure high stability.

Tests of quality, correct function and stability of measuring instruments are usually divided in time into two groups :

From an organizational point of view, each measuring instrument for detecting radiation have drafted regulation for setting , monitoring and measurement methodology , test results should be recorded in the technical diary of the instrument, or evaluated and archived by computer.

Statistical check of instrument response stability
If the radiometric instrument is properly calibrated and its correct setting is verified, it will not show coarser measurement errors, but in principle smaller deviations may occur due to instabilities, which do not significantly affect the frequency of measured pulses of background, samples and standards, and "at first glance" we do not seen. We can then verify the correct and stable function of the device using a suitable statistical criterion - whether the measured pulse frequency is subject only to statistical fluctuations, or whether it is also affected by other factors. This method of verification is based on the knowledge of statistical fluctuations given in the following §2.11; here we will only present the procedure.
One way to evaluate the proper function of the device is to repeated measurement of the same sample on the instrument, thus finding a set of frequencies N1 , N2 , ..., Nn . We calculate the average value N´ = (N1+N2+...+Nn)/n for the standard deviation of the measurement s = Ö(N1²+N2²+...+Nn²)/n. This we compare the standard deviation with the standard deviation given exclusively by statistical fluctuations of radioactive transformations ÖN´. If the standard deviation s during the measurement significantly exceeds the theoretical value ÖN´, the instrument contributes to error by its instability !
For a quick orientation check, it is enough to measure the same sample twice, which gives two values of the number of pulses N1 and N2 . To assess whether the difference between these two values is still within the range of statistical fluctuations, use the following criterion: if the difference exceeds |N2 -N1| between the measured numbers of pulses, approximately three standard deviations of the statistical fluctuations, ie 3.Ö[(N1²+N2²)/2], this indicates a suspicion of instrument instability.

2.11. Statistical fluctuations and measurement errors
Like all other measurements of real natural quantities, radiation detection and spectrometry methods are subject to certain errors. However, the nature and origin of these errors have their own specifics in nuclear and radiation measurements, which we do not usually encounter in other areas. These are irremovable statistical fluctuations. *)
*) In everyday life, we do not encounter these fluctations because we mostly observe macroscopic objects and the amount of photons of light with which we observe is so large that the fluctuations are negligible. However, in astronomy, for example, in the observation and spectrometric measurement of the faint flow of light from distant galaxies, statistical fluctuations are exactly the same as in the detection of faint ionizing radiation. Quantum - statistical fluctuations are generally encountered wherever the measured signal is so weak that quantum fluctuations of the measured quantity are manifested.

Statistical fluctuations
The emission of quantum ionizing radiation, as well as its interaction with the atoms of the material environment (and thus the mechanisms of radiation detection) takes place at the microscopic level through events governed not by the deterministic laws of classical physics, but by the laws of quantum mechanics. These quantum regularities are in principle stochastic, probabilistic (see §1.1). The transformation of radioactive atoms is a completely random process and the resulting ionizing radiation is emitted randomly, uncorrelated, incoherently. The flow of ionizing radiation is therefore not smooth but fluctuating. Equally fluctuating will be the response of each device detecting this radiation. In repeated measurements of the same sample under the same conditions, we therefore measure every time somewhat different values of the number of pulses, which fluctuate around a certain mean value. These are deviations that can not be eliminated by any improvement of the device or method, these fluctuations have their origin in the very essence of the measured phenomena.
The influence of statistical fluctuations on the results of radiation detection and spectrometric measurements can be expressed in a simplified (but apt) way by the following rule :

More precisely, the standard deviation s (also called the root mean square deviation) of an individual measurement is given by the square root of the measured number of pulses N: s = ± Ö(N). This means that when measuring repeatedly, approximately 68% of the total number of measured values lie in the interval (N- s, N + s) , 95% of the values lie in the interval (N- 2s, N + 2s) and 99% of the values in the interval ( N- 3s, 3s + N). *)
*) The probability of occurrence of a measured value of the number of pulses is generally expressed by the so-called Poisson law of distribution (which is asymmetric in areas of small numbers of pulses), at higher number of pulses it then turns into a symmetric normal (Gaussian) distribution (Fig.2.11.1 left).

Fig.2.11.1. Left: Distribution of the probability of occurrence of measured values of the number of pulses according to the Gaussian normal distribution.
Right: Comparison of spectrometric measurements at low (top) and high (bottom) number of detected pulses.

The relative error (coefficient of variation) of the measurement is then D = s/N = Ö(N)/N = 1/Ö(N), or x100 if we want to express it in%. Thus, the higher the number of pulses we measure, the lower the measurement error - and this is also the only way to reduce the errors caused by statistical fluctuations! If we measure 10 pulses, the error is 1/Ö(10) @ 33%, at 100 pulses the error will be 1/Ö(100) = 10%, at 1000 pulses 1/Ö(1000) @ 3%, and only when we measure 10000 pulses, the statistical error will be only 1%: 1/Ö(10⁴) = 1%.
Thus, the only way to reduce statistical fluctuations is to increase the accumulated number of pulses - the number of "useful" photons g from which the response in the detection device arises. Thus, at low radiation intensity or radioactivity of the measured sample, it is necessary to increase the measurement time in order to accumulate the number of pulses needed to achieve the required accuracy (relative error) of the measurement.
In Fig.2.11.1 on the right is an example of the scintillation spectrum of a ¹³¹I radioiodine sample measured by the same detector at a maximum accumulated number of pulses N = 50 imp/cell (measuring time 5 sec. - top) and N = 15000 imp./cell (measuring time 300 sec. - bottom). The difference in the quality and accuracy of the spectrum is evident - with a low number of registered pulses, the details in the shape of the spectrum are "drowned out" by statistical fluctuations, while with a high number of pulses the spectrum is "drawn" smoothly and in detail, with minimal fluctuations. In the same way, statistical fluctuations are manifested in all radiation measurements, eg in scintigraphic images (Chapter 4 - Radioisotope scintigraphy).

Total measurement error
The resulting measurement error generally consists of individual partial errors, which can be divided into three groups :

If individual partial errors have a statistical character, the resulting measurement error according to the laws of mathematical statistics is given by their geometric sum : s = (s₁² + s₂² + s₃² +....+ s_n²)^1/2 .

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