Radioactive isotopes for research, medicine, technology

1. Nuclear and radiation physics
1.0. Physics - fundamental natural science
1.1. Atoms and atomic nuclei
1.2. Radioactivity
1.3. Nuclear reactions and nuclear energy
1.4. Radionuclides
1.5. Elementary particle and accelerators
1.6. Ionizing radiation

1.4. Radionuclides
In this chapter we will approach the origin and properties of the most important radionuclides - important either in terms of physical or general science, or radionuclides used in various fields of science and technology, including medicine, in industrial applications, radionuclides occurring in the environment, etc. Mendeleev's periodic table contains 118 now known elements. However, there are significantly more radionuclides than stable nuclides, a total of over 2000 are known. Within a single element, several radioisotopes are usually represented, sometimes even ten or more.

Natural radionuclides
In addition to stable chemical elements, radioactive elements of natural origin also occur in very low concentrations in the natural environment. These natural radionuclides can be divided into three categories according to their origin and formation :

• Primary (primordial) radionuclides ([great]original, fossil)
  These are radionuclides that formed together with other (stable) nuclei of heavier elements during cosmic nucleogenesis by thermonuclear reactions in the interior of stars (as mentioned in §1.1. in the paragraph "Cosmic alchemy" - "We are the descendants of the stars!"), which then exploded as supernovae and enriched with these elements the germinal cloud from which our Sun and the solar system formed. They became part of the Earth during the formation of the solar system about 4-5 billion years ago, the Earth to bring them from space. To date, however, only those radionuclides have been preserved that have a very long half-life - greater than about 10⁸ years.
  Note: Some primary radionuclides have, among other things, geological significance. The heat released by the radioactive decay of natural radionuclides, uranium ^235,238U, thorium ²³²Th and potassium ⁴⁰K, is probably an important source of geothermal energy, heating the Earth's interior (see below "Geological significance of natural radioactivity").
    The most common primary radionuclide in terrestrial nature is potassium ⁴⁰K, whose average content in the earth's crust is about 3.10^-3 %. Potassium 40 decays with a half-life of T1/2 = 1.27.10⁹ years to beta^-- radioactivity to argon ⁴⁰Ar (89%) and electron capture to calcium ⁴⁰Ca (11%) - see below " Potassium - 40-K "; both of these daughter isotopes are stable, further decay no longer continues.
    Another widely used natural primary radionuclide is thorium ²³²Th (concentration in the earth's crust approx. 8-12.10^-6), which with a half-life T1/2 = 1.39.10¹⁰ years decays by alpha-radioactivity (in combination with beta) gradually into a series of radionuclides of the so-called thorium series (Fig.1.4.1 left).
    However, the most important natural radionuclides of this primordial origin in the earth's crust are uranium ²³⁸U (average concentration in the earth's crust approx. 2-4.10^-6, T1/2 = 4.51.10⁹ years), and uranium ²³⁵U (concentration approx. 2-3.10^-8, T1/2 = 7.1.10⁸ years). Both of these isotopes of uranium with alpha-decay (in combination with beta) are gradually converted into a series of radionuclides of both uranium decay series - Fig.1.4.1 in the middle and right, is described below.
  Note: The element uranium, first isolated in pure form in 1841, got its name from the then newly discovered planet Uranus (which in turn was named after the god Uranus in ancient Greek mythology). It is a heavy silvery metal (density 19 g/cm³), oxidizing in air with a dark gray coating. It was used to color glass. In 1896, radioactivity was first discovered in natural uranium ore by H. Beckerel. Due to its high density, ²³⁸U ("depleted uranium") is also used for some "non-nuclear" applications (eg projectiles with high penetration, or for shielding). However, uranium has the main use in nuclear technology as fissile material - see §1.3 "Nuclear reactions", especially the section "Fission of atomic nuclei".
    Other primordial radionuclides with long half-lives also occur in small trace amounts in nature: chlorine ³⁶Cl (T1/2= 3.10⁵ years), beryllium ¹⁰Be (T1/2 = 1,52.10⁶ years), lutetium ¹⁷⁶Lu (T1/2 = 3,8.10¹⁰ years), rhenium ¹⁸⁷Re (T1/2 = 4,16.10¹⁰ years), rubidium ⁸⁷Rb (T1/2 = 4,88.10 ¹⁰ years), samarium ¹⁴⁷Sm (T1/2 = 1,06.10¹¹ years), .... Some of them are used for radiometric dating of rocks (see "Radioisotope dating" below).
  Note:  Insignificant from the radiation point of view are some isotopes with an extremely long half-life (usually between 10¹⁴ and 10¹⁸ years), whose radioactivity is often not even safely proven - eg ⁴⁸Ca, ^64,70Zn, ⁷⁶Ge, ⁸²Se, ^92,100Mo, ¹¹⁶Cd, ¹²⁴Sn, ¹²³Sb, ^136,142Ce, ^144,145,150Nd, ^147-149Sm, ¹⁵²Gd, ¹⁵⁶Dy, ¹⁶⁵Ho, ^{180,182,183,186}W, ¹⁹²Os, ^190,192,198Pt, ¹⁹⁶Hg, ²⁰⁹Bi.

  Fig.1.4.1. Natural decay series of thorium 232Th and uranium 235U and 238U . The Neptunium decay series is shown below in the passage "Actinium 225 Ac", in the diagram at the top left. Sorry: ... the picture is unfinished! -they will come to add halves, energy + graphic design ......

• Secondary radionuclides - decay products of primary radionuclides
  By the decay of primary heavy radionuclides, a whole series of secondary radionuclides is created continuously. The natural radionuclides ²³²Th, ²³⁸U and ²³⁵U are transformed by alpha (and later even by beta) decay into nuclei, which are also radioactive, as well as their further and further transformation products. We say that these radionuclides generate radioactive decay series - chain (decay chain), where the individual daughter products show both alpha and beta radioactivity and the excited nuclei emit gamma radiation. The so-called secular radioactive balance is established in these decay series (see §1.2 "Radioactivity").
    In the terminology of the passage "Stability and instability of nuclei" §1.2 "Radioactivity", it can be said that heavy thorium and uranium nuclides "jump" down the energy levels and "rolls" into the valley of stability, until they reach an equilibrium configuration of lead or bismuth.
  Radioactive decay series
  There are three radioactive decay series in nature (Fig.1.4.1): decay series of thorium²³²Th (left), decay series of uranium ²³⁸U (uranium-radiun series - it includes the radium ²²⁶Ra - in Fig. right) and decay series of uranium ²³⁵U (middle) called uranium-actinium series *). The neptunium ²³⁷Np decay series can be artificially obtained (shown below in the passage "Actinium ²²⁵ Ac", the picture top left).
  *) Actinium ²²⁷Ac is a part of the decay series of uranium-235. In the older literature, ²³⁵U it was often called actinouran and its decay actinium series.
    These decay chains of heavy nuclei are somewhat similar :
  ¨ Primary parent nuclides have very long half-lives - millions to billions of years. As a result, a permanent (long-term) so-called secular radioactive equilibrium *) is established in the decay series (see §1.2, section "General laws of atomic nucleus transformation").
  *) More precisely, this would be the case with hermetically sealed preparations. In nature, this one is the equilibrium is disturbed by the escape of some isotopes of the decay series (especially radon gas) from the deposit.
  ¨ The decay series are isotopes of heavy elements showing mostly alpha radioactivity (to a lesser extent also beta).
  ¨ The nucleon (mass) numbers of the members of the series correspond to the formulas (n is an integer): 4.n for the thorium series, 4.n+1 for the neptunium series, 4.n+2 for the uranium series ²³⁸U and 4.n+3 for ²³⁵U series (actinium). This is due to the fact that a-decay reduces the nucleon number by 4 ( b -decay does not change them). It follows from this regularity that there are exactly 4 basic independent decay series.
  ¨ About halfway trought the series, the isotopes of gaseous radon (formerly called emanation) occurs.
  ¨ Some daughter nuclide (such as ^{211, 212, 213}Bi and ²²⁷Ac) are converted by both to a and b radioactivity, leading to branching of the decay chain. The decay b is then followed by the decay a and the decay a vice versa the decay b, so that the two branches merge again.
  ¨ Natural decay series end with stable isotopes of lead, neptunium series with bismuth.
    Natural decay series are elaborated in more detail in Fig.1.4.1, in summary they can be written as follows :
  ²³²Th ® 6 a + 4 b + ²⁰⁸Pb ; ²³⁸U ® 8 a + 6 b + ²⁰⁶Pb ; ²³⁵U ® 7 a + 4 b + ²⁰⁷Pb ; ²³⁷Np ® 7 a + 4 b + ²⁰⁹Bi .
  The Neptunium decay series is drawn in more detail below in the figure in passage Aktinium-225.
  The details of the transformations of individual radionuclides in decay series are quite complex and do not fit into draw them in Fig.1.4.1. Some nuclides of decay series are pure emitters a (eg ²³²Th, ²³⁸U, ²¹⁶Po, ......) or b (eg ²²⁸Ra, ²⁰⁶Tl, ........), however, most nuclei are transformed into excited levels of daughter nuclei and therefore emit also g radiation (they are eg ²²⁸Ac, ²¹⁴Pb, ^214,212Bi, ²¹⁰Tl, ..... .and others, but for some g is weakly represented, eg for ²²²Rn, ²³⁹Pu, ...).
  Decay series of transuranics
  Analogous decay series are also for artificially produced transurans, which ultimately follow to the mentioned basic series. E.g. ²⁴¹Am ® a + ²³⁷Np ® 7 a + 4 b + ²⁰⁹Bi - neptunium decay series; ²³⁹Pu ® a + ²³⁵U ® 7 a + 4 b + ²⁰⁷Pb - ²³⁵U-actinium decay series; ²⁵²Cf ® a + ²⁴⁸Cm ® a + ²⁴⁴Pu ® a + ²⁴⁰U ® b + ²⁴⁰Np ® b + ²⁴⁰Pu ® a + ²³⁶U ® a + ²³²Th ® 6 a + 4 b + ²⁰⁸Pb - thorium decay series. In the case of heavy transuraniums, this is accompanied by the spontaneous fission of nuclei (§1.2, section " "Exotic "types of radioactivity").

• Cosmogenic radionuclides
  These are natural radionuclides that are continuously formed by nuclear reactions during the passage of high-energy cosmic radiation (its secondary components) through the Earth's atmosphere. This includes especially radiocarbon ¹⁴C and tritium ³H, in very small quantities arise some other cosmogenic radionuclides - e.g. ^7,10Be, ³²P, ³⁵S, ³⁶Cl. The mechanism of formation of cosmogenic radionuclides is outlined in §1.6, part "Cosmic radiation", Fig.1.6.7.
  Cosmogenic radiocarbon ¹⁴C is used in archeology for radiometric age determination of objects of biological origin (see "Radioisotope dating" below).

To sum up, long- lived radioisotopes with a half-life of more than about 100 million years occur in our terrestrial nature. Of the shorter ones, only those that are continuously created by natural processes - cosmic radiation or in the decay chains of long-term isotopes. All other short-lived radioisotopes, formed during stellar nucleogenesis in large quantities (especially in supernovae), have not been preserved on Earth - they are sometimes called extinct, defunct, vanihed radionuclides; their former existence is evidenced by the observed surplus of stable products of their decay (cf. below "Radiometric dating", passage "Dating using decayed radionuclides"). Such important extinct radioisotopes are iodine ¹²⁹ I, aluminum ²⁶Al, and iron ⁶⁰Fe, whose radioactivity may have been involved in the formation of the protoplanetary disk, planets, and asteroids at the beginning of the solar system's development.

Radioactivity in the natural environment
All nature (terrestrial and space) contains a small amount of radioactivity, especially the above-mentioned natural radioactive elements. Compounds of primary and secondary radionuclides (radioactive decay series) enter the soil, water and air (especially through gaseous radon) from rocks during their erosion. During the combustion of coal, some natural radionuclides are released into the air (especially radon ²²²Rn, polonium ²¹⁰Po and lead ²¹⁰Pb), which accumulate at greater depths due to the decay of the primary natural radionuclides uranium and thorium. During volcanic activity, the ejected clouds of volcanic smoke and dust contain a significant amount of radon radionuclides, polonium-210, lead-210 from great underground depths. Compounds of cosmogenic radionuclides also enter the biosphere from the atmosphere. From soil, water and air, natural radionuclides get into plants and in the food chain into animals and humans.
  In our environment, therefore, we are constantly exposed to ionizing radiation from cosmic rays and natural radionuclides in the air, in surrounding objects, in soil and rocks, building materials, even in our bodies.

Fig.1.4.2. Scintillation spectrum of gamma radiation of clay (sample of 200g of arable land from Central Moravia). Weak gamma peaks from the secondary radionuclides of the uranium and thorium decay series (isotopes of bismuth, thallium, lead) and a relatively significant 1460 kV peak of the primary radionuclide potassium 40-K are evident.

In recent decades, this has been approached by radiation exposure to artificial radiation sources - X-rays, accelerators, artificial radionuclides. Especially in targeted use in medical radiodiagnostics and radiotherapy, and possibly also from unwanted radioactive contamination (radiation accidents, nuclear waste) - §5.2, part "Sources of radiation by ionizing radiation". The favorable and unfavorable biological effects of that natural and artificial radiation are discussed in detail in §5.2 "Biological effects of ionizing radiation".

Geological significance of natural radioactivity
Although the relative content of natural radionuclides in the "building" material of the Earth is not high, their total amount in the Earth's interior and crust is so large, that the energy released by them can have considerable geothermal significance.
  According to current geological knowledge, our planet Earth consists of several layers. The solid surface consists of a relatively thin layer of earth's crust, the so-called lithosphere (Greek lithos = stone), about 5-50 km thick (depending on whether we are in the sea, land, mountains). The Earth's crust is not solid, but is "broken" into individual lithospheric plates which move slowly relative to each other. Below it lies the Earth's mantle (further divided into the upper and lower mantle), which is to some extent malleable (plastic) and forms the largest part of the volume and weight of the globe. It consists of partially molten rocks with a temperature of about 600-1250 °C. Thermal convection takes place in the mantle, through which heat is transferred from the inner part of the Earth to the surface. The plasticity of the mantle, on which the individual parts (plates, "floes") of the earth 's crust "float", and the convection of heat is the driving force of continental shifts, plate tectonics and volcanic activity *). Inside the Earth is the Earth's core (Moon size) in which the temperature is likely to exceed 4000 °C; its outer part is fluid, the inner core at the very center of the Earth is (according to indirect geological measurements) solid. The solid iron inner core of the Earth "floats" and rotates in the liquid outer core, which generates a geomagnetic field. This magnetic field creates a "shield" against ionizing cosmic radiation and the solar "wind". Without him, life on the planet would not be possible.
*) These are "ordinary" volcanoes located in places where lithospheric plates collide. However, beneath the thin shell of the earth's crust, in the earth's mantle, like a "time bomb", massive streams of hot molten rocks rise by thermal convection . If it melts to the surface, under great pressure they erupt as destructive supervolcanoes .
  Total heat flux from the Earth's interior is estimated at about 45 Terawatts *). Such a massive heat flux is difficult to explain by the heat remaining inside the Earth (due to the long time of about 4.5 billion years since the Earth's origin), or tidal gravitational action during the Earth's rotation, the Moon's orbit around the Earth and the Earth around the Sun (§1.2, passage "Gravitational gradients - tidal forces" in the book "Gravity, black holes ..."). The radioactive decay of natural radionuclides could contribute about 60% to the development of heat in the Earth's interior. After 8-10 TW, the decay series of ²³²Th and ^{238 + 235}U isotopes could supply, ⁴⁰K of radioactive potassium would contribute 3-5 TW of heat flux. Without heat from naturally occurring radioactivity, the Earth's core would have cooled and solidified billions of years ago, which would probably have prevented the origin and development of life on Earth ("Anthropic Principle or Cosmic God", part "Stars, Planets, Life") ..!..
*) The average density of geothermal heat flux at the Earth's surface is about 65-100 mW/m², which is less than ten thousandths of the intensity of incident solar radiation.
  It has also been hypothesized that a natural fission nuclear reactor similar to the one found in the Oklo mine could operate inside the Earth (see §1.3, section "Nuclear reactors", section "Natural nuclear reactors? "). Billions of years ago, when the concentration of fissile uranium ²³⁵U was still high enough, this is quite likely. In order for such a reactor to function even at the present time, when the share of fissile ²³⁵U considerably decreased, the concentration of uranium in the material inside the Earth would have to be significantly higher than in the rocks we know of the earth's crust; about it we have no evidences.
  We have relatively little information obtained indirectly about the structure of areas inaccessible to us. Important data on the distribution of radioactive elements in the Earth's interior could be obtained by detecting neutrinos, so-called geoneutrinos, formed during b- radioactive decay of natural radionuclides, which freely pass from the Earth's interior through thick rock layers to the surface (see §1.2, section "Neutrinos - "ghosts" between particles", passage "Neutrinos from natural radioactivity").

Radioisotope (radiometric) dating
The independence of the rate (half-life) of radioactive decay from external conditions *) allows the use of the exponential decay law of radioactivity as a kind of clock - a natural "chronometer".
*) Situations where the course and rate of radioactive decay may depend somewhat on external radiation or chemical factors are discussed in §1.2, section "Independence of radioactive decay on external conditions".
  The basic idea of using radioactive decay to measure time is simple. If we know the initial number N₀ (at time t = 0) of radioactive nuclei of the parent nuclide X with a known half-life T_1/2 in the sample, then by measuring the absolute activity A(t) of the sample, or the ratio of the concentration of parent X and daughter Y isotopes, at some later time t we can determine from the decay law this time t , elapsed from the sample (t = 0) to the time of measurement - thus the age of the sample. From the decay law of radioactivity (derived in §1.2, part "General laws of transformation of atomic nuclei") N_X(t) = N_X(0).e^-l.t = N_X(0).e^{-t.(ln2/T1/2)} = N_X(0).2^{-t /T1/2} ; N_Y(t) = N_X(0).[1-e^-l.t] = N_X(0).[1-e^{-t.(ln2/T1/2)}] = N_X(0).[1-2^{-t /T1/2}], for the sought age t the formula follows
         t = T_1/2 . [1 + N_X(t) / N_Y(t)] ,
where N_X(t) is the current amount of the parent element X and N_Y(t) is the current amount of the daughter element Y in the test sample (the initial amount of N_X(0) of the parent radionuclide is usually unknown, sometimes we try to estimate it, eg at ¹⁴C).
  All materials (on Earth and in space) contain a small amount of natural radionuclides with long half-lives. The rates of their radioactive transformation can, under certain conditions, be used to determine the ages of various objects and samples of materials. This method of determining the age of samples is generally called radioactive, radioisotope or radiometric dating, or radioisotope chronometry; according to the investigated nuclides then eg radiocarbon dating (using carbon-14, described below), potassium-argon or uranium-lead dating. It is used in archeology, paleontology, geology (geochronology) and astronomy (age of meteorites and planets).
  There are two basic conditions that should be met for accurate radioisotope dating :
1. The initial conditions are known - the concentrations or ratios of the parent and daughter isotopes at the time of the natural origin of the investigated material (at time "0");
2. The investigated materials must be closed or isolated systems from their inception, so that no parent or daughter isotopes have escaped or entered them.
  These conditions are never 100% met, so "straightforward" radiometric dating is not completely accurate. It will be outlined below which methods can be used to perform independent calibrations and increase the accuracy and reliability of radioisotope dating (so-called isochronous and cocondon dating is described).
 Radiocarbon dating method (also called carbon chronometry)
using radiocarbon ¹⁴C, which is formed by the action of neutrons ejected by cosmic radiation from the nuclei of atoms, on nitrogen in the upper layers of the Earth's atmosphere: n^o + ¹⁴N₇ ® ¹⁴C₆ + p⁺ (see §1.6, section "Cosmic radiation", Fig.1.6.7). This creates about 2 atoms of ¹⁴C per second per 1 cm³ of atmosphere. Carbon ¹⁴C, as a long-term radionuclide (T1/2 = 5730 years, pure b^-, energy 158keV) constantly contaminates the biosphere, oxidizes to ¹⁴CO₂ in the atmosphere, enters the biocycle - the food chain of living organisms on Earth. Through photosynthesis, it gets from the atmosphere into plants, from there through food into the bodies of animals. It is therefore contained in all living organisms. The concentration of 1 atom of ¹⁴ C is stabilized to about 8.10¹³ atoms of ordinary ¹²C; one gram of natural carbon in all living organisms contains an activity of about 0.25 Bq ¹⁴C. After the organism dies, its metabolic contact with the atmosphere and the supply of ¹⁴C are interrupted, so that the concentration of radium carbon begins to decrease by its radioactive b -decay ¹⁴C ® ¹⁴N + e^- + n´ with a half-life of 5730 years. This also changes the relative proportion between the carbon isotopes ¹⁴C, ¹³C and ¹²C.
  From the ratio between the relative proportion of radioactive isotope ¹⁴C and stable isotopes of carbon in the studied historical object of biological origin (eg wood, remains of organisms, etc.) we can approximately determine the age of this object - the time that has elapsed since the death of the organisms from which the object originated. This method was first used by W.F.Libby in 1946.
  In the simplest case, we measure the specific activity of ¹⁴C in the investigated historical object of biological origin and compare it with the equilibrium specific activity of radiocarbon in the atmosphere and in living organisms. Sensitivity of ¹⁴C activity measurements using proportional or scintillation detectors with liquid scintillators (see §2.6, section "Liquid scintillators"), due to the half - life of ¹⁴C 5730 years, limits the time range of this method to about 30 000 years. Substantially lower values of ¹⁴C/¹²C can be determined by mass spectrometry (see §2.6 , section "Magnetic spectrometers"). The precondition for the correctness of radiocarbon chronometry is that the ratio of ¹⁴C/C¹² in the past, was always the same during the period from which the measured samples originated. In order for this ratio to remain constant, the intensity and composition of cosmic rays and their effects on the upper atmosphere must remain constant. The primary cosmic rays coming from interstellar space are likely to be constant for at least 10⁵ years. However, the component coming from the Sun is time-varying depending on solar activity (occurrence of sunspots). The effect of cosmic rays on the upper atmosphere depends on how strong the shielding from the Earth's magnetic field is. The intensity of the geomagnetic field fluctuates by about 50% in time periods of about 10⁴ years. Another problem is the anthropogenic influence (human civilization activity) on the distribution of radionuclides in the atmosphere. It is both the burning of fossil fuels that affect the CO ₂ content in the atmosphere, and the radiocarbon released into the atmosphere by nuclear tests, especially in the 50s. Determining the concentration of radiocarbon is thus also of considerable ecological importance. For accurate radiocarbon chronometry, all these influences are distorting, it is necessary to take a correction, compile a calibration curve by comparison with other independent methods (eg with dendrochronology - dating using annual rings in the wood of old trees).
 Chronology of natural events using ¹⁰Be
Another cosmogenic radionuclide with a long half-life is beryllium ¹⁰Be. It is formed in the upper layers of the atmosphere from oxygen and nitrogen by nuclear reactions with secondary neutrons ejected by high-energy cosmic rays. ¹⁰Be with a half-life T1/2 of 1.6x10⁶ years by beta^- -radioactivity decays into the stable isotope ¹⁰B. It is used to investigate rock weathering, soil formation and erosion, lake sediment chronology. It is interesting to measure the concentration of the beryllium isotope ¹⁰Be in different layers of glaciers as an indicator of solar activity in ancient times - as a result of the interaction of cosmic rays and the solar wind (the modulation of cosmic rays by the solar wind is discussed in §1.6, the passage "Stellar - solar - "wind"").
 Luminescent dating - optical and thermoluminescent , 
is based on the "deposition" of electrons released during long - term irradiation of materials with natural radiation in metastable levels and their subsequent release by heating or light irradiation of the sample (see §2.2, passage "Thermoluminescence and photoluminescence dosimetry", paragraph "Luminescent archaeological dating").
 Long-time minerals dating
Radiocarbon method is not applicable for dating inorganic materials such as rocks, and also for very long periods of time over millions or billions of years. Here, under certain circumstances, the decays of other long-term natural radioactive isotopes can be used, such as the decay of potassium ⁴⁰K to argon, the decay of the radioactive isotope rubidium 87 to strontium, or the decay of uranium and thorium to the final element of the decay series - lead. Radioactive dating by determining the relative proportion of daughter radiogenic decay products with respect to the parent nuclides makes it possible in geology to determine the absolute age of rocks *), the duration of individual geological epochs, the age of meteorites, the Earth, the Moon and the solar system. However, the accuracy of these methods is, in addition to the technical difficulties of determining small amounts of nuclides, limited by the variety of samples found and their previous destinies.
*) Age of rocks
Under the age of minerals in mineralogy and geology, the time interval from the time of mineral formation by solidification and crystallization from molten matter to the present (measurement times) is understood. It is assumed that during solidification, the material composition of the mineral is closed ("preserved"), which then does not change otherwise than radioactive transformation.
Note: Due to the small concentrations of the investigated radionuclides and their long half-lives, a simple method of measuring the radioactivity of samples cannot be used. Determination of the concentration of analyzed nuclides is performed by mass spectrometry (see §2.6 , section "Magnetic spectrometers").
 Potassium - argon method for determining the age of minerals
The K-Ar dating method in nuclear geochronology uses the decay of natural (primordial) radioactive potassium ⁴⁰K with a half-life of 1.26 billion years to stable argon ⁴⁰Ar. Natural potassium consists of three isotopes: ³⁹K (93.258% - stable), ⁴⁰K (0.0117% - radioactive) and ⁴¹K (6.73% - stable). The radioactive isotope ⁴⁰K decays with a half-life of 1,28.10⁹ years in two ways: b^-  (89.1%) ⁴⁰K ® ⁴⁰Ca + e^- + n to calcium; b⁺  (10.9%) ⁴⁰K ® ⁴⁰Ar + e⁺ + n to argon. In a mineral containing potassium from the moment of its formation in crystalline form (and closure), the radioactive isotope of potassium ⁴⁰K decreases and a stable isotope of argon ⁴⁰Ar, resulting from the conversion of ⁴⁰K, accumulates. The age of the mineral can be determined by measuring the content of both isotopes. The ⁴⁰K content is determined by measuring the potassium content of the mineral and the known proportion of the isotope ⁴⁰K in the potassium. To determine the content ⁴⁰Ar, the sample is heated in vacum to a temperature of about 2000 °C, whereby argon gas is released from the crystal lattice and the ⁴⁰Ar content is determined by mass spectrometry.
  A complementary and refining method of the K-Ar dating method is the argon-argon (⁴⁰Ar /³⁹Ar) dating method. The mineral sample is first irradiated with neutrons in a nuclear reactor, whereby a reaction of ³⁹K(n, p)³⁹Ar takes place on the nuclei of a stable isotope of potassium ³⁹K. The irradiated sample is then heated in vacum to release both argon isotopes and their content is determined by mass spectrometry. The age of the mineral is determined from the ratio of the contents of the two isotopes of argon (since the amount of ³⁹Ar formed by the reaction with neutrons is proportional to the potassium content of the mineral).
 Rubidium-strontium dating
is based on the beta^- -radioactive conversion of the natural primordial isotope rubidium-87 : ⁸⁷Rb ® ⁸⁷Sr + e^- + n´ to strontium-87 with a half-life of 4,8.10¹⁰ years. If the mineral contains at least a small amount of rubidium, this very slow radioactive transformation causes the content of natural rubidium ⁸⁷Rb to decrease and the content of radiogenic strontium ⁸⁷Sr to increase since the formation of the mineral by crystallization from molten rock. The age of the mineral can be determined from the measured ratio of both isotopes. A complication, however, is that minerals may contain certain amounts of natural strontium and thus of the ⁸⁷Sr isotope of non-radiogenic origin *). Therefore, in order to accurately determine the age of the analyzed mineral, it is necessary to correct the determined content of ⁸⁷Sr to the content of non-radiogenic ⁸⁷Sr. The determination of another isotope strontium - ⁸⁶Sr is used for this (again by mass spectrometry). On the basis of the known ratio of ⁸⁷Sr/⁸⁶Sr isotope in natural non-radiogennic strontium (in minerals containing no rubidium), can then be from determined whole content of ⁸⁷Sr, to subtract the content of non-radiogenic ⁸⁷Sr.
*) The nuclei of the ⁸⁷Sr isotope of non-radiogenic origin were formed together with other strontium isotopes during the nuclear synthesis of elements in space (in supernovae), not by radioactive transformations of ⁸⁷Rb.
 Dating of rocks by decay of uranium and thorium to lead
This method U-Pb, Th-Pb is based on measuring the current amount of the parent element X (uranium ²³⁵U, ²³⁸U or thorium ²³²Th) and the end daughter element Y of the respective decay series (lead ²⁰⁷Pb, ²⁰⁶Pb or ²⁰⁸Pb) - see above "Natural decay series", Fig.1.4.1. From the decay law of the relevant parent element X with a half-life T_1/2, we then obtain for the resulting age t the relation:
             t = T_1/2 . [1 + N_X(t) / N_Y(t)] ,
where N_X(t) is the current amount of the parent element X and N_Y(t) is the current amount of the daughter element Y (of the relevant lead isotope).
A suitable mineral that serves as a "carrier" for uranium or thorium is zirconium silicate ZrSiO₄, which is commonly found in rocks of volcanic origin. During the formation of a zirconium crystal, uranium or thorium, but not lead, easily enters its crystal lattice. Therefore, when dating, we can assume that all the lead in the sample is of radiogenic origin - it was formed by the decay of uranium or thorium. .............
..... concordant dating - below ...........
 Dating using decayed radionuclides
The above methods of radiometric dating require that a certain amount of a small, but measurable portion of the initial parent radionuclide. This can be a problem with the oldest samples originating, for example, from the beginnings of the formation of our solar system. In such a case, paradoxically, dating with radioisotopes with a shorter half-life that have already decayed ("died out") and are not present in the sample, may help. However, their breakdown products, stable daughter nuclides, are present in the sample. By measuring the concentration of these extinct radionuclide daughter products by mass spectrometry, the relative age of the analyzed sample can then be determined. In co-production with the isochronous technique, it is possible to calibrate, for example, the U-Pb method and specify the determination of absolute age.
  This category includes ¹²⁹I - ¹²⁹Xe iodine-xenon chronometry. When the supernova explosion occurs, among others, as well as large amounts of radioactive iodine ¹²⁹I is created. The radionuclide iodine ¹²⁹ I with a half-life of 15.7 million years (which is the current view seems long, but the astronomical point of view is quite short ...) converts by beta^- -radioactivity to the stable xenon isotope ¹²⁹Xe. In xenon isolated from stone meteorites of chondrites, a higher content of the isotope xenon ¹²⁹Xe was found, than corresponds to its usual representation in natural xenon. Surplus ¹²⁹Xe in chondrites was creates by radioactive decay of the isotope ¹²⁹I (it is radiogenic ¹²⁹Xe), which was chondrite material enclosed in the formation of a solid silicate composition after cooling the hot gaseous nebula of supernova. In the protoplanetary stage of our solar system, this occurred in the period between about 4.8-4.5. 10⁹ years, before the formation of our planetary system.
  In practical use, iodine-xenon chronometry is a relatively complex isochronous laboratory method. The samples are irradiated with neutrons in a nuclear reactor, whereby the stable iodine ¹²⁷I isotope is converted to radioactive ¹²⁸I by neutron capture and the subsequent beta conversion to stable xenon ¹²⁸Xe. After irradiation, the sample is heated and the released xenon is analyzed in a mass spectrometer, comparing the content of 129-I and 129-xenon. ......
 Determining the time of formation of meteorites
Meteorites, especially some stone types called chondrites, are among the oldest bodies in our solar system. They were formed when the protoplanetary disk cooled, before the formation of planets (.....). ... link .....  Isochronous dating method
Simple dating methods can be adversely affected by ignorance and variability of initial conditions (different concentrations of parent and daughter nuclides) and the possibility of migration of relevant nuclides between the analyzed material and the environment. To eliminate these effects and refine long-term radioisotope dating, the so-called isochronous method was developed. This more complex (but very elegant) method uses the collection of mineral samples from two or better several different parts (components) of the analyzed rock and performs isotope analysis using three isotopes: not only the parent and daughter element, but also the content of another isotope of the daughter element.
  Thus, we have in the analyzed material the starting parent radioactive nuclide X , which decays with a time T_1/2 to a stable daughter radiogenic nuclide Y´; the relevant daughter element has yet another stable Y isotope (of non-radiogenic origin). Because all isotopes of a daughter elementY have the same chemical properties, the ratio of these isotopes N_Y´ / N_Y in the whole analyzed rock is the same. In contrast, the X isotope has different chemical properties and the initial N_X / (N_Y´ + N_Y) ratio is different for different minerals at the time of rock formation. Due to the decay of the radioactive isotope X, the relative proportions of N_X / N_Y and N_Y´ / N_Y in different rock minerals will be different after a sufficiently long time.
  The amount of nuclide Y´ in the analyzed material consists of the original initial amount N_Y´(0) and the nuclei formed by the radioactive decay of the radionuclide X. From the law of exponential decay of the parent radionuclide X follows for the time increase of the concentration of the daughter stable radoiogenic nuclide Y' the relation N_Y´(t) = N_Y´(0) + N_X(t).[e^l.t -1] . Dividing this relationship by the amount N_Y of another stable isotope Y we get the equation for the nuclide concentration ratios :
             [N _Y´ / N _Y ] _(t) = [ N _Y´ / N_Y ] ₍₀₎ + [N _X / N _Y ] _(t) . [e ^{l . t} - 1] .
If we choose the time t as a parameter, it is in the ratios of nuclide concentrations the linear equation y = a.x + b, whose graph is a line called an isochron (Greek isos = the same, chronos = time - isochron is a line connecting on the graph of a place with the same time occurrence of the displayed phenomenon). The slope of this line tg a º a = e ^{l . t} - 1determines the time t (age), the intersection point (intercept) with a vertical axis b = [N_Y' / N_Y]₍₀₎ specifies otherwise unknown initial ratio nuclides Y' and Y .
  Therefore, we measure the current content of N_X(t), N_Y´(t), N_Y(t) of these three isotopes in several samples and plot the ratio N_X / N_Y on the horizontal axis and the ratio N_Y´ / N_Y on vertical axis (Fig.1.4.3 left). Using the least squares method, we interpolate the linear regression function - representing the line isochron. If the dependence N_Y´ / N_Y is a linearly increasing function of N_X / N_Y (individual points "fit" well on a straight line), this indicates a good correlation between the measured loss of radioisotope X and the measured increase of the daughter isotope Y´. The regression line has the form y = a.x + b, where b represents the original ratio of the elements N_Y´(0) / N_Y(0). The resulting age t is then determined from the relation :
             t = (ln2 / T_1/2 ) . [N _Y´ (t) / N _Y (t) - N _Y´ (0) / N _Y (0)] / [N _X (t) / N _Y (t)] ,
where T_1/2 is the half-life of the initial parent nuclide X . The initial ratio N_Y´(0) / N (0) is found from the regression line.

Fig.1.4.3. Isochronous and concordant analysis in long-term radiometric dating. Left: Linear regression function - isochron for Rb/Sr dating - interpolated points [NX/NY, NY´/NY] from several samples of the same rock. Right: Concordia curve for 235U + 238U dating, together with discordia (error line) fited with measured values of samples of the same rock.

  The great advantage of the isochronous method is its independence from the original isotope ratio of the daughter element: this unknown original ratio is obtained from the regression line. The original ratio of Y and Y´ isotopes may have been very different in the past, and yet the same age comes out. If the points in the isochron graph do not lie on a straight line, this indicates some events that have disrupted a closed rock system throughout history. The resulting value of age will then not be accurate, and from the regression analysis we can determine the mean square error of the obtained average value.
  The most commonly used triplets of isotopes for the isochronous dating method are listed in Table ( X- the default parent radoionuclide, Y´ - its stable daughter nuclide, Y - another stable isotope of this daughter element) :

As mentioned above, the reliability and accuracy of long-term dating techniques is, in addition to technical difficulties, limited by the variety of samples found and, in particular, by ignorance of their previous destinies over millions or even billions of years in their history. In exact archaeological, paleontological and geological dating, therefore, great emphasis is placed on the agreement of the results obtained by various independent methods - we are talking about the so-called concordant dating (lat. Concordantiae = agreement, consent, conformity) .
 Concordant radioisotope dating
In radioisotope dating, compliance can be analyzed using two different radionuclides, mainly uranium ²³⁵U and ²³⁸U. It is used here that two radioactive clocks imaginarily, "ticking" inside the sample: the faster "ticking" uranium-235 transforms with a half-life of 700 million years, the slower clock is based on uranium-238 with a half-life of about 4.5 billion years. Comparing the results from both of these chronometers makes it possible to refine the determination of the age of the sample.
  Two isochronous equations follow from the decay laws for both uranium :
          [ ²⁰⁶ Pb / ²⁰⁴ Pb ] _(t) = [ ²⁰⁶ Pb / ²⁰⁴ Pb ] ₍₀₎ + [ ²³⁸ U / ²⁰⁴ Pb ] _(t) . [e ^l238U ^{. t} - 1] ,
          [ ²⁰⁷ Pb / ²⁰⁴ Pb ] _(t) = [ ²⁰⁷ Pb / ²⁰⁴ Pb ] ₍₀₎ + [ ²³⁵ U / ²⁰⁴ Pb ] _(t) . [e ^l 235U ^{. t} - 1] .
If from several measured samples of the same rock we get using these equations two identical independent values of age t - there was a concordance (consent), it is a significant indication of accuracy of the dating method.
  From these two isochronous equations we can also create a so-called concordance diagram (Fig.1.4.3 on the right). Plot the ratio ²⁰⁷Pb/²³⁵U on the horizontal axis (on a linear scale) and the ratio ²⁰⁶Pb/²³⁸U *) on the vertical axis. We use the time t as a parameter: for different values of t we graphically plot the points {[²⁰⁷Pb/²³⁵U]_(t) ; [²⁰⁶Pb/²³⁸U]_(t)}. This creates a theoretical curve called a concordia, each point of which gives a concordant value of age t and the ratio of the concentrations of lead and uranium isotopes, provided that no nuclides have entered or escaped from the sample. The values of specific samples from the analyzed mineral are then plotted in this graph. We get points that do not generally lie in the concordia, because the assumption of closure may not be met. Since all isotopes of uranium and isotopes of lead have the same chemical properties, their possible leakage from the material is the same and the measured values of the uranium to lead ratio should lie on a straight line. Therefore, we interpolate a straight line with the measured points - called discordia (Latin inconsistency, disagreement , discrepancy), whose intersections with the concordia represent the initial time t0 crystallization of the material ("maximum age") and time t´ ("minimum age") corresponding to a possible metamorphosis event during the history of the sample. The concordant diagram serves as an internal check of the dating method, allowing to detect events that violated the conditions of correct dating.
*) These are ²⁰⁷Pb and ²⁰⁶Pb radiogenic lead : the initiation of ²⁰⁷Pb (0) and ²⁰⁶Pb (0) is subtracted from the total measured amount of these isotopes using the isochronous method .
 Determination of the age of the Earth and the Solar system 
Radiometric dating with the help of radionuclides with a very long half-life has been significantly applied not only to geological minerals, but also to determine the age of our planet Earth and the entire solar system. Using only geological methods, determining the age of the Earth is problematic, inaccurate, basically impossible. Due to geological processes - weathering, plate tectonics, volcanism, hydrothermal processes - the chemical and physical composition of the rocks changed significantly.
  In the first half of the 20th century was the main pioneer of radiometric dating of rocks, geochronology, A.Holmes, who with the gradual refinement of uranium-lead methods determined the age of rocks in the range of about 1.5-3 billion years. His successor, C.C.Patterson, also used the uranium-lead method on the age of meteorites from the early periods after the formation of our planet. Meteorites as cosmic bodies are more advantageous for dating because they have not been altered by any geological processes. In 1965, Patterson measured samples from meteorites found near the Barringer impact crater in Arizona and reached an age value of 4.55 billion years. These measurements were repeated many times, averaging 4.56 billion years (± 1% deviation).
  So this is the value of the age of the planet Earth and at the same time the whole Solar system. All the material in the solar system was formed at about the same time, the various chemicals, including radioactive isotopes, formed together. This is shown by measurements of different meteorites from different regions of the Solar system - individual planets formed at virtually the same time (from an astronomical point of view).
  On the formation of stars and planets and their chemical evolution, see §4.1, part "Evolution of stars", on primordial cosmological nucleosystesis §5.4, part "Lepton era. Initial nucleosynthesis" in monograph "Gravity, black holes and space-time physics". For determining the ages of various objects in the universe (stars, galaxies, the entire universe), see §4.1, passage "Ages of objects in the universe".

Production of artificial radionuclides
For the needs of current science and technology, industry and healthcare, we are far from sufficient with a few radionuclides of natural origin (natural radionuclides uranium 235 and 238 are, however, the basis of fission nuclear reactors and nuclear energy based on them). So we have to make radionuclides artificially :

Fig.1.4.4. By bombarding the target nucleus A with an accelerated elementary particles, the nuclear reactions produces the resulting core B, which may be raduoactive.
The resulting nucleus B is initially formed usually in the excited state B', followed by deexcitation of gamma photon emissions. This is usually not important for the production of radionuclides, except in situations where the excited nucleus is metastable with a longer half-life.

In order to produce a radioactive nucleus from a stable nucleus, it is necessary to change the number of protons or neutrons so that the equilibrium configuration is disturbed. As discussed in the previous §1.3 "Nuclear reactions", we achieve this according to Fig.1.4.4 by bombarding initial target nucleus A suitable particles - protons or neutrons (or alpha-particles, deuterons, occasionally heavier ions) that enter into the nucleus and bring about appropriate changes there - nuclear reactions; the resulting nucleus B is formed (mostly in the excited state B*, after emission the gamma radiation then in the ground state), which is often radioactive.
Production equation and yield 
Thus, if we irradiate a target containing N atoms of the initial irradiated element (nuclei A) with a beam of particles (protons or other charged particles from a cyclotron, or neutrons from a nuclear reactor) with intensity I [number of particles/cm² /sec.], the atoms of the resulting radionuclide (B) will gradually accumulate in the target. During the irradiation time t , the activity A(t) of the desired radionuclide B in the target will be approximately given by the production equation
                         A(t) = I. N. s . (1 - e ^{-l .t} ) ,
where s [cm²] is the effective cross section of a given nuclear reaction and l [s^-1] is the decay constant of the emerging radionuclide B (related to the half-life by the relation l = 0.693/T_1/2). The amount of activity produced is thus directly proportional to the intensity of the irradiating beam I, the amount of target substance and the effective cross section of the reaction *). Initially, this amount is approximately proportional also to the irradiation time t , but the effect resulting from radioactive decay of the radionuclide, expressed saturation factor (1 - e^{-l T}), the increase in the number of generated nuclei gradually slows down and after about 5-6 half-lives of the resultant radionuclide B, the saturation state (approx. 98%) is already achieved, the rate of production and disintegration is balanced, the activity no longer increases during further irradiation. The resulting activity of the produced radionuclide B is then A = I.N.s .
*) These regularities apply under simplified assumptions of a homogeneous and time-constant beam of radiation and a thin target containing many times more starting atoms (A) than the number of emerging nuclei (B).

^{A typical dependence of the effective cross section of nuclear reactions on the energy of bombarding with neutrons (left) and protons (right).}

The effective cross section of a nuclear reaction, and thus the yield of production, depends significantly on the energy of the irradiating particles. This dependence is generally complex and diverse for different types of production reactions.
  When irradiated with neutrons, the effective cross section for slow neutrons is usually higher (although some reactions take place on the contrary with higher energy neutrons). With increasing energy, the efficiency decreases monotonically, as faster neutrons remain in the field of nuclear forces for a shorter time, thus reducing the likelihood of a nuclear reaction. In the region of tens and hundreds of eV, the energy dependence appears to be a complex structure of resonant maxima and minima (caused by discrete levels of nucleon energies in the nuclei).  
  Irradiation with protons (as well as deuterons or heavier positive particles) leads to nuclear reactions only when a certain threshold energy required to overcome the repulsive electrical (Coulomb) barrier around the nucleus *) is reached, with the cooperation of the tunneling phenomenon. Therefore, the effective cross section initially increases significantly with energy, reaches a maximum and then decreases monotonically (because energy protons fly quickly through the region of the nucleus and in this short time the nuclear reaction is less likely to take place). For the simplest reaction (p, n) in medium-heavy nuclei, the threshold energy of protons is about 5 MeV and a maximum yield is reached around 10 Me. For more complex reactions, with alpha-particles and heavier nuclei, the yield curve is shifted to higher energies, 20MeV and higher.
*) At lower energy, a proton can penetrate the nucleus only through a quantum tunneling phenomenon (§1.1, passage "Quantum tunneling phenomenon"), with a much lower probability.
  These laws of energy dependence apply not only to the required production reactions, but also to possibly other parallel "parasitic" reactions running in the target material, in which radionuclides other than the required ones are formed - radionuclide impurities. It is therefore necessary to set a certain optimal energy, guaranteeing a high production yield with a minimum content of radionuclide impurities.

Fig.1.4.5. Production of radioisotopes by irradiation of target nuclei in a nuclear reactor (left), a neutron generator (middle) and a cyclotron (right).

Production of radionuclides in a nuclear reactor
The easiest way is to irradiate the nuclei with neutrons - since the neutron does not have an electric charge, it does not cause electric repulsive forces and even a slow neutron willingly enters the nucleus. The most common reaction here is simple neutron capture (n, g) : ^NA_Z + n^o ® ^N+1B_Z + g *) , but reactions of type (n, p), (n, a) can also occur. Irradiation with neutrons generally produces nuclei with an excess of neutrons, which usually show radioactivity b^-. The nuclear reactor is an intense source of neutrons (§1.3, part "Nuclear reactors"), so that these b^- radionuclides are produced by irradiating a suitable target material in the irradiation chamber of the reactor - Fig.1.4.5 on the left. Some reactions of radionuclide production by neutron irradiation are, for example: ⁶Li(n,a)³H, ¹⁴N(n,p)¹⁴C, ³²S(n,p)³²P, ⁹⁸Mo(n,g)⁹⁹Mo, .... Specific methods for producing a number of important radioisotopes are described below in the section "Properties of some of the most important radioactive isotopes".
*) Note: Neutron capture during the formation of radioactive nuclei is also used in a very sensitive method of chemical composition analysis - neutron activation analysis. Irradiation of the examined sample with neutrons results in the formation of radionuclides ("activation"), after which therelevant radionuclide and the corresponding (inactive) starting nuclide can be determined by spectrometric analysis of the emitted radiation energies (especially g) of the activated sample, using calibration also its content in the investigated material. The method is described in more detail in Chapter 3 "Application of ionizing radiation", §3.4, section "Neutron activation analysis".
  Another frequently used method for the production of radionuclides in a nuclear reactor is the irradiation of uranium ²³⁵U with neutrons, which causes the fission of uranium nuclei into smaller nuclei that are radioactive, eg :
²³⁵U + n ® ²³⁶U ® ¹³¹I + ¹⁰²Y + 3n
                         ® ¹³⁷Cs + ⁹⁷Y + 2n
                         ® ¹³³Xe + ¹⁰¹Sr + 2n
                         ® ⁹⁹Mo + ¹³⁵Sn + 2n
                         ® ¹⁵⁵Sm + ⁷⁸Zn + 3n
            ......... and other radionuclides.
  From these fission products, the required radionuclides (e.g. ¹³¹I, ⁹⁹Mo, ¹³³Xe and others) are then isolated by radiochemical methods. Since the heavy nuclei of uranium have a significantly higher percentage of neutrons than the medium - heavy nuclei formed by their fission, these radionuclides have an excess of neutrons and show radioactivity b^-.
  A less commonly used method for the production of radionuclides is their chemical separation from fission products of uranium as fuel in the reactor. In a nuclear reactor, ²³⁵U (or ²³⁸U) uranium nuclei split after the entry of neutrons into two nuclei, chemically falling into the middle part of Mendeleev's periodic table, which are mostly radioactive. The most common nuclei formed in this way are, for example, ¹³¹ I, ¹³⁷ Cs, ⁹⁰ Sr, .... Spent fuel cells from the reactor contain a large amount of these radionuclides (of the order of TBq). However, it is very difficult to radiochemically isolate individual radionuclides from this diverse mixture so that the radionuclide obtained does not contain traces of other radionuclides - in order to have a satisfactory radionuclide purity, was not contaminated.
Accelerator-controlled neutron generator
In addition to nuclear reactors, accelerators can also be intense sources of neutrons. Protons accelerated to high energies are allowed to strike a (primary) heavy metal target (lead, bismuth, tungsten), where they cause fragmentation reactions in which a number of particles and fragments, especially large numbers of neutrons, are ejected from the target nuclei. The neutrons slow down in the moderator (it can be water, which also cools the target) and hit the production targets, located around the place of neutron formation, in which the nuclear reactions produce the desired radioisotopes - Fig.1.4.5 in the middle.
  This method is still rather experimental, but it seems relatively promising. In addition to the production of radionuclides, it also enables the disposal and reprocessing of radioactive waste with long-term radioisotopes and the extraction of nuclear energy from thorium - it is discussed in more detail in §1.3, section "Nuclear reactors", section "Accelerator-controlled transmutation technology ADTT".

Production of radionuclides in the accelerator
For the production of positron b⁺ -radionuclides, on the contrary, it is necessary to add protons to the nucleus. In order for the p⁺ proton to enter the nucleus, it must be accelerated to a high energy of the order of hundreds of keV to several MeV in order to overcome the repulsive electrical Coulomb force of a positively charged nucleus with its kinetic energy. The most common proton accelerators are cyclotrons (§1.5, passage "Cyclotron"), which accelerate protons by electromagnetic forces during many orbits in a circular path (maintained by a magnetic field) to high energies. The proton beam is then led out from the circular path by the magnetic field and impinges on a suitable target material - Fig.1.4.5 on the right. Depending on the energy of the protons, a number of reactions can take place. The simplest of these is the radiation capture of a proton (p, g): ^NA_Z + p⁺ ® ^N+1B_Z+1 + g, but reactions of the type (p, p), (p, n), (p, d), (p, a) also occur, especially at higher energies and in heavier nuclei.
  For the purpose of the nuclear reaction and transmutation, in addition to protons, the nuclei can be irradiated with other fast charged particles: deuterons d - take place mainly reactions (d, n), (d, p), a-particles - reactions (a, p), (a, n) *) occur, or even heavier nuclei or ions.
*) Note: Nuclear reactions (a, n) are also used as neutron sources. For this purpose need not have a helium nucleus artificially accelerated, but suffice with suitable a -radionuklides which we mix homogeneously with a suitable target material - some light elements, which give a high yield of neutrons in reaction (a, n). The most suitable is beryllium in the reaction ⁹Be(a, n)¹²C, which we mix with a suitable a-radiator - used eg ²¹⁰Po, ²²⁶Ra, ²³⁹Pu, ²⁴¹Am. These mixtures are hermetically closed or sealed in metal or glass containers and serve as portable laboratory sources of neutrons, so-called neutron generators, used eg in neutron activation analysis (§3.4 "Neutron activation analysis").
  Nuclei with an excess of protons are mostly beta⁺ -radioactive or decay by electron capture; according to the method of their production, they are sometimes referred to as cyclotron radionuclides. Some reactions of radionuclide production by proton irradiation are, for example: ¹⁸O(p,n)¹⁸F, ¹³C(p,n)¹³N, ¹¹B(p,n)¹¹C, ....; deuterons eg ¹⁰B(d,n)¹¹C, ⁵⁶Fe(d,n)⁵⁷Co, ...... Specific methods for producing a number of important radioisotopes are described below in the section "Properties of some of the most important radioactive isotopes".
Acceleration of negative ions - the possibility of increasing the fluence power of the external beam from the cyclotron
In the cyclotron is a standard accelerated heavy positively charged particles - protons, deuterons, alpha particles, or heavier nuclei such as carbon ¹²C. For small cyclotrons used for the production of radioisotopes, an important requirement is the high intensity - fluence power - of proton or deuteron beams. At energies around 40MeV, a relatively large current in the beam of about 2-5 mA is achieved. However, this maximum power can only be fully utilized when irradiating an internal target installed inside a vacuum accelerator tube. However, for the routine production of radionuclides, it is more advantageous to bring out the particle beam to irradiate the external targets. In classical cyclotrons accelerating positive particles, the resulting beam is extracted with an electrostatic deflector. However, considerable dissipative heat is generated at the partition of this deflector, which is a limiting factor for achieving a high fluency performance of the extracted beam.
  This disadvantage is largely eliminated by the technology of acceleration of negative ions (§1.5, part " Cyclotron ", passage "Acceleration of negative ions"). Hydrogen or deuterium atoms are supplied with two electrons in an ion source in an electric discharge, creating negative H^- or D^- hydrogen ions with two electrons. These are then accelerated in the cyclotron. After the necessary acceleration, a thin carbon foil is inserted into the path of negative ions H^- in the appropriate path, which by "stripping" removing their both light electrons and releases the desired heavy p⁺ or d⁺. This reverses the direction of curvature in the magnetic field, causing their rapid brought out from the field of the cyclotron to the external volume with corresponding energy, with minimal thermal dissipation. This leads to considerably higher performance production of radionuclides in the outer target. This is especially important for the production of larger radioisotope activities for scintigraphic diagnostics (§4.8 "Radionuclides and radiopharmaceuticals for scintigraphy ') and a biologically-targeted radionuclide therapy (§3.6"Radioisotope therapy") in nuclear medicine.

Modification of irradiated material in the target. Radionuclide purity.
The basis for the production of the required radionuclide is :
¨ Selection of a suitable production nuclear reaction
- the starting nuclide and the type of firing particles and their energy, which implies the required irradiation equipment (nuclear reactor, neutron generator, cyclotron) and its properties.
¨ Preparation of a suitable target
of irradiated nuclide, its chemical form and design. We can irradiate either the starting element directly in elemental form or its suitable compound. Isotopic enrichment of irradiated materials in the target is often required - this increases the yield of the reaction and facilitates the subsequent radiochemical separation. Isotopic enrichment of target materials is technologically very demanding and expensive. Therefore, after irradiation and separation of the formed radionuclide, the remaining enriched material is recycled for repeated irradiation.
  The material to be irradiated in the target is used in all three common states :
l   Target in the solid phase consists of a crystalline form, powder or amorphous material of the starting target element or its compound. It is often a metallic form of a given heavier element or its alloy. After irradiation, the target material is used either directly (encapsulated and a closed emitter is formed), or dissolves in a suitable acid or hydroxide and performs radiochemical separation and preparation of the required chemical form of the radioisotope (or radioisotope labeling of a radiopharmaceutical for nuclear medicine).
l A liquid target consists of an ampoule with a starting element or its compound which is liquid at normal temperature or is dissolved in a suitable solvent - most often an aqueous solution. After irradiation, a radiochemical separation is performed in the liquid preparation and the resulting radioisotope is introduced into the required chemical form or radiopharmaceutical.
l The gas target consists of compressed gas enclosed in a suitable ampoule or chamber  (most often they are inert gases xenon, argon, krypton, ...). At the end of the irradiation, the radioisotope formed (contained in the enclosure of the chamber or absorbed on the walls) is washed with water or dilute acid; other radiochemical modifications are analogous to the above targets. In the case of isotopically enriched gas, it is recycled for reuse.
  After irradiation, the target material contains not only the desired radionuclide (at least never in 100% concentration), but also a number of other atoms and possibly other radionuclides formed by other (parallel, "parasitic") reactions. As a rule, therefore, the irradiated material must be subjected to a demanding procedure of radiochemical separation of the required radionuclides.
Radionuclide purity ,   
indicating the percentage ratio of the activity of the desired radionuclide to the total activity of the preparation, is an important parameter of the quality of the produced radionuclide. For technological and medical applications, a high radionuclide purity is generally required, better than 99.9% - or a radionuclide impurity content of less than 0.1%. Radioinuclide impurities can be disruptive during analytical or imaging measurements, or cause increased radiation exposure of the patient (also discussed §4.8, section "Radionuclides and radiopharmaceuticals for scintigraphy", passage "Radionuclide purity of radiopharmaceuticals").

Secondary radionuclides from decay products. Radionuclide generators.
Some radionuclides are transformed into daughter nuclei, which are not stable, but are again radioactive - they are secondary radioisotopes. Obtaining these secondary radionuclides from the decay products of other radionuclides can be an efficient way to "produce" them.
  This method is of particular importance for short-lived radionuclides, which are formed as daughter nuclei of radionuclides with a substantially longer half-life. The relevant parent radioisotope, prepared by irradiation at an accelerator or reactor, can be easily transported to a remote laboratory, where a daughter short-lived radionuclide can be separated from it continuously or repeatedly, which is thus available for a much longer period of time (given by the half-life of the parent radionuclide). A device that makes it possible to repeatedly separate a short-lived radionuclide formed by the decay of another longer-lived radionuclide is called a radionuclide generator. Different physico-chemical properties make it possible to separate the parent and daughter elements in the generator. A generator is a system containing a tightly bound parent radionuclide with a longer half-life, from which the resulting daughter radionuclide with a shorter half-life (which is no longer firmly bound to the parent radionuclide carrier) can be separated (detach) either chemically (in the liquid phase), hydrodynamically (elution) or by blowing with air. The advantage of radionuclide generators is the possibility to use appropriate short-term radionuclides even in workplaces remote from the nuclear reactor or cyclotron. The kinetics of radionuclide generators in terms of decay equilibrium of parent and daughter radionuclides is analyzed in §1.2, section "Mixtures of radionuclides, decay series, radioactive balance".
  A typical example of a radionuclide generator is a molybdenum-technetium generator ⁹⁹Mo/^99mTc (described in more detail in §1.2, section "Gamma radiation", passage "Radionuclide generators", see also below "Molybdenum-Technetium"), where beta-decay of molybdenum ⁹⁹Mo (T1/2 = 66 hours) produces metastable technetium ^99mTc (T1/2 = 6 hours), which is a pure gamma emitter (Eg = 140keV) and has a wide application in scintigraphy in nuclear medicine - see chapter 4 "Radionuclide scintigraphy", §4.8 "Radionuclides and radiopharmaceuticals for scintigraphy", where the principle of operation and technical design of the ⁹⁹Mo-^99mTc generator is drawn in Fig.4.8.1. A rubidium-krypton generator used in ventilatory lung scintigraphy is described below in the section "Rubidium-Krypton". In the field of PET scintigraphy, the germanium-gallium generator ⁶⁸Ge/⁶⁸Ga is finding an increasingly important application (see gallium Ga-68 below).
  The  table shows several more frequently used radionuclide generators :

"In vivo generators" in nuclear medicine
In nuclear medicine, suitable compound of radionuclides - the radiopharmaceutical - are applied to the internal environment of the organism, where their enter into metabolic processes, and by their biochemical pharmacokinetics may accumulate in certain target tissues and organs. If this radiopharmaceutical is labeled with a radionuclide that converts not to a stable, but to another radioactive isotope with a shorter half-life, then after its uptake, another shorter radionuclide is generated and accumulated in vivo in the target tissue, which "cooperate" with the primary parent radionuclide. If this in vivo generated daughter radionuclide emits g- photons or positrons, can be used for scintigraphic imaging (planar, SPECT, PET - Chapter 4 "Radioisotope scintigraphy"); if emits alpha particles or beta^- (event. Auger electrons), can serve (or contribute to) the radionuclide therapy - §3.6 "Radioisotope therapy". This situation, when a longer-term radionuclide applied to the organism, by its radioactive transformation creates a daughter short-term radionuclide (or the whole decay series) in the target tissue, is sometimes called an in vivo radionuclide generator - in the context with the above laboratory radionuclide generators.
  A certain problem with in vivo generators is the release - dissociation - of daughter atoms from radiopharmaceutical molecules, leading to impaired stability and redistribution of daughter radionuclides. In addition to chemical processes - changes in the valence (oxidation number) of atoms during radioactive transformation - the backscattering of nuclei during radioactive emission of alpha, beta and partially gamma quanta also contributes to this (§1.2, passage "Accompanying phenomena during radioactivity", paragraph "Backscattering cores"). The kinetic energy of the backscattering of nuclei usually exceeds the binding energy many times the relevant atoms in the chemical bond *). Radiochemical methods evolve labeling of biomolecules, which penetrate inside the target cells and which are internalized, while the daughter atoms may be sufficiently long to keep in target cells.
*) This manifests itself mainly in alpha-radioactivity. E.g. with an alpha particle emission of 4-7 MeV, a kinetic energy of approx. 60-100 keV is transmitted to the daughter nucleus with a nucleon number of approx. 220 by back reflection. The chemical binding energy of the respective atoms in the biomolecules (conjugates, for example with monoclonal antibodies) is only about 2-5 eV.
  A typical example of an in vivo generator used is radium ²²³Ra which is applied as a radiopharmaceutical in the form of chloride. It is taken up in bone metastases, in which 223-radium decays "in vivo" with a half-life of 11.4 days by a whole cascade of alpha-transformations (in combination with an insignificant alpha-beta branch) to other short-lived radionuclides: ²²³Ra(11,4d.; a) ® ²¹⁹Rn(4s.; a) ® ²¹⁵Po(1,8ms.; a) ® ²¹¹Pb(36,1min.; b^-) ® ²¹¹Bi(2,2min.; a) ® ²⁰⁷Tl(4,8min.; b^-) ® ²⁰⁷Pb(stab.)- see radium ²²³ Ra below for details. One complete radioactive transformation of the ²²³Ra nucleus in the whole decay series to a stable ²⁰⁷Pb releases a total nuclear energy of almost 30 MeV, mainly by four alpha-particles, with a high radiobiological effect; gamma photons are also generated, which can be used to gammagraphically monitoring the distribution of the radiopharmaceutical. However, radium ²²³Ra does not allow chelating bonds to more complex biomolecules such as monoclonal antibodies, so its use is very limited ( ²²³Ra-chloride for palliative therapy of bone metastases).
   A more promising radionuclide type "in vivo generator" is thorium ²²⁷Th, which (unlike radium) allows using type macrocyclic ligand DOTA chelating binding of ²²⁷Th with monoclonal antibodies to form radioimmunoconjugates, which are specifically sequester in tumor cells. High energy a particles capable emitted in radioactive transformations, they can effectively destroy these tumor cells - see thorium ²²⁷ Th below for details.
   Another radionuclide that could work very well as an in vivo generator in targeted alpha-therapy is actinium ²²⁵Ac, which decays with a half-life of 10 days by a cascade of 4 alpha transformations (in combination with an insignificant alpha-beta branch) to other short-lived radionuclides: ²²⁵Ac(10d.; a) ® ²²¹Fr(4,8m.; a) ® ²¹⁷At(32ms.; a) ® ²¹³Bi(46m.; b^-) ® ²¹³Po(4ms.; a) ® ²⁰⁹Pb(3,3h.; b^-) ® ²⁰⁹Bi(stab.), is released energy about 27 MeV - see actinium ²²⁵ Ac below for details. Here, too, the accompanying gamma radiation is generated, which can be used for scintigraphic imaging. Radiopharmaceuticals labeled with ²²⁵Ac (including monoclonal antibodies, eg ²²⁵Ac-Trastuzumab or ²²⁵Ac-PSMA-617) are being tested for the treatment of leucemia, lymphomas, neuroendocrine tumors, gliomas, melanomas, and are very promising in the prostate. This "in vivo generator" method of therapy proves to be significantly more effective than the previously tested application of ²¹³Bi alone (the disadvantage of which is the short half-life of 46 minutes).
  Therapeutic use of in vivo radionuclide generators is discussed in more detail in §3.6, passage "Alpha and beta radionuclides for therapy".

Chemical compounds of radionuclides. Radioisotope marking. Radioactive preparations.
Radioactive nuclei - radionuclides - are normally part of the atoms (which have the same chemical properties as non-radioactive atoms) that make up the radioactive substance. Only in exceptional cases is it a pure radioactive element, mostly radioactive compounds of own radioisotope atoms with other non-radioactive atoms, often in a mixture with other substances. A radioactive substance specifically prepared for laboratory, technical or medical use is often called a radioactive preparation.
  Natural radionuclides (described above in the section "Natural radionuclides") are dispersed in the natural environment with a very low concentration. The heavy elements uranium-238,235 and thorium-232 are contained in the earth's crust in minerals in the form of oxides, silicates or phosphates. Potassium K-40 is abundant together with normal non-radioactive potassium. Tritium H-3 is in the form of "heavy" water ³H₂O, carbon C-14 is in the atmosphere in the form of carbon dioxide ¹⁴CO₂ . In plants, radio-carbon and tritium are incorporated into virtually all biomolecules in cells, and later in animal and human cells.
  A special field of radiochemistry deals with chemical reactions with the participation of radioactive atoms. The targeted chemical attachment of the atoms of a particular radionuclide to the molecules of a given substance is called radioisotope labeling. The labeled substance - radio-preparation - is then mostly used as a radioindicator for various analytical and diagnostic procedures (§3.5 "Radioisotope tracking methods" and §4.8 " Radionuclides and radiopharmaceuticals for scintigraphy"), or as a radiotherapeutics in biologically targeted radioisotope therapy (§3.6, section "Radioisotope therapy").
  Chemical reactions of labeling with the desired radionuclide generally do not proceed in 100% yield. Therefore, in the resulting preparations, in addition to the required radioactive substance itself, there is always a small amount of unbound activity and possibly other radioactive substances, that have different radiochemical properties and may be disruptive impair the binding specificity of the labeled substance in laboratory, diagnostic or therapeutic applications. In addition to the radionuclide purity discussed above, the radiochemical purity of the preparations is therefore an important quality parameter. It is the share of the declared chemical compound of a given radionuclide in the total activity of the preparation.
  Part of the generated ionizing radiation is absorbed inside material of the radioactive preparation, self-absorption of radiation in the sample occurs. This absorbed radiation can cause chemical changes in the material (§5.1, section "Effects of radiation on the substance") - radiolysis of the labeled substance by its own radiation (most often beta or alpha). During this radiation decomposition, the required labeled substance decreases and other substances with different properties are formed instead. This worsens the radiochemical purity of the preparation. In particular, radiolabeled complex organic molecules readily undergo radiolysis. The higher the specific activity of the preparation, the faster the radiation decomposition takes place.

Radionuclide decay (transformation) schemes
The so-called transformation schemes are used for a clear and comprehensive presentation of various types of radioactive transformations and energy levels in specific atomic nuclei (Fig.1.4.6). The parent and daughter nuclei are represented in these diagrams by means of horizontal lines (representing the energy levels of the nuclei), the position of which in the diagram is determined as follows: the proton number Z is on the horizontal axis, the position in the vertical direction is given by the nucleus energy E *). The basic energy state of each nucleus is marked by a thick line, the excited states of the nucleus are drawn in thin commas (with data on energy and possibly other characteristics), at the appropriate vertical height above the baseline. For the basic states of radioactive nuclei, the half-life is indicated, for special purposes event. also other characteristics (eg spin). The basic state of a stable core is sometimes drawn by a combination of a thick solid line with hatching below. Metastable energy levels are drawn by semi-bold dashes with an indication of the lifetime (half-life) of this metastable excited state.
*) In the practical drawing of decay schemes, the exact proportions of energy values and proton numbers are usually not strictly observed, only the relevant relations are observed - states with higher energy are drawn more above, nuclei with larger proton number Z are more to the right of nuclei with smaller Z.
  The radioactive alpha and beta transformation of nuclei is to draw by an oblique arrow to the left or right, connecting the parent and daughter nuclei at their respective energy levels, which takes place in a given process; next to this arrow is writen the type of transformation (a, b, EC) and the corresponding quantum energy of the radiation. Deexcitation of excited levels, ie isomeric transitions g, are drawn by vertical arrows connecting the higher levels with the corresponding resulting lower levels, or with the baseline state of the daughter core. For arrows showing nuclear transformations and dexcitation, their relative representation [%] (probability, intensity) is given - the average number of emitted quanta (alpha, electrons or positrons, photons) per 100 transformations. At the bottom of the decay scheme (below the daughter nucleus line, or to save space in another free space in the figure), the total conversion energy Q [keV or MeV] is listed.
  Close to the horizontal lines showing the fundamental and excited energy states of nuclei, their energies are given in the decay diagrams. The values of this energy are determined relative to the ground state of the daughter nucleus, to which the energy "0" is assigned. The basic state of the parent nucleus then has the energy Q and possibly the excited states of the daughter nucleus have correspondingly lower energies.
Branched transformation 
A more complex situation occurs in the case of branched transformation, when a given parent nucleus is transformed by two different types of radioactivity (with a certain probability) into two different daughter nuclei with different ground state energies - see §1.2, passage "Mixed (combined) radioactivity - branched transformations". Then we have two different values of the total energy of transformation Q and two series of energy levels of daughter nuclei. For each branch of radioactive transformation, energies are calculated independently. The ground state of one daughter nucleus is assigned energy "0". The same is done for the second daughter nucleus in the second branch of the transformation. The parent nucleus then has two different initial energy values, which we attribute to it from the side of the diagram to which the type of transformation is directed. A typical example of this situation can be seen in the decay scheme of ¹⁸⁶ Re , ¹⁹² Ir , ¹⁵² Eu and several others.
  Figure 1.4.6 shows some of the simplest typical decay schemes :

Fig.1.4.6. The simplest typical conversion schemes of radioactivity a, b⁺, b^-, b^-+ g and branched transformations EC+ b^- .

On the far left it is a pure decay a (mechanism according to Fig.1.2.2 in §1.2), where with the radiation of the particle a (helium nuclei ⁴He₂) the parent nucleus ^NA_Z transforms into the ground state of the daughter nucleus ^N-4B_Z-2 about lower energy; the nucleus B is shifted to the left by two places, as it corresponds to the proton number Z-2, and down according to the energy difference. For the arrow (a double arrow is used for the alpha) showing the transformation itself, the type of transformation and the corresponding quantum energy of the emitted radiation are indicated.
  Next to it is the conversion scheme of pure radioactivity b⁺ ( ^NA_Z ® ^NB_Z-1 + e ⁺ + n), where the daughter nucleus B is shifted by one place to the left relative to the parent nucleus A, which corresponds to a reduction of the proton number by 1.
  Furthermore, Fig.1.4.6 shows the decay scheme of pure radioactivity b^- (^NA_Z ® ^NB_Z+1 + e^- + n´, according to Fig.1.2.3 in §1.2), where the parent core A is transformed into the basic state of the daughter core B, shifted by one place to the right.
  For simplicity, we have so far disregarded the fact that the net conversion of a or b to the basal level of the daughter nucleus occurs in only a small percentage of cases; usually the daughter nucleus is formed in an excited state, followed by deexcitation - combined radioactivity a+g or b+g. The penultimate decay scheme in Figure 1.1.5 on the right represents an example of the radioactivity b of a specific ¹³⁷Cs nucleus, which with a half-life T1/2 = 30 years is transformed into a daughter nucleus ¹³⁷Ba, which is stable. Only about 6.5% of cases go to the basal state of barium, while as many as 93.5% of cases go to the excited state of the nucleus ¹³⁷Ba with an energy of 662 keV, shown by a horizontal comma. The vertical down arrow shows the deexcitation of this excited state by emitting a photon of radiation g with this energy 662 keV (the properties of this important radionuclide ¹³⁷Cs are described in more detail below in the passage "Cs-137").
  On the far right of Fig. 1.4.6 is an example of the above-mentioned branched radioactive transformation of one parent nucleus by two different types of radioactivity to two different daughter nuclei (the example is a simplified scheme of radinuclide ¹⁸⁶Re, described in more detail below in passage ¹⁸⁶ Re ).
  The decay patterns of some radionuclides are quite complex, with a number of cascading transformations of corpuscular and a number of excited energy levels, between which isomeric transitions occur accompanied by gamma radiation quanta. That correspond to the complex spectra of such radionuclides. Spectrometric analysis of the emitted radiation is then the main method of recognizing the structure of nuclides.
  In the following section "Properties of some of the most important radionuclides" we present specific decay schemes of a number of more important and more frequently used radionuclides, together with their radiation spectra and other properties, including applications :

Properties of some most important radioactive isotopes
Of the large number of radionuclides (now more than 2000 are known), some of which occur in nature, but most are produced artificially, only less than a tenth are important and practical. Here we will get acquainted with some radioisotopes that are particularly interesting or important from the point of view of natural science or for practical applications. We will describe these important radionuclides in more detail with the indication of their properties, decay schemes and radiation spectra *), methods of origin or production and their use. In the introduction to the description of the properties of individual radionuclides, we always make a brief mention of the physico-chemical properties of the relevant elements; although the radiation behavior of the respective radionuclides is not directly related to these properties (radioactivity is a property of the atomic nucleus, not the electron shell), they are important for radiochemistry of radioisotope preparation and their behavior and distribution in nature, including living organisms, or applications in medicine. In addition, many non-radioactive isotopes are important in nuclear and radiation processes: whether as a source of bombardment particles, as target materials, components of detection media, shielding and collimating materials. For a comprehensive understanding of nuclear and radiation physics, it is useful to reflect all these contexts...
*) Gamma radiation spectrometry
of some used radionuclides we performed at our Department of nuclear medicine in Ostrava-Poruba, within its modest possibilities, in the 70's and 80's on a scintillation NaI (Tl) detector (size 5x5cm) and a semiconductor Ge(Li) detector with the help of a 4096-channel analyzer ICA-70, later using a Canberra-Packard computer analyzer. We no longer have a Ge(Li) detector at our workplace (ended service...) and the semiconductor spectra below were acquired at the HPGe detector of the spectrometric laboratory of the SÚJB and SÚRO regional center in Ostrava-Zábøeh with the kind cooperation of colleagues Ing. J.Lušnák and Ing. J.Rada- the author thanks them very much !
  The spectra of soft gamma radiation and characteristic X-rays (with energies lower than 30 keV, for which the detection efficiency of the coaxial high-volume HPGe detector is already very low) were measured separately on a planar semiconductor detector with a beryllium input window.
Some of these measurements were mostly performed many years ago on analog spectrometers, so we built them into our spectra by scanning and interpolating the original graphs of the spectra - we apologize for event. distortions and degraded quality.
   Many years ago, we tried the beta radiation spectrometry very improvised with the help of plastic scintillators and liquid scintillators, which is definitely not optimal (unfortunately we never owned a magnetic spectrometer ...). We do not mention continuous spectra of beta radiation for individual radionuclides in our treatise also because they are quite "dull" and uninteresting - visually they are similar to "eggs like eggs", only stretched to higher or shrunk to lower maximum energies. Relevant information from them can be obtained only by demanding computer analysis using the Fermi-Kurie graph method (§2.6 "Measurement of beta, proton and neutron radiation. Liquid scintillators."; at that time we calculated it manually and plotted it graphically on graph paper...). Conversion and Auger electrons with discrete spectra of characteristic energies would be interesting, but at our workplace we didn't have an instrument to measuring...

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

Common features of gamma-spectra of radionuclides
Despite all the differences between the energy and the intensity of gamma rays emitted by different radionuclides, the gamma-spectra of all radionuclides have some similar features :
¨In the beginning photon spectrum in low energy are often seen the peaks of the characteristic X-rays, emitted at electron jumps between the inner shells in the excited atomic shells of the daughter element. These excitations of atoms during radioactive transformations occur in two ways :
1. Internal conversion of gamma radiation (§1.2., passage "Internal conversion of gamma radiation and X"), when electrons from higher energy levels in the atomic shell jump to the vacancies after conversion electrons. Particularly g -fotons low energy (units or tens of keV) to have a high conversion ratio. Also, some isomeric transitions, highly forbidden due to the spin "mismatch" between the excitation and the ground state of the nucleus (an example is the isomeric ^131m Xe), are realized by an internal conversion mechanism.
2. Electron capture (§1.2, passage "Electron capture (EC)"), in which electrons from higher levels of the atom immediately jump to the vacancies after the captured electrons (usually in the K shell). Thus, especially with radionuclides transformed by electron capture, that the characteristic X-rays are highly represented or even dominant (see eg ¹²⁵ I).
  In our gamma spectra, measured by scintillation NaI(Tl) and semiconductor HPGe detector, peaks Ka,b of characteristic X-rays are displayed only for medium and heavy radionuclides (for some lighter radionuclides we measured low-energy peaks of characteristic X-rays separately on silicon semiconductor detector as mentioned above). We will present and analyze the characteristic X-rays in our spectra, only if it is significant - it is clearly visible in the spectra and has a radiation significance.
¨ If a radionuclide emits more gamma-ray energies, the strongest gamma-lines are usually in the lower and medium energies (tens to hundreds of keV), while higher energies are usually represented with significantly lower intensity (see "Magnified sections of spectra" below).
Magnified sections of spectra
In our basic spectra are displayed the most important nuclear levels and radiation energies of a given radionuclide, which are used in applications and are measurable by commonly available detection techniques. The peaks of the weakly represented gamma radiation energies are lost in the spectra graphically displayed on a normal scale (given by the height of the most intense peak) in the region around zero values. To display them, we therefore use an enlarged section of the spectrum, shifted above the horizontal axis; while the energies correspond to the basic scale on the horizontal axis. These magnified sections are marked with a magnification sign "< ", an up arrow and a magnification multiple - eg " < á 16 x "- slight magnification, or " << á 256 x "- strong magnification. This situation often occurs when the radioactive transformation occurs to a larger number of excited states of the daughter nucleus. Then it is usually more likely to lower energy levels than to higher excited states - the gamma spectra are represented with a higher intensity peaks at lower energy as the high energy peaks are much weaker, are often visible only at high magnification and long acquisition time. This is just shown by the magnified sections of the spectra.
Differences in scintillation and semiconductor gamma spectra
If we look at the images below gamma spectra of a number of radionuclides, we can at a glance see some significant differences between spectra measured by scintillation and semiconductor detector :
¨   Photopeaks for scintillation spectrum are rounded and soft, as if "blurred" - energy resolution is relatively imperfect (approx. 10% for test line 662keV ¹³⁷Cs) , close gamma-lines merge into one photopeak. The semiconductor spectrum consists of very sharp and narrow peaks - the energy resolution is about 30 times better. Some compact peaks from the scintillation spectrum are decomposed into several gamma lines on the semiconductor spectrum...
¨   In scintillation spectrum shows a significantly represented continuous component of Compton scattered radiation, especially in the region of lower energies. This continuous background is disturbing (especially in the "peak" region of the backscatter, which can interfere with the actual gamma peak of the radionuclide being measured). 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 on a graphical representation of the spectrum, normalized to the maximum of the peak.
¨   We can observe some differences in the relative intensity of the peaks, which are caused by different energy dependence of the detection efficiency. The scintillation NaI(Tl) detector also measures the gamma line with high efficiency with energies of about 20-40keV, for which the coaxial HPGe detector (used by us) already has a very low (or zero end) sensitivity. Therefore, for example, characteristic X-rays usually have a significantly lower content on the semiconductor spectrum than on scintillation. For lighter radionuclides, X-ray peaks do not appear at all on this detector. A planar Ge(Li) or Si detector was used to measure them in some spectra.
Author's apology - distortion in the display of spectra
The original measured spectra of radionuclides from a multichannel analyzer (with high energy resolution and a number of details) had to be significantly reduced graphically for capacity reasons to display in our treatise. This often led to geometric distortion of the spectra, especially from semiconductor detectors - for example, to "shrinkage" of the lines of photopeaks, loss of some points in the curves and their disconnection, merging of nearby lines. As far as possible, I tried to "retouch" these distortions and liken the displayed graphs to the original spectrum. However, this has not always been completely successful, I apologize and welcome the comments of colleagues - experts of spectra ...
  The same applies to the display of more complex decay schemes of some radionuclides, where the plotting of nearby energy levels and arrows of transformations and transitions can also overlap and merge... For similar reasons, the energy scales below the horizontal axes of the spectra are only approximate (we are able to ensure the accuracy of displaying the positions of numerical values not better than about ± 10%). For our purposes, however, this does not matter, because the exact values of the energies of the individual peaks, read from the original spectra (uncompressed, in digital form on the spectrometer), are explicitly descripted by the arrows denoting the respective photo peaks.
  The scale on the vertical axes of the measured number of pulses is relative, normalized to the value of 100.10³ pulses.
  The individual radionuclides are basically listed in the order of proton and nucleon numbers, but with a number of minor exceptions - on the one hand according to the sequence of radioactive transformations (eg radium-223 is listed after radium-226, from which it is prepared), on the second hand, according to the importance and method of use of the respective radioactive isotopes (e.g. cobalt 57-Co is mentioned up to the far more important 60-Co). If, for a certain element, its radioactive isotope do not "deserve" a separate section by their number or significance, two or three close elements are combined into one passage (eg nitrogen + oxygen + fluorine, chromium + iron, copper + gallium + germanium, transurans) and their isotopes are discussed in mutual context. This is logical especially in the case of continuity of parent-daughter radionuclide relationships (eg rubidium-krypton, molybdenum-technetium, decay series of heavy alpha-radionuclides).
Diversity of radionuclides
Every radionuclide is certainly something interesting. However, describe in detail the properties of all known radioisotopes would be too lengthy and confusing *) (and it would certainly go beyond the powers of the author...). Therefore, we do not mention here those radioisotopes that were once or several times, rather accidentally, in the context of the time, used in research of some natural processes, material and biological, or in nuclear medicine, and then no longer used - either because they have their one-off role already fulfilled, or have been replaced in practice by more advantageous radionuclides (which we therefore present). We analyze in more detail radionuclides of particular interest from a nuclear and general natural-scientific point of view, or widely used in scientific and technical applications, medicine, industry (especially those that the author personally uses in analytical and measuring methods, or as calibration standards). This choice may be somewhat subjective - I welcome the comments and suggestions of colleagues..!..
*) It is not important to deal with, for example, extremely short-lived radionuclides that can not be used in any way - can be interesting at most in terms of nuclear physics, studies of strongly nonequilibrium nuclear configurations.
  For individual radionuclides, we present and display in the spectra mainly relevant energy levels and radiation, which can be detected by available radiometric techniques. Radiation intensity is given numerically in percentages (eg "gamma 320keV (10%)" means that "10 gamma photons with an energy of 320keV are emitted per 100 conversions of the respective radionuclide"). A large number of other, low-saturated levels and very poorly represented radiation energies, as well as their other characteristics (such as spin, multipolarity, parity, which are important only for nuclear research) can be found in detailed isotope decay tables. At our workplace, we mainly used the book edition of the "Table of isotopes" by Lederer, Hollander, Perlman (the new electronic version is "http://ie.lbl.gov/toipdf/toi20.pdf"). Other new detailed tables in the electronic version are "http://ie.lbl.gov/toi/nucSearch. Lund univ.") and "http://www.nucleide.org" from "Henri Becquerel Laboratory".
Short-term and long-term radionuclides
One of the main factors determining the importance and use of radionuclides is the half-life. As mentioned above in section "Natural radionuclides", these natural radionuclides (primordial and cosmogenic) have very long half-lives. Also, the vast majority of significant artificial radionuclides used in science and technology or industry, have a sufficiently long half-life - months, years, decades or more, which allows their long-term use, especially in the form of closed radiators.
  Exception are some short-term radionuclides used in nuclear medicine, which due to their chemical and pharmacokinetic properties find application in radionuclide diagnostics or therapy in the form of open emitters - labeled radiopharmaceuticals, applied directly to the body (usually intravenously or orally, see Chapter 4 "Scintigraphy", §4.9 "Clinical scintigraphic diagnostics in nuclear medicine"). In this case, the short half-life may be an advantage in terms of the radiation exposure of the organism.
  Such short - lived radionuclides are mainly technetium ^99m Tc (T1/2= 6 hours) and also light positron radionuclides: carbon ¹¹C (T1/2 = 20.4 min.), nitrogen ¹³N (T1/2 = 10 min.), oxygen ¹⁵O (T1/2 = 122 sec.) and especially fluorine ¹⁸F (T1/2 = 110min.), which is taken up in the form of ¹⁸F-deoxyglucose and accumulates especially in tumor tissues, which are then imaged by positron emission tomography based on the coincident detection of gamma 511keV annihilation radiation (see § 4.3 "Tomographic cameras" and §4.8 "Radionuclides and radiopharmaceuticals for scintigraphy", part "Positron radionuclides"). Their properties, decay schemes and the spectrum of 511 keV are shown below (passage "oxygen, fluorine"). The shortest radionuclide used in nuclear medicine is metastable krypton ^{81 m} Kr with a half-life only 13.1 seconds.

Hydrogen
The lightest and most widespread element in nature (in universe) is hydrogen H₁ (hydrogenum - water-forming), whose proton nuclei formed just after the Big Bang in the hadron era of the universe (§1.1, part "Cosmic nucleogenesis"); accounts for 75% of total mass (baryonic) in the universe. It is the main "fuel" of thermonuclear fusion inside stars ("Gravity and evolution of stars", part of the "Thermonuclear reaction inside stars"). It is very reactive, so in terrestrial nature it occurs practically only in compounds (elemental hydrogen occurs only in natural gas and volcanic gases), of which the most important is water H₂O. Along with carbon, hydrogen is the most important biogenic element. It has three important isotopes (in total, the isotopes ¹H₁ to ⁷H₁ are known). Basic "light" hydrogen ¹H₁ (called sometimes protium) - relative representation of 99.9885 %, "heavy" hydrogen, deuterium, ²H₁ (0.0115%) and "extra heavy" hydrogen tritium ³H₁ (cosmogenic nuclide with trace representation), which is already radioactive.
Hydrogen ¹ H ,
as already mentioned, is the main "fuel" nuclear fusion inside stars. In nuclear technologies, hydrogen nuclei - protons are main shelling particles in nuclear research, in the preparation of artificial radioisotopes (see above "Production of artificial radionuclides"), in proton radiotherapy (§3.6, section "Hadron radiotherapy").
Deuterium ² H
- a heavier isotope of hydrogen, formed just after the beginning of the universe during primordial nucleosynthesis (it is analyzed in more detail in the section "Lepton era. Initial cosmological nucleosynthesis" §5.4 monograph "Gravity, black holes and space-time physics"). Deuterium is another non-radioactive isotope important in nuclear and radiation physics. Deuterium nuclei deuterons d = ²H are often used as shelling particles in cyclotrons. Heavy water is sometimes used as a moderator and coolant in fission nuclear reactors (§1.3, section "Nuclear reactors"). Together with tritium, deuterium is most promising fuel for controlled thermonuclear fusion (§1.3, section "Merging nuclei"); direct nuclear fusion of hydrogen nuclei ¹H = proton in terrestrial conditions we cannot yet perform.
Tritium ³ H
Leaving aside the free neutron (which is b^- -radioactive n^o ® p⁺ + e^- + n´ with a half-life of » 13 min., max. energy beta 782keV), the lightest radionuclide is the hydrogen isotope tritium ³H, which is with a half-life of 12.3 years converts by b^- -radioactivity to the basic state of the helium isotope ³He: ³H₁ ® ³He₂ + e^- + n´ (its simple decay diagram is on the left in Fig.1.4.7) . Tritium is a pure beta emitter with a relatively low maximum energy of emitted electrons of 18.6 keV (red curve in Fig.1.4.7 on the right).

Fig.1.4.7. Beta ^- - radioactivity of some simplest isotopes.
Left: Conversion schemes of tritium ³H, carbon ¹⁴C and phosphorus ³²P. Right: Continuous beta spectra of these radionuclides.
Note 1: The energy axis is nonlinear and irregular (illustrative only) in order to draw very energetically different spectra .
Note 2: The spectra were measured with a MarkIII Nuclear Chicago instrument with a toluene liquid scintillator (§.2.6, section "Liquid scintillators", Fig.2.6.2), plotted and (with modifications) interpolated.
Note 3: The shape of the low-energy part of the spectrum (smooth growth from zero values - which is somewhat different from the actual shape of the initial part of the spectrum b^- - cf. §1.2, passage "Difference of energy spectrum b ^- and b ⁺ ", spectrum in the left part of the picture) is affected by low sensitivity of the instrument for low beta energy and electronic signal filtering to reduce noise pulses.

In terrestrial nature, tritium occurs as a cosmogenic radionuclide (see above the section "Natural radionuclides", or §1.6, part "Cosmic radiation", passage "Secondary cosmic radiation"). It also arises during the so-called ternary fission of heavy nuclei, especially uranium (§1.3, section "Fission of atomic nuclei"). The tritium content in nature has been significantly affected by human activity in the last few decades. A large increase in the content of ³H in the environment occured in 1960s as a result of tests of thermonuclear weapons in the atmosphere (at thermonuclear explosion of lithium deuteride ⁶Li²H the tritium is formed by the reaction ⁶Li (n, a) ³H - see §1.3, section "Compounding of atomic nuclei", passage "Explosive thermonuclear reactions"). In fission nuclear reactors, tritium is formed in circulating cooling water by the reaction of neutrons with deuterium ²H (n, g) ³H; to a small extent with deuterium contained in ordinary water, more effectively when using heavy water as a moderator and coolant. Furthermore, in cooling water containing boric acid to control the reactivity of the fission reactor, tritium is formed by the reaction of ¹⁰B (n, 2a) ³H. During the operation of nuclear power plants, therefore, a certain smaller amount of ³H (in the order of hundredths of cosmogenic tritium) enters the water and gas discharges.
  Tritium is a suitable excitation radionuclide in small electrical sources - beta - voltaic cells - see §1.3, passage "Radionuclide volta cells" ("atomic batteries").
  For many applications in nuclear physics (especially for thermonuclear fusion, in the future probably for energy use - §1.3 "Nuclear reactions and nuclear energy", part "Fusion of atomic nuclei"), in biology and medicine, tritium is produced artificially by reacting neutrons with lithium:  ⁶Li (n, a) ³H, or is obtained from heavy water in reactors.

Helium
The second lightest and most widespread element in the universe, helium He₂ ("sun god element"), formed in the Lepton era after the Big Bang (primordial nucleosynthesis is analyzed in more detail in the "Lepton Era. Primary Cosmological Nucleosynthesis" section in §5.4 of the monograph "Gravity, Black Holes and space - time physics"). However, it is rare on Earth - the reasons are given in §1.1, section "Cosmic nucleogenesis". All helium in terrestrial nature is a product of the radioactive alpha-decay of uranium and thorium. Under normal conditions, helium is a chemically inert gas which, due to the very low liquefaction temperature (-269.9 ^oC = 4.2 ^oK) has an important application in cryogenic technology, especially in superconducting electromagnets. It has two stable isotopes: ⁴He (98.999863%) and ³He (0.000137%). Helium-4 is a very strongly bound nucleus, as it has both the proton and neutron shells filled, which are the lowest. Radioactive isotopes of helium have no practical significance, as they are very short-lived *). Of the 7 known radioisotopes of helium, ⁵ He is the "most stable" (formed by irradiation of beryllium with neutrons: ⁹Be₄ + ¹n₀ ® ⁶He₂ + ⁴He₂), which has a half-life of only 0.81sec! However, in nuclear physics, helium (⁴He) is important as an efficient cooling medium (superconducting electromagnets of accelerators and tokamaks, cooling of sensitive detectors) and also as a product of thermonuclear hydrogen fusion (§1.3 "Nuclear reactions and nuclear energy", part "Fusion of atomic nuclei"). Helium nuclei - alpha particles - are the essence of alpha-radioactivity.
*) Diproton: the short-term isotope of helium ²He₂ , also called diproton 2p, has a certain interest in nuclear physics - consists of two protons, without neutrons. This state is very unstable and breaks down almost immediately by proton emission or beta⁺ -decay. A separate diproton was not observed, only in highly excited states, eg ¹⁸Ne, the simultaneous emission of two protons was observed, which was interpreted as originating from the short-term bound state 2p.

Lithium, Berylium, Boron
Elements of this group, despite being very light, are relatively under-represented in nature for astrophysical reasons. They formed, as primordial elements, in small quantities in a rapidly expanding universe at the end of the Lepton era ("Lepton era. Initial cosmological nucleosynthesis") and in later stellar nucleosynthesis they no longer form, but are burned (§1.1, part "Cosmic Alchemy - we are descendants of stars! , passage "Representation of elements in nature" and §4.1 "The role of gravity in the formation and evolution of stars", part "Evolution of stars" in book "Gravity, black holes, and physics of space-time").
Lithium Li₃ is a very soft light metal from the alkaline group (it is the lightest metal, and the same time the lightest element in a solid state at room temperature), chemically highly reactive, so they occur in nature only in compounds. It has two stable isotopes ⁶Li (7.5%) and ⁷Li (92.5%). Although lithium has no significant longer -lived radionuclides (the longest half-life 0.84 s. has ⁸Li), this element is important in nuclear physics. ⁶ Li serves as a neutron absorber and source material for tritium production in controlled thermonuclear fusion (§1.3, part "Tokamak"). A mixture of lithium and deuterium - lithium-6 deuteride ⁶Li²H was misused as fuel for the "hydrogen" thermonuclear bomb (§1.3, part "Fusion of atomic nuclei", passage "Thermonuclear explosion").
Beryllium Be₄ is a hard gray metal that oxidizes easily in moisture; it is rare in nature (approximately 3-10 mg/kg in the earth's crust) in compounds such as emerald. It is used in special alloys in metallurgy. In nuclear physics, its low absorption (high transmittance) is used for low-energy X and gamma radiation - beryllium entrance windows of sensitive detectors. From beryllium is also fabricated some sections of tubes in accelerators, in which there is interaction of the particles - to make the flying out particles easier (without significant absorption) to penetrate to the detectors. In a mixture with a-radionuklides, beryllium serves as a laboratory source of neutrons (see, e.g. passage "Neutron radiation and its interaction" in §1.6). Beryllium has the only one stable isotope ⁹Be. Of the radioactive isotopes of beryllium, two cosmogenic radionuclides are of some scientific importance :
  Beryllium  ⁷Be , with a half-life of 53.3 days, is converted by electron capture to a stable isotope ⁷Li - in 89.5% to the ground state, in 10.5% to the excited level of 478keV, during the deexcitation of which gamma radiation of this energy is emitted. The ⁷Be isotope is formed in nature by cosmic rays in the atmosphere. These are mainly fission reactions of high-energy protons with nitrogen nuclei ¹⁴N (p, 2a) ⁷Be or oxygen ¹⁶O (p, ¹⁰B) ⁷Be, then nuclear reactions of neutrons with nitrogen nuclei ¹⁴N (n, ⁸Li) ⁷Be and oxygen ¹⁶O (n, ¹⁰B) ⁷Be. Its detection is used to study transport processes in the atmosphere. For research purposes in nuclear physics, the ⁷Be isotope is artificially prepared by irradiating lithium with accelerated protons in a cyclotron by the reaction ⁷Li (p, n) ⁷Be. The isotope ⁷Be is interesting for nuclear physics in that it first proved the dependence of the rate of radioactive transformation by electron capture on the chemical state of the isotope - see §1.2, section "Electron capture", passage "Two peculiarities of EC".
  Beryllium  ¹⁰Be is transformed into a stable isotope ¹⁰B by b^- radioactivity with a half-life of 1.6.10⁶ years in the basic state. In the atmosphere, the action of cosmic radiation creates reactions with released neutrons: ¹⁴N (n, p a) ¹⁰Be. Atoms of ¹⁰Be are trapped in the atmosphere on aerosol particles and with rainwater reach the earth's surface, where they settle in the soil, oceans and glaciers. Measurement of this ¹⁰Be deposition (by mass spectrometry), due to its long half-life, is used to monitor some geological and oceanographic processes.
  A very hidden (deep inside massive stars) natural important radionuclide is one very short-lived isotope of beryllium :
  Beryllium ⁸Be , due to its extremely short half-life 6.7.10^-17 seconds, is completely insignificant from the point of view of "terrestrial" nuclear physics. Almost immediately after its formation, beryllium-8 breaks down into 2 alpha particles (helium nuclei). However, it is very important from the point of view of nuclear astrophysics: via Be-8, nuclear "helium" burns to carbon in the late stages of massive star evolution. In the specific conditions of high temperatures and pressures inside helium-rich massive stars (after "burning out" of hydrogen), even such a short lifetime of ⁸Be is enough for the capture of ⁴He nuclei in ⁸Be to produce a large amount of carbon ¹²C - it is discussed in §4.1 "The role of gravity in the formation and evolution of stars", part "Evolution of stars" passage "Combustion of helium" book "Gravity, black holes and space-time physics".
Boron B ₅ is a semi-metallic element found only in compounds in terrestrial nature and has two stable isotopes: ¹⁰B (19.9%) and ¹¹B (80.1%). Although boron has no useful radionuclides (all are very short-lived, the longest 0.77s. has ⁸B), this element is very important in nuclear technology. The high effective cross section of the isotope ¹⁰B for the absorption of slow neutrons makes it very suitable material for control rods in nuclear reactors, or the addition of boric acid into cooling water for reactivity control (§1.3, section "Nuclear reactors").

Carbon
Carbon C₆ (Carboneum) is a very important element in the universe, where it is formed by the thermonuclear fusion of helium in the interior of massive stars (§1.1, passage "We are descendants of stars! ", in more detail "Thermonuclear fusion in the interior of stars"). In massive stars of the 2nd and subsequent generations, carbon also participates in the thermonuclear fusion of hydrogen into helium (as a "catalyst" - CNO cycle). Carbon is the fourth most abundant element in the universe. Atomically, carbon is a non-metallic element which, in addition to the amorphous form, occurs in several crystalline structures: graphite (solid - hexagonal structure), diamond (cubic structure, forming very hard, optically transparent crystals), fullerene (spherical "molecules" from networks of carbon atoms, e.g. C₆₀).
  Carbon is extremely important in terrestrial nature (content in the earth's crust approx. 200-800 mg/kg), where it occurs mainly in compounds, the most important of which is gaseous carbon dioxide CO₂ (approximately 0.04% in the Earth's atmosphere - it is important for photosynthesis in plants), and of minerals, as calcium carbonate CaCO₃. CO₂ and some other carbon gases (e.g. methane) show a considerably high reflective capacity for thermal infrared radiation ("greenhouse effect") and thus act as a thermoregulatory component in the atmosphere of the Earth and other planets.
  Thanks to the specific configuration of the atomic shell, carbon is able to form a huge amount of so-called "organic" compounds with hydrogen, oxygen, nitrogen, phosphorus and other elements, often to form very long, branched and cyclic molecules. Thanks to these very diverse combinations, which can react together again to form other complex specific substances, carbon compounds have become the basic building block of living matter - carbon is an essential biogenic element.
  Carbon has a number of isotopes (⁸C - ²²C), of which only two isotopes ¹²C (98.93%) and ¹³C (1.07%) are stable. Important are two radioisotopes of carbon :
Carbon ¹⁴ C
From the radioactive carbon isotope is most important radiocarbon ¹⁴C₆, which with a half-life of 5730 years converts by b^- -radioactivity ¹⁴C ® ¹⁴N + e^- + n' to the ground state of nitrogen ¹⁴N₇. ¹⁴C is a pure beta emitter with a maximum energy of emitted electrons 156.5 keV (blue curve in the right part of Fig.1.4.7 mentioned above in passage ³ H). It occurs in nature as an important cosmogenic radionuclide, which is formed by the action of neutrons ejected by cosmic radiation from the nuclei of atoms, on nitrogen in the upper layers of the Earth's atmosphere: n^o + ¹⁴N₇ ® ¹⁴C₆ + p⁺ (see §1.6, section "Cosmic radiation", Fig.1.6.7). It is the basis of the radicarbon method of determining the age of archaeological objects (described above in the section "Radioisotope (radiometric) dating", passage "Radiocarbon dating method").
  The content of radiocarbon-14 in nature is also influenced by human activity. To a lesser extent there is a reduction in the content of ¹⁴C in the environment by burning fossil fuels, in which over millions of years, the original content ¹⁴C has already disappeared by radioactive decay; thus, CO₂ generated by the combustion of fossil fuels does not contain ¹⁴C and the proportion of natural radioactive ¹⁴CO₂ is thus diluted. Nuclear technologies, on the other hand, increase the content of radiocarbon-14. The ¹⁴C content increased significantly in the 1960s during nuclear weapons tests due to the ¹⁴N (n, p) ¹⁴C nuclear reactions by the effect of neutrons released during the explosion, on atmospheric nitrogen. A smaller amount of radio-carbon ¹⁴C is also formed during the operation of fission nuclear reactors by the nuclear reaction ¹⁷O (n, a) ¹⁴C on oxygen in cooling water and by reacting ¹⁴N (n, p) ¹⁴C on nitrogen dissolved in cooling water; from the cooling water with ventilation, this small amount of ¹⁴CO₂ gets into the air through the ventilation chimneys of the power plant.
  Like tritium, ¹⁴C radio-carbon is produced artificially by neutron activation of ¹⁴N (n, p) ¹⁴C in a nuclear reactor for many applications, mainly biological ones, especially tracking methods (§3.5 "Radioisotope tracking methods").
Carbon ¹¹ C
Another somewhat important radioisotope of carbon is short-lived positron ¹¹C, which with a half-life of 20.36 min. converts mainly by beta⁺ -radioactivity (99.75%) and to a small extent by electron capture (0.25%) to the ground state of boron ¹¹B. It is used (relatively rarely) in positron emission tomography (§4.3 "PET cameras", § 4.8 "Radionuclides and radiopharmaceuticals for scintigraphy"). The isotope ¹¹C is prepared in a cyclotron either by irradiating boron with accelerated deuterons in reactions ¹⁰B (d, n) ¹¹C, ¹¹B (d, 2n) ¹¹C (taking place simultaneously with both stable isotopes of natural boron), or by irradiating nitrogen with protons: ¹⁴N (p, a) ¹¹C.
  In this connection we will mention three other light positron radionuclides used in positron emission tomography :

Nitrogen, Oxygen, Fluorine
Nitrogen N ₇ ( Nitrogenium ) is an inert gaseous element at normal temperatures, forming the main part of the Earth's atmosphere (78% by volume). At -195 °C it changes to a liquid state; liquid nitrogen is a very important cryogenic medium. Along with carbon, hydrogen and oxygen, nitrogen is an important biogenic element as part of the amino acids that make up proteins. Nitrogen has two stable isotopes ¹⁴N (99.64%) and ¹⁵N (0.36%). Radioactive isotopes of nitrogen have relatively short half-lives, less than 10 minutes. It is worth mentioning two of them :
Nitrogen ¹³ N
with a half-life T1/2 = 9.96 min. converts by beta⁺ -radioactivity (99.82%) and to a small extent by electron capture (0.18%) to the basic state of carbon ¹³C. The ¹³N isotope is prepared in a cyclotron either by irradiating oxygen (in water) with accelerated protons by a nuclear reaction of ¹⁶O (p, a) ¹³N, or by irradiating carbon with deuterons in the reaction ¹²C (d, n) ¹³N. Nitrogen ¹³N is occasionally used in positron emission tomography in the form of ammonia and ¹³N-labeled amino acids.
Note: Isotope ¹³N played an important role in the process of studying radioactivity: it was the first artificially prepared radioactive isotope. In 1934, F.Joliot and I.Curie discovered it in experiments with irradiation of boron with alpha particles (from polonium); was formed here by the reaction of ¹⁰B (a , n) ¹³N.
Nitrogen ¹⁶ N
with a half-life T1/2 = 7.13 sec. converts beta^-- radioactivity (E_bmax = 4290keV and 10420keV) to the ground state (28%) and to the highly excited states of 6130keV (67%) and 7115keV (5%) of oxygen ¹⁶O. During deexcitation, high-energy gamma photons 6.13MeV and 7.1MeV are emitted. Isotope ¹⁶N is formed by the reaction of ¹⁶O (n, p) ¹⁶N fast neutrons with the basic oxygen isotope ¹⁶O, mainly in the cooling water of the primary circuit of water-cooled nuclear reactors. The activity of the ¹⁶N isotope in the circulating cooling water is proportional to the number of neutrons in the reactor core, i.e. the intensity of the chain fission reaction (the number of fissiones per second) and the thermal power of the reactor. Measurement of ¹⁶N activity by means of gamma-detectors attached from the outside of the cooling water circulation pipe of the primary circuit can therefore monitor the correct operation of the reactor.
Oxygen O ₈ (Oxygenium) is a reactive gaseous element at normal temperatures, making up 21% (by volume) of the Earth's atmosphere. Together with carbon and hydrogen, it is the most important biogenic element. It has three stable isotopes: ¹⁶O (99.76%), ¹⁷O (0.04%), ¹⁸O (0.2%). The radioactive isotope ¹⁵O is sometimes used in positron emission tomography :
Oxygen ¹⁵ O
with a half-life T1/2 = 122 sec. converts by beta⁺ -radioactivity (99.82%) and to a small extent by electron capture (0.12%) to the basic state of nitrogen ¹⁵N. Isotope ¹⁵O is prepared in a cyclotron either by irradiating nitrogen (enriched with the ¹⁵N isotope ) by accelerated deuterons in a nuclear reaction of ¹⁵N (d, 2n) ¹⁵O, or by irradiating oxygen with protons in a ¹⁶O (p, pn)¹⁵O reaction. Its use in PET is relatively rare due to the short half-life.
Fluorine F ₉ is a green-yellow gas at normal temperatures, very reactive, so it occurs on Earth only in compounds. It belongs to the group of halogens - salt-forming elements (Greek halos = salt). It is relatively widespread (540mg / kg in the earth's crust). It has a single stable isotope of ¹⁹F. Radioactive isotope ¹⁸F is very widely used in positron emission tomography :
Fluorine ¹⁸ F
with half-life T1/2 = 110 min. converts by beta⁺ -radioactivity (96.86%) and electron capture (3.14%) to the basic state of oxygen ¹⁸O. The isotope ¹⁸F is prepared in a cyclotron most often by irradiating of oxygen (in water enriched with the isotope ¹⁸O) by accelerated protons in reaction ¹⁸O (p, n) ¹⁸F, less often by irradiation of compressed neon with accelerated deuterons by nuclear reaction ²⁰Ne (d, a) ¹⁸F. In positron emission tomography PET is mostly used in the form of ¹⁸F-fluoro-deoxyglucose (FDG - §4.8 "Radionuclides and radiopharmaceuticals for scintigraphy", part "Positron radionuclides").
Positron radionuclides
All positron radionuclides, if they are contained in the substance environment (which is practically always), emit gamma radiation with an energy of 511 keV (§1.2, part "Radioactivity b⁺ ") during the annihilation of emitted positrons with electrons e⁺ + e^- ® 2 g (§1.2, part "Radioaktivity b⁺" and §1.6, section "Interaction of charged particles- direct ionizing radiation", Fig.1.6.1 below part). The gamma-spectrum of "pure" light positron radionuclides, which we have discussed so far, is formed by a single annihilation e⁺e^- peak 511keV *) with an intensity close to 200% - in ¹¹C (199.5%), ¹³N (199.6%), ¹⁵O (199.7%), ¹⁸F (193.7%). Some other (heavier) positron radionuclides have a positron content of less than 100% and therefore the intensity of annihilation radiation is often significantly lower than 200% - see eg ²² Na (180.7%), ⁵⁸Co (29.8%), ⁶⁴Cu (35%), ⁶⁸ Ga (177.8%), ⁸⁹ Zr (45.6%); other gamma peaks are also present, from nuclear deexcitations.
*) It is interesting that the annihilation gamma peak 511keV is slightly wider in the spectrum, compared to the surrounding "nuclear" photopeaks, due to the Doppler expansion caused by different braking rates of positrons in the substance before annihilation with electrons (discussed in §1.2, passage "Spectrum gamma radiation"). This extension is only about 1.2 keV and is manifested only on semiconductor spectra (we have clearly observed them in our detailed spectrometric measurements, but these differences are not visible on the strongly grapfically reduced and contracted spectra displayed below...).

Conversion schemes of positron radionuclides ¹¹C, ¹³N, ¹⁵O, ¹⁸F and gamma spectrum of their annihilation radiation 511 keV.

Positron radionuclides are used mainly in nuclear medicine in the form of suitable radiopharmaceuticals, which are captured and accumulated especially in tumor tissues, the distribution of which is then imaged by PET positron emission tomography based on the coincidence detection of gamma 511keV annihilation photon pairs (see §4.3 "Tomographic cameras" and §4.8 "Radionuclides and radiopharmaceuticals for scintigraphy", part "Positron radionuclides"). Of the above-mentioned light positron radionuclides, only fluorine ¹⁸F is widely used, other positron radionuclides (C-11, N-13, O-15) only rarely, due to their short half-life.
  In our treatise we will gradually present a number of other important light, medium and finally heavy nuclides :

Phosphorus, Sulfur
These are important biogenic elements, abundant in the earth's crust, seawater and living organisms.
Phosphorus P ₁₅ (lat. Phosphorus) is a relatively widespread non-metallic element - content in the earth's crust about 1 g/kg. Pure phosphorus occurs in several allotropic modifications, the most famous of which are three named according to their color appearance: White (yellowish) phosphorus formed by P₄ molecules, which is soft and highly reactive, especially with oxygen (can spontaneously ignite). Red phosphorus with a polymer structure that is relatively stable. Black phosphorus with a layered polymer structure is the most stable and also exhibits metallic electrical, thermal and optical properties. In nature, however, phosphorus is only found in compounds.
  Phosphorus is a very important biogenic element found in all plant and animal cells. It is a binding phosphate component of genetic biomolecules DNA and RNA, energy molecules adenosine triphosphate, phospholipid cell membranes (§5.2, part "Cells - basic units of living organisms"). It is also stored in bones in calcium phosphate, hydroxiapatite.
  Phosphorus has a single stable isotope ³¹P. From a number of radioactive isotopes ^24-46P most have short half-lives (minutes, seconds, milliseconds) . Due to the longer half-life, only two phosphorus radioisotopes are important :
Phosphorus ³² P 
With a half-life of 14.27 days, is converted by beta^- radioactivity (E_{b max} = 1710 keV) to sulfur ³²S in the ground state, it is a pure beta emitter. In nature, a small amount of the ³²P isotope is formed as a cosmogenic radionuclide in the atmosphere by nuclear reactions of secondary neutrons from cosmic rays. It is produced artificially in a nuclear reactor by irradiating of phosphorus in the reaction ³¹P (n, g) ³²P, or by irradiating sulfur-32 with fast neutrons by the reaction ³²S (n, p) ³²P.
  Radioactive ³²P is used as a radioindicator in laboratory methods of molecular biology and genetics for radiolabeling. ³²P -phosphate groups are incorporated into genetically important molecules of nucleotides, DNA, RNA, which can then be sequenced and detected radiometrically (autoradiographically) - §2.2, passage "Autoradiography". ³²P can also be used to diagnose and treat cancer - tumor cells tend to take up more phosphorus compounds than normal cells.
Radiophosphorus ³²P, as a pure beta-radionuclide, was used for the treatment of hematological malignancies (iv application of about 200-500 MBq in the form of phosphate), especially polycythemia - §3.6 "Radioisotope therapy", passage "Treatment of hematological diseases of radiophosphorus ³²P".
Phosphorus ³³ P
is converted with a half-life of 32.97 days by beta^- radioactivity (E_{b max} = 248 keV) to sulfur ³³S in the ground state. Radioactive ³³P is used in similar laboratory applications as phosphorus-32, in methods where lower beta electron energy is preferred (eg better resolution in autoradiography).

Conversion schemes of radionuclides ³²P, ³³P, ³⁵S and their beta spectra (the same note applies to the beta spectrum as in Fig.1.4.7) .

  Sulfur S ₁₆ (lat. Sulfur) is also highly reactive and therefore occurs in nature above all in compounds, mainly in sulfides. Contents in the earth's crust of about 0.03 to 0.09 %, concentration in sea water of about 900 mg/liter. As a pure element, it occurs during volcanic activity, where it crystallizes from hot volcanic gases containing sulfur fumes. Melting point 115°C, boiling point 445°C. Sulfur is also an important biogenic element, it is part of amino acids (cysteine, methionine) forming proteins.
  It has four stable isotopes: ³²S (94.99%), ³³S (0.75%), ³⁴S (4.25%) and ³⁶S (0.019%). Of the radioactive isotopes of sulfur, one has a practical application :
Sulfur ³⁵ S
is converted with a half-life of 87.25 days by beta^- radioactivity (E_{b max} = 167.3 keV) to chlorine ³⁵Cl in the ground state. Like ³²P, ³⁵S sulfur is formed in small amounts in the atmosphere as a cosmogenic radionuclide. The ³⁵S isotope is artificially prepared in a nuclear reactor by irradiating chlorine (potassium chloride) with neutrons by reacting ³⁵Cl (n, p) ³⁵S. Radioactive sulfur-labeled amino acids ³⁵S-cysteine and ³⁵S-methionine is used in biochemical research to study amino acid metabolism.

Sodium, Potassium
Sodium and potassium are the most common elements of the alkali metals, abundant in the earth's crust, seawater and living organisms. They are soft (they can be cut with a knife), light (they float on water), silvery shiny metals, easily melted (sodium has a melting point of 97.7°C, potassium 63.4°C). They are very reactive (they react particularly violently with water), so they occur in nature only in compounds.
Sodium Na ₁₁ (lat. Natrium) is the most common alkaline element - content in the earth's crust 2.4-2.6 %, concentration in seawater 10.5 g/liter. Sodium is one of the biogenic elements and is found in all cells of plant and animal tissues, as well as in extracellular fluid, cca 4% of salt NaCl.
It has a single stable isotope of ²³Na. Of the radioactive isotopes, sodium-22 is particularly important :
Sodium ²² Na
is converted with a half-life of 2.6 years predominantly by beta⁺ -radioactivity (90%, E_{b max} = 500keV) and partly by electron capture (10%) to ²²Ne in the excited state of 1275keV; during deexcitation, gamma photons with the same energy of 1275keV are emitted. Only 0.056% are converted to baseline ²²Ne. The isotope ²²Na is prepared in a cyclotron either by irradiating magnesium metal with deuterons in the nuclear reaction ²⁴Mg (d, a) ²²Na, or by irradiating fluorine with alpha-particles in the reaction ¹⁹F (a,n) ²²Na.
  The annihilation peak 511 keV (180%) dominates in the gamma spectrum of sodium-22, in the area of higher energies there is a significant peak 1274 keV (100%).

Conversion scheme and gamma spectrum of sodium ²²Na.

Radionuclide ²² Na is mainly used as a laboratory source of positrons for atomic and nuclear physics (see eg §1.5, section "Antiparticles - antiatoms - antimatter - antiworlds", passage "Artificial production of antimatter") and for material analysis of samples *). For some PET cameras, sealed Na-22 emitters serve as calibration and adjustment sources of 511 keV annihilation gamma radiation (in addition to ¹⁸F samples and Ge ⁶⁸ -Ga ⁶⁸ standards ) - see §4.3, section "Positron emission tomography of PET".
*) Analysis of materials using positrons, so-called positron annihilation spectrometry (briefly described in §3.3, section "Positron annihilation spectrometry"), is based on the behavior of positrons as they pass through the test substance. The lifetime of the positron is measured, ie the time interval between its formation in beta⁺ -radioactivity of ²²Na (indicated by photon emission 1275keV) and extinction (accompanied by radiation of annihilation photons 511keV), which can provide information about structural irregularities - dislocations, vacancies, impurities in crystal structure.

 The alkali metal potassium K ₁₉ (lat. Kalium) is also very reactive and therefore occurs in nature only in compounds. Contents in the crust of about 2.0 to 2.4 %, concentration in sea water of 380 mg/liter. Potassium is also a biogenic element.......
It has two stable isotopes ³⁹K (93.3%) and ⁴¹K (6.73%). Natural potassium also contains 0.0017 % of the long-lived radioactive isotope ⁴⁰K :
Potassium ⁴⁰ K
is a widespread natural (primary) radionuclide with a very long half-life of 1,25.10 ⁹ years. Decays branched by beta^- -radioactivity (89%) to the ground state of calcium ⁴⁰Ca and by electron capture (11%) to argon ⁴⁰Ar - to its excited state of 1460 keV. Both of these daughter isotopes are stable, further decay no longer continues. The characteristic gamma peak of 1460 keV (10.5%) of potassium is clearly visible in all spectrometric measurements of natural samples with an acquisition time of several hours (cf. Fig.1.4.2 above in the section "Natural radionuclides").

Conversion scheme and gamma spectrum of potassium ⁴⁰K.

Scandium
Scandium Sc ₂₁ (the name comes from its discovery in Scandinavia - L.F.Nilson, 1879, Sweden) is a silvery white soft and light metal somewhat similar to aluminum, its proportion in the earth's crust is about 5-2 mg/kg. It has a relatively small use, it is used in alloys with aluminum. It has a single stable isotope of ⁴⁵Sc. Of the about 25 known radioactive isotopes of scandium, ⁴⁴Sc and ⁴⁷Sc have promising applications in nuclear medicine :
Scandium ⁴⁴ Sc
Transforms with a half-life of 3.97 hours, predominantly beta⁺ -radioactivity (94%, E_b+ _max = 1474keV) and partially electron capture (5.7%) to ⁴⁴Ca in the excited state of 1157keV (higher excited levels of 2656 and 3301 keV are only weakly represented); during deexcitation, gamma photons are emitted mainly with this energy 1157keV. The annihilation peak 511keV (188%) dominates in the gamma spectrum of scandia-44, in the area of higher energies is the peak 1157keV (99.8%); faint higher g -peaks 1499, 2144, 2556 and 3301 keV are only visible at high magnification.

Conversion scheme and gamma spectrum of scandium ⁴⁴Sc.

Positron radionuclide ⁴⁴Sc has promising use in nuclear medicine for scintigraphic imaging by PET positron emission tomography (see §4.3 "Tomographic cameras" and §4.8 "Radionuclides and radiopharmaceuticals for scintigraphy", section "Positron radionuclides"). Trivalent skanium binds well, using proven bifunctional chelating agents of the DOTA type, to vector biomolecules, mainly monoclonal antibodies. Compared to ¹⁸F and especially ⁶⁸Ga, a longer half-life of almost 4 hours is also advantageous, allowing imaging even with heavier biomolecules with slower pharmacokinetics. It can also be used theranostically in combination with analogous therapeutic radiopharmaceuticals labeled with ⁹⁰Y, ¹⁷⁷Lu, or ideally ⁴⁷Sc.
  Its great advantage is the production method: Although it can be produced by nuclear reaction of ⁴⁴Ca (p, n) ⁴⁴Sc on a small cyclotron, in nuclear medicine workplaces (without the need for a cyclotron) ⁴⁴Sc can be continuously and long-term obtained by elution from ⁴⁴Ti/⁴⁴Sc generator :
The parent titanium ⁴⁴Ti for the generator is obtained on a cyclotron by a nuclear reaction of ⁴⁵Sc (p, 2n) ⁴⁴Ti. In the column of the generator, the parent ⁴⁴Ti with a long half - life of 60.4 years is transformed by electron capture into the daughter ⁴⁴Sc, which is eluted with a suitable solution (H₂C₂O₄ + HCl). Due to the long half-life of the parent ⁴⁴Ti (approximately 130,000 times longer than the daughter ⁴⁴Sc), secular equilibrium is maintained in the generator (see section "Radionuclide Generators"), so that in the long run, for many years, the required ⁴⁴Sc can be eluted every day, with the same activity, given by the activity of the default ⁴⁴Ti...
  Given these advantageous properties, it can be expected that scandium ⁴⁴Sc can in come cases replace the existing major PET radionuclides ¹⁸F and ⁶⁸Ga ..?..
  A certain disadvantage of ⁴⁴Sc is the simultaneous emission of high-energy gamma radiation 1157keV, which increases the radiation dose of patients and PET workers. Therefore, there are considerations about the use of the neighboring radionuclide scandium ⁴³Sc (T1/2 3.89 hours, beta⁺ 88%, gamma 373keV (23%)), which has properties similar to ⁴⁴Sc, but shows much lower energy and intensity of the accompanying gamma radiation ...
Scandium ⁴⁷ Sc
With a half-life of 3.35 days, it is converted by beta^- -radioactivity to ⁴⁷Ti (which is a stable nuclide), in 31.6% to baseline and in 68.4% to an excited level of 159 kV. Max. the energy of the beta electrons for both cases is 600keV and 441keV, the mean beta energy is 162keV. The ⁴⁷Sc gamma spectrum consists of a single 159keV peak (68%).

Conversion scheme and gamma spectrum of scandium ⁴⁷Sc.

The ⁴⁷Sc isotope can be prepared by neutron reactions ⁴⁷Ti (n, p) ⁴⁷Sc, ⁴⁶Ca (n, p) ⁴⁷Ca .. ... ⁴⁷ Sc .... ... in a nuclear reactor, or in a cyclotron by reactions ⁴⁸Ca (p, 2n) ⁴⁷Sc, ⁴⁶Ca (p, g) ⁴⁷Sc, ........
  Scandium ⁴⁷Sc is a promising beta^- radionuclide for therapy in nuclear medicine. In this case, the gamma radiation of 159 keV can advantageously be used for scintigraphic imaging (planar/SPECT) and monitoring of radionuclide therapy. Sequence ⁴⁴Sc/⁴⁷Sc can be an excellent teranostic isotope pair for PET imaging + radionuclide therapy.

Chrome, Iron
Chromium Cr ₂₄ is a light white hard metal, resistant to corrosion. It is relatively abundant in terrestrial nature (in the earth's crust about 0.1-0.2 g/kg). It is mainly used in metallurgy as an alloying additive or for plating. It has 4 stable isotopes: ⁵⁰Cr (4.35%), ⁵²Cr (85.8%), ⁵³Cr (9.5%), ⁵⁴Cr (2.37%) . Of the radioactive isotopes, one found practical application :
Chromium ⁵¹ Cr
It is converted with a half-life of 27.7 days by electron capture to the stable isotope ⁵¹V - in 90% of the transformations it is to the ground state and in 10% to the excited state 320keV, during the deexcitation of which gamma photons of the same energy are emitted. The very simple gamma spectrum of chromium-51 consists of a single 320keV photopeak (10%). Compared to most other beta (EC) -gamma radionuclides, 51-chromium is, in recalculation on the activity value, a relatively weak gamma emitter, about 10 times weaker than cesium ¹³⁷Cs, cobalt ⁶⁰Co or radioiodine ¹³¹I. Isotope ⁵¹Cr is prepared by nuclear reaction ⁵⁰Cr (n, g)⁵¹Cr by irradiating chromium (enriched to about 80% with the isotope ⁵⁰ Cr) by neutrons in a nuclear reactor.

Decomposition scheme and gamma spectrum of chromium ⁵¹Cr.

The radionuclide ⁵¹Cr is used as a tracer radioindicator in some applications in industry, geology and nuclear medicine. In nuclear hematology, by means ⁵¹Cr-chroman ions were labeled the red blood cells, or event. white blood cells. Using the autologous erythrocytes labeled in this way, the lifespan (or half-life) of the blood cells and, if appropriate, the place of their destruction (§4.9 "Survival and sequestration of erythrocytes"). The use of ⁵¹Cr in nuclear medicine is almost abandoned.
  Radionuclide ⁵¹Cr was too used several times to track groundwater pathways. A solution of radiochrome was poured into an immersion spring, after which water samples were taken from several nearby watercourses and measured on a sensitive well scintillation detector - whether ⁵¹Cr radioactivity appeared in them, for what time and in what quantity.

  Iron Fe ₂₆ (Ferrum) is a ferromagnetic metal element, relatively abundant in nature (4-6% in the earth's crust). This well-known metal is a basic construction material in mechanical engineering, construction, electrical engineering and many other technical fields, as well as in household and everyday life. It has four stable isotopes: ⁵⁴Fe (5.8%), ⁵⁶Fe (91.7%), ⁵⁷Fe (2.2%) and ⁵⁸Fe (0.28%). Of the many radioactive isotopes of iron, two are of practical importance :
Iron ⁵⁵ Fe
is converted with a half-life of 2.74 years by electron capture to the ground state of manganese ⁵⁵Mn. The characteristic X-rays K_a,b with energies around 6keV are emitted. ⁵⁵Fe
emitters with sufficiently high activity are used as sources of soft X-rays for X-ray fluorescence analysis of light elements (lighter than manganese), eg in geological survey of rocks. Iron ⁵⁹ Fe
It is converted with a half-life of 44.5 days of beta^- -radioactivity to stable cobalt ⁵⁹Co, mainly to excited states of 1099keV (53%) and 1292keV (45%). During deexcitation, g radiation is emitted mainly with these two energies (with low representation then 142, 192, 335, 1482 keV). It was used in ferrokinetic tests in hematology in nuclear medicine to study iron metabolism in connection with the processes of red blood cell production in anemia or leukemia (§ 4.9.9. , passage "Examination of iron kinetics with ⁵⁹ Fe"). In plant biology, the isotope ⁵⁹Fe has been used to monitor the uptake of iron from soil and nutrient solutions and its storage in various parts of plants.

Cobalt
Cobalt Co ₂₇ is a ferromagnetic metal element relatively similar to iron, its proportion in the earth's crust is about 25 mg/kg. Its main use is in metallurgy. It has only one stable isotope ⁵⁹Co. The most important cobalt radioisotopes are ⁶⁰Co and ⁵⁷Co :
Cobalt ⁶⁰Co
Of the medium-heavy radionuclides, cobalt ⁶⁰Co in particular is widely used as a source of hard radiation with gamma energies of 1173 + 1332 keV for radiotherapy (§3.6, part "Isocentric radiotherapy"), defectoscopy (§3.3, part "Radiation defectoscopy") and other technical application. ⁶⁰Co, with a half-life of 5.27 years, is transformed by beta^- -radioactivity into excited states of nickel ⁶⁰Ni (which is a stable nuclide). It is mainly, in 99.88%, the level of 2506 keV, which cascades deexcites first to the level of 1332.5 keV, which then to the ground state of ⁶⁰Ni. The spectrum of gamma radiation is formed by two peaks 1173 and 1332 keV, in the scintillation spectrum the continuous Compton scattered radiation is also significantly shown.
  The ⁶⁰Co isotope is prepared by neutron irradiation of cobalt metal in a nuclear reactor by the reaction of ⁵⁹Co (n, g) ⁶⁰Co.

Conversion scheme and gamma spectrum of cobalt ⁶⁰Co.

Cobalt ⁵⁷ Co
Another important radioisotope of cobalt is ⁵⁷Co, which is used as a source of softer gamma radiation 122 +136 keV. ⁵⁷Co with a half-life of 271.8 days is converted by electron capture to excited levels of 706.4keV (0.18%) and especially 136.5keV (99.82%) of iron ⁵⁷Fe. The most saturated level of 136.5 keV is deexcited in 10% to the ground state of ⁵⁷Fe and in 85.5% to the level of 14.4keV with the emission of main energy gamma 122 keV. After electron capture, photons of the characteristic X-ray K_a,b are emitted during electron jumps between the L and K shells of iron with energies of 6.4-7.1 keV, as well as conversion and Auger electrons. Gamma spectrum ⁵⁷Co consists above all of the main peak 122keV (85.5%), with the lower neighboring peak 136keV (11%); in the area of higher energies, a very weak peak of 692keV (0.16%) can be seen only after high magnification.
  Isotope ⁵⁷Co is prepared by deuterone irradiation of metallic iron in a cyclotron by a nuclear reaction of ⁵⁶Fe (d, n) ⁵⁷Co.
  

Conversion scheme and gamma spectrum of cobalt ⁵⁷Co.

⁵⁷Co is used as a source of gamma radiation for Mösbauer spectrometry of iron and its compounds (§3.4, part "Mössbauer spectroscopy"). In nuclear medicine, vitamin B12 labeled ⁵⁷Co was used to determine the intake of this vitamin by intestinal resorption (§ 4.9.9, passage "Schilling test").
  Both mentioned cobalt radionuclides ^57,60Co are also used as reference gamma emitters. For the proximity of gamma radiation energy 122keV with energy 140keV ^99mTc, with point sources ⁵⁷Co  they are used as pointers in scintigraphy and planar homogeneous sources ⁵⁷Co are used to adjust and test the homogeneity of the field of view of scintillation gamma cameras (see "Phantoms and phantom measurements in nuclear medicine").
Cobalt ⁵⁸Co
For radioisotope diagnosis in nuclear medicine in the 60s-80s was also used the cobalt ⁵⁸Co, which is a 70.8 day half-life of the electron capture (84%), and b⁺ -radioactivity (15%) is converted to the excited states of iron ⁵⁸Fe - 811keV (84 + 15%) and 1675keV (1.2%). During deexcitation, gamma photons are emitted mainly with an energy of 811keV (99.4%), with a much lower intensity of 864keV (0.7%) and 1675keV (0.5%). In nuclear physics, it is sometimes used as a source of positrons. In nuclear medicine, vitamin B12 labeled ⁵⁸Co was used in the 1970s and 1980s, similar to the above ⁵⁷Co. All these methods are now abandoned.

Nickel ⁵⁶Ni --> Cobalt ⁵⁶Co
In a somewhat atypical way, we present here the following two interrelated radionuclides, which are important in nuclear astrophysics during supernova explosions :
Nickel ⁵⁶Ni
according to astrophysical analyses, it is produced in colossal quantities (on the order of the mass of our globe..!..) during the explosion of supernovae, especially thermonuclear supernovae of type Ia - it is described in §4.2, section "Supernova explosion. Neutron star. Pulsars." monograph "Gravity, black holes and space-time physics".
  With a half-life of 6.1 days, ⁵⁶Ni is converted by electron capture to the excited 1.72 MeV level of cobalt ⁵⁶Co. During deexcitation through the three lower levels, gamma radiation with energies of 158keV (99%), 269keV (37%), 480keV (36%), 750keV (49%), 812keV (86%), 1562keV (15%) are emitted.
The daughter ⁵⁶Co is also radioactive :
Cobalt ⁵⁶Co
with a half-life of 77.27 days is converted by beta⁺-radioactivity (20%, E_b+_max=1.49 MeV) and electron capture (80%) to relatively high excited states of iron ⁵⁶Fe (2085keV (20%), 3120keV (15%) , 3451keV (21%), 3830keV (15%), 4050keV (24%), 4300keV (1.4%)), which is stable. During deexcitation, hard gamma rays of many energies are emitted, the most prominent of which are 847keV (100%), 977keV (1.4%), 1038keV (14%), 1175keV (2.3%), 1238keV (67%), 1360keV (4.3%), 1771keV (15%), 2015keV (3.1%), 2035keV (8%), 2598keV (17%), 3009keV (1%), 3202keV (3.2% ), 3253keV (8%), 3451keV (1%).

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Transformation scheme and gamma spectrum of ⁵⁶Ni and ⁵⁶Co (the spectrum will be measured and refine the decay scheme, when we get a sample of ⁵⁶Ni...).

Both of these radionuclides ⁵⁶Ni and ⁵⁶Co emit a huge amount of energy by their radioactive decay in supernovae, thanks to which the supernova can shine for many days with the brightness of billions of Suns (passage "Supernova radiation. Light curve. Spectrum of radiation") ..!..
  These radionuclides are of no importance for technical or laboratory applications.

Copper, Galium, Germanium, Selenium
Copper Cu₂₉ (Cuprum) is a well-known yellow-red shiny metal with very good electrical and thermal conductivity. The content in the earth's crust is about 50-70 mg/kg, pure metallic copper occurs only rarely, it is mostly found in compounds - sulfides, oxides, in combination with iron compounds and others. In addition to metallurgy (alloys with tin - bronze or zinc - brass), mechanical engineering and construction, the main use of copper in electrical engineering is due to excellent electrical conductivity and corrosion resistance. Copper has two stable isotopes, ⁶³Cu (69.15%) and ⁶⁵Cu (30.85%). Some radioactive isotopes of copper are sporadically used or tested in nuclear medicine (especially PET scintigraphy) and biochemical studies: ⁶¹Cu (T1/2 = 3.3 hours, b⁺, EC), ⁶²Cu (T1/2 = 9, 7min., b⁺, EC), ⁶⁴Cu (T1/2 = 12.7 h, b⁺, EC), ⁶⁷Cu (T1/2 = 61.8 h, b^-, g). Two copper radionuclides appear promising :
Copper ⁶⁴ Cu,
which with a half-life of 12.7 hours is converted by beta⁺ -radioactivity (17.5%) and electron capture (44%) to the basic (53%) and excited (0.5%) state of ⁶⁴Ni; further beta^- -radioactivity (38.5%) to the basic state of ⁶⁴Zn. In the gamma spectrum of ⁶⁴Cu dominates (as with any positron radionuclide) e^- e⁺ annihilation peak 511 keV (35%), in the area of higher energies a weak peak 1345.7 keV (0, 47%) can be seen only at a significant magnification .

Conversion scheme and gamma spectrum of copper ⁶⁴Cu .

The positron radionuclide Cu-64 is occasionally used in positron emission tomography ("§4.3 "Positron emission tomography PET", §4.8 "Radionuclides and radiopharmaceuticals for scintigraphy", section "Radionuclides and radiopharmaceuticals for PET"). Complex ⁶⁴Cu-ATSM (acetyl methyl-thiosemicarbazone) are rapidly and selectively taken up in hypoxic tissues, used for diagnosis of hypoxia myocardium and brain, as well as tumor hypoxia. ⁶⁴Cu-TETA-octreotide permits PET imaging neuroendocrine tumors. It is also tested for labeling of monoclonal antibodies, e.g. ⁶⁴Cu-DOTA-cetuximab, bombesin peptide.
Copper ⁶⁷ Cu
is converted with a half-life of 61.8 hours by beta^- -radioactivity to basic (20%) and excited states of zinc ⁶⁴Zn, during their deexcitation gamma radiation with energies of 91keV (7%), 93keV (16%), 185keV (49%) is emitted; three other higher energies up to 393keV are weak, <1%....
....... picture - decay scheme + gamma spectrum ....add......
Combination of the designation of the same biochemical carrier with the isotope Cu-64 for the diagnosis of PET and Cu-67 for beta-rays therapy are promising for theranostics in nuclear medicine...

  Galium Ga ₃₆ is a soft, very easily fusible metal (melts already at 30 °C) in a light blue-gray color. It occurs relatively rarely (representation in the earth's crust about 15 mg/kg). Its main use is in electronics as a component of a number of semiconductor materials in the manufacture of transistors and light emitting diodes (LEDs). It has two stable isotopes ⁶⁹Ga (60.1%) and ⁷¹Ga (39.9%). Two of the radioactive isotopes are used :
Galium ⁶⁷ Ga
With a half-life of 3.26 days, is transformed by electron capture into excited states of ⁶⁷Zn with energies mainly 93keV (52.5%), 184keV (22.7%) and 393keV (23.6%), the basic state is only 3%. During deexcitation of the daughter ⁶⁷Zn, photons of gamma radiation with energies mainly of 93, 184 and 393 keV are emitted. The gamma radionuclide radiation spectrum of ⁶⁷Ga consists mainly of three main lines 93keV (38%), 184kev (21%) and 300keV (17%), the weaker line is 394keV (5%). In the higher energy region, weak peaks of 494, 794 and 887 keV (representation around 0.1%) are visible in the spectrum only at high magnification.

Decomposition scheme and gamma spectrum of gallium ⁶⁷Ga.

The ⁶⁷Ga isotope is prepared by irradiating zinc or copper in a cyclotron with accelerated protons, deuterons or helium nuclei (a -particles) by nuclear reactions: ⁶⁷Zn(p,n)⁶⁷Ga, ⁶⁸Zn(p,2n)⁶⁷Ga, ⁶⁷Zn(d,2n)⁶⁷Ga, ⁶⁵Cu(a,2n)⁶⁷Ga.
  ⁶⁷Ga is used in nuclear medicine (in the form of a gallium-citrate complex) to image sites in tissues and organs affected by inflammatory processes or tumor foci (§4.8 "Radionuclides and radiopharmaceuticals for scintigraphy").

Galium ⁶⁸ Ga
is converted with a half-life of 67.7 minutes by electron capture (8.7%) and mainly by b⁺-radioactivity (87.9%) to ⁶⁸Zn, most often to the ground state (just over 1% of the transformations are to excited states ⁶⁷Zn, mainly to the level of 1077keV). The gamma spectrum of gallium-68 is dominated (as with any positron radionuclide) by e^-e⁺ annihilation peak 511 keV (178%), in the area of higher energies weak peaks 1077 (3%), 1261 (0.1% ) and 1883 (0.14%) keV are visible only at high magnification.

Conversion scheme and gamma-spectrum of gallium ⁶⁸Ga.

Radiopharmaceuticals labeled with ⁶⁸Ga are used in nuclear medicine for PET imaging (§4.3 "Positron emission tomography of PET", §4.8 "Radionuclides and radiopharmaceuticals for scintigraphy", passage "Radionuclides and radiopharmaceuticals for PET"). The ⁶⁸Ga isotope is used in workplaces most often obtained from germanium-gallium generators ⁶⁸Ge/⁶⁸Ga (mentioned a bit below in the passage "Germanium ⁶⁸ Ge", including a germanium phantom for PET cameras). Galium ⁶⁸ Ga is to some extent "PET analog" of usual technetium ^99mTc for SPECT and planar scintigraphy. Allows chelating binding to a variety of radiopharmaceuticals, including lighter monoclonal antibodies (of Fab fragments). So far, the most frequently used for display of neuroendocrine tumors (somatostatin receptors - labeled octreotide type ⁶⁸Ga-DOTATOC and its derivatives). Very promising seems PET imaging of prostate tumors using labeled prostate membrane antigen ⁶⁸Ga-PSMA (J591, 617, I & T, ...), followed by biologically targeted radionuclide therapy using the same antiPSMA monoclonal antibodies, labeled with beta or alpha radionuclides.
  Imaging of peptide receptors expressing gastrin- bombesin receptors , eg with ⁶⁸Ga-DOTA-PEG2 -bombesin, ⁶⁸Ga-BZH3 , is also tested. Furthermore, epidermal growth factor receptors HER using the labeled Fab fragment of trastuzumab, also vascular endothelial growth factor receptors VEGF. ⁶⁸Ga-Annexin can be used for PET to image apoptosis.
Galium-68 is a very promising diagnostic PET radionuclide, which has - in combination with therapeutic radionuclides  ⁹⁰Y, ¹⁷⁷Lu, ²²⁵Ac, ²²⁷Th - high teranostic potential (discussed in §4.9, passage "Combination of diagnostics and therapy - teranostics").

  Germanium Ge ₃₆ is a gray-white solid semi-metallic element, which occurs relatively rarely in nature (representation in the earth's crust approx. 5-7 mg/kg) . Its main use is in electronics as a component of a number of semiconductor materials in the manufacture of transistors, diodes, integrated circuits; Germanium semiconductor detectors (Ge (Li), HPGe - §2.5 "Semiconductor detectors") are important for our field of nuclear physics. Germanium has 4 stable isotopes: ⁷⁰Ge (20.4%), ⁷²Ge (27.3%), ⁷³Ge (7.8%) and ⁷⁴Ge (36.7%). Natural germanium also contains 7.83% of the very long- lived radioactive isotope ⁷⁶Ge (T1/2 = 1.7.10²¹ years; its radioactivity is negligible, it can be considered almost stable - see below). Of the radioactive isotopes, we mention three - one practically used, the second used in an interesting experiment and the third remarkable for its "exotic" way of decay :
Germanium ⁶⁸ Ge
is converted with an half-life of 270.9 days by electron capture to the ground state of the positron radionuclide ⁶⁸Ga. Based on this radioactive transformation is a ⁶⁸Ge/⁶⁸Ga radionuclide generator, from which a short-lived radioisotope gallium ⁶⁸Ga (half-life of 68 minutes - difficult transport to places outside the cyclotron) can be continuously obtained at nuclear medicine workplaces for use in PET scintigraphy ( ⁶⁸ Ga mentioned above). The Ge/Ga generator based on the principle of ion chromatography is of a similar type as the known Mo/Tc generator (described below - ^99m Tc ). It is a glass chromatographic column in which the parent ⁶⁸Ge is adsorbed in insoluble form on titanium oxide, aluminum or tin oxide. They tested also "metal-free" carriers in organic basis, such as trihydrohybenzene (pyrogallol) formaldehyde resin, and porous sorbents based on nanomaterials could be promised (zirconium and cerium nanomaterials are being tested). After the radioactive conversion of the ⁶⁸Ge nuclei to the ⁶⁸Ga daughter nuclei, the gallium atoms formed are exported from the insoluble bond and can be eluted from the column by weak hydrochloric acid solution (0.1M). Elution can be performed repeatedly (several hundred times), with a correspondingly decreasing activity, the generator can serve for about 1-3 years. Positron gallium-68 is thus operatively and long-term available for clinical use in PET at the workplace of nuclear medicine.
  The sequence ⁶⁸Ge --> ⁶⁸Ga is also used in closed "germanium" phantoms for calibration and testing of PET gamma cameras (see "Phantoms and phantom measurements in nuclear medicine", section "Tomographic phantoms"). The source of 511keV annihilation radiation, detected by a PET camera, is daughter gallium-68 (formed by the interaction of positrons emitted by ⁶⁸Ga with electrons of the material), the parent germanium does not participate in the radiation.
  The actual parent isotope ⁶⁸Ge is prepared by irradiating gallium isotopes in a cyclotron in nuclear reactions ⁶⁹Ga(p,2n)⁶⁸Ge, ⁷²Ga(p,4n)⁶⁸Ge, or ⁶⁶Zn(a,2n)⁶⁸Ge, resp. by fragmentation strip reactions (p, p-xn) by ejecting x- neutrons from bromine or germanium isotopes.
Germanium ⁷¹ Ge
is converted to the ground state ⁷¹Ga by electron capture with a half-life of 11.4 days, a characteristic gallium X-ray is emitted. This isotope was used in experiments with radiochemical detection of solar neutrinos using the reaction ⁷¹Ga (n, e^-) ⁷¹Ge. After radiochemical separation of the germanium formed, the characteristic X-rays and Auger electrons emitted from gallium atoms after conversion by ⁷¹Ge electron capture was measured (§1.2, part "Neutrinos - "ghosts" between particles", passage "Neutrino detections").
Germanium ⁷⁶ Ge
was previously considered stable isotope. Later experiments have shown that with an enormously long half - life of 1,7.10²¹ years, it is transformed by double beta decay b^- b^- to selenium ⁷⁵Se (§1.2, part "Radioactivity beta^-", passage "Double beta decay" ). .........