Neutrinos in nature, universe, laboratory

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 particles and accelerators
1.6. Ionizing radiation
1.7. Neutrinos - "ghosts" between particles

1.7. Neutrinos - "ghosts" between particles
Although elementary particles will be systematically discussed in §1.5 "Elementary particles", beta radioactivity is a good opportunity to mention in more detail here very interesting and remarkable particles of the microworld - neutrinos. We will do so somewhat more generally, in a separate chapter, not only in direct connection with radioactivity b *). However, the overall classification of neutrinos in the systematics of other elementary particles is discussed in §1.5.
* ) The rationale for the existence of neutrinos and the origin of their name was discussed above in the section "Radioactivity b^-", passage "Radiation spectrum b .Neutrinos". Neutrinos, once formed as an additional not very convincing hypothesis trying to explain "something that was missing", have become real and very interesting particles not only for nuclear physics, but also for astrophysics and cosmology.
  Neutrinos are tiny particles (with a rest mass close to zero - see below passage "Rest mass of neutrinos"), which do not have an electric charge and do not show a strong nuclear interaction; they show only a weak nuclear interaction *), which is so weak and short-range, that neutrinos almost do not interact with the substance and fly freely (like "ghosts"; in addition, it shows the ability to "reincarnate" each other - oscillations between three different types, see below).
*) And, of course, universal gravitational action is assumed, which is a negligible force at the microscopic level and we are not interested in it yet. However, for astrophysics and cosmology, the gravitational action of neutrinos, of which there are huge quantities in the universe, can be of considerable importance, see the passage "Rest mass of neutrinos" below.
  Many billions of neutrinos pass through our bodies every second. It is estimated that here on Earth, every cm², including the surface of our body, flies about 50 billion neutrinos every second *) (coming mainly from thermonuclear reactions inside the Sun), but we do not have to worry about their harmful effects on our health, during one lifetime only one or two of these neutrinos will be trapped in our body. The vast majority of neutrinos are able to fly freely throughout our globe. It is estimated that the neutrino could completely capture up to a layer of lead 1000 light-years thick!
*) This huge number of neutrinos occurs here on Earth near the Sun and in space near every star, in which huge amounts of neutrinos are formed during thermonuclear reactions. In distant interstellar and intergalactic space, the density of neutrinos is estimated at about 300 neutrinos/m³, which are mainly relict neutrinos.
  Neutrinos are produced in huge numbers in a various processes in space - from the "big bang" lepton era, to thermonuclear reactions in stars, to supernova explosions (see below). Due to their stability and permeability, these particles are constantly accumulating in the world. So it can be judged that (along with photons) neutrinos are the most abundant particles in the universe - we are as if "immersed in the invisible sea of neutrinos", which was born at different times and in different parts of the universe. They are ubiquitous, but almost elusive particles..!..

Formation and types of neutrinos
Neutrinos - very light particles (at rest mass close to zero), without electric charge, with spin 1/2, moving at a speed close to the speed of light - are inseparable accompanying particles in all processes with elementary particles with weak interaction. Their emissions accompany the formation of electrons during the decay of pions and muons, the mutual conversion of protons and neutrons (especially during radioactivity b), as well as a number of processes in the collisions of elementary particles at high energies. Neutrinos, along with photons, are among the most abundant particles in the universe.
  According to its origin, specific place and mechanism of origin, we can divide neutrinos into five groups :

• Relict neutrinos
  from the earliest periods of the universe's evolution. In the so-called lepton era, less than 1 second after the Big Bang, when the temperature dropped below about 10¹⁰ °K, the neutrinos practically stopped interacting with other substances (electrons, neutrons, protons). Since then, huge amounts of "relict" neutrinos have moved freely through the expanding universe (now their density is estimated at about 300 neutrinos/cm³ in every bit of outer space, even here on Earth). As a result of the cosmological expansion of the universe, the energy of relic neutrinos has dropped to very low values, so we have no reaction available to detect them.
  The cosmological aspects of these processes are described in §5.4 "Standard Cosmological Model. The Big Bang." of the book "Gravity, Black Holes and the Physics of Spacetime".
• Stellar neutrinos
  In the interior of all stars, the thermonuclear synthesis of hydrogen nuclei to helium takes place (whether it is a direct p-p chain or CNO cycle), in the later stages of stellar evolution also the synthesis of heavier elements (see the passage "Cosmic alchemy - we are descendants of stars!" in §1.1, too §4.1 "Gravity and evolution of stars" of the book "Gravity, Black Holes and the Physics of Spacetime", or the syllabus "Cosmic Alchemy") . In the chain of these nuclear reactions, in addition to strong interactions, the weak interactions also participate - beta decays, in which neutrinos are formed with energies up to about 20MeV *). Thanks to its permeability, neutrinos easily escape from the interior of stars and spread to the surrounding space. A large amount of neutrinos is emitted from the interior of the Sun, which "floods" the entire solar system. In our Earth, the flux of these solar neutrinos is about 6.10¹⁰ neutrinos/second/cm², most of which fly freely across the globe.
  *) Most neutrinos are formed in the "start" proton-proton reaction p⁺ + p⁺® ²H + e⁺ + n_e, but their energy (<0.42MeV) is low for detection methods. Suitable for our detection methods are neutrinos formed in one of the sub-branches of the reaction, in which the boron nucleus changes by b⁺ decay to beryllium nucleus, positron and neutrino: ⁸B ® ⁶Be + e⁺ + n_e, where the neutrino can have maximum energy up to about 14MeV. This reaction is only about 0.01%, but the corresponding solar neutrinos are well detectable.
• Neutrinos from a supernova explosions
  A supernova explosion is accompanied (and actually caused) by the rapid absorption of almost all electrons by protons (p⁺ + e^- ® n^o + n - a inverse b-decay), with a sudden colossal amount of neutrinos is emitting (estimated at 10⁵⁷ neutrinos). There is also a massive neutron fusion of nuclei in the outer layers, accompanied by subsequent b^- decay, also with the emission of neutrinos.
  Several neutrinos of this origin were detected in 1987 after the explosion of the supernova SN 1978A in the Large Magellanic Cloud, see below. The processes during the supernova explosion are described in more detail in §4.2 "The Final Phases of Stellar Evolution. The Gravitational Collapse" of the book "Gravity, Black Holes and the Physics of Spacetime".
  High-energy neutrinos 
  In addition to low- and medium-energy neutrinos (of the order of MeV), high-energy neutrinos can also be formed during a supernova explosion. The rapidly expanding shell of the ionized mass in a supernova explosion can use the Fermi mechanism to accelerate protons to high energies. The interaction of these protons with the shell material produces (via pions and muons), among other things, high-energy neutrinos (1 ¸1000 TeV), which are then part of the primary cosmic rays.
• Neutrinos from secondary cosmic radiation (atmospheric neutrino)
  Interactions of hard cosmic radiation (primary) particles with nitrogen and oxygen nuclei in the upper atmosphere (at altitudes of about 20-30 km above the ground) create sprays of secondary cosmic radiation, of which neutrinos are a tertiary part. In primary interaction occurs there produce pions p^± (and also K mesons), which disintegrate rapidly on muon m^± and (muon's) neutrinos: p^- ® m^- + n'_m , p⁺ ® m⁺ + n_m. Muons continue to decay continuously into electrons, positrons and neutrinos (muon's and electron's): m^- ® e^- + n'_e+ n_m , m⁺ ® e⁺ + n_e+ n'_m . Neutrinos of this origin are referred to as atmospheric neutrinos. Cosmic radiation is discussed in more detail in §1.6, section "Cosmic radiation".
• Neutrinos from natural radioactivity , geoneutrinos
  In the Earth's crust there are radioactive decays of natural radionuclides, especially uranium, thorium and potassium 40 (see §1.4 "Radionuclides", part "Natural radionuclides", passage "Geological significance of natural radioactivity"), during which electron (anti) neutrinos are formed, which due to their origin are called geoneutrinos.
  Detection of geoneutrin , which from the inaccessible depths of the Earth's interior passes freely through thick layers of rock to the surface, could provide valuable information on radioactive elements inside the Earth. By analyzing the directions of arrival of neutrinos in detectors, located in different places, we can get information about the spatial distribution of radioactive elements. By spectrometric analysis of neutrino energy it is possible to find out in principle which radioactive nuclei emit them: neutrinos from the decay of potassium 40 and uranium 235 have a maximum energy of about 1.3MeV, from the decay series ²³²Th about 2.2MeV, from the series ²³⁸U the maximum energy of neutrinos is about 3.2MeV. After the improvement of the detection technique, it will be possible to use the detection of geoneutrinos for the geological search of uranium or thorium deposits deep underground.
    In the air, in water and in the bodies of plants and animals, there is also a beta- decay of cosmogenic radionuclides - radiocarbon ¹⁴C and tritium ³H, also with the emission of neutrinos.
• Neutrinos from nuclear reactors and accelerators (neutrinos of artificial origin)
  Here on Earth, nuclear reactors are intense sources of neutrinos in modern times. During the itself fission of uranium or plutonium nuclei, neutrinos are not formed, but they are subsequently formed during the radioactivity of the fission products. Heavy nuclei (such as ²³⁵U) have a higher neutron to proton ratio for their stability than stable medium-heavy nuclei. The medium-heavy nuclei that are formed during fission therefore have a significant excess of neutrons, which they "get rid of" with a few b^- radioactive transformations until stable nuclei are formed. This produces "beta" electrons and electron (anti) neutrinos, and gamma radiation during deexcitation of nuclear levels. After each fission, about 5-6 neutrinos are formed. During this subsequent b- radioactive decay of fission products with an excess of neutrons, a large amount of electron antineutrins (with an average energy of about 4MeV) is formed. They are sometimes called "reactor neutrinos". A powerful reactor produces about 10²⁰ neutrinos per second.
    To a lesser extent, neutrinos are formed as "by-products" of particle interactions in accelerators (there are energies of tens of MeV to hundreds of GeV). Accelerators then enable the targeted production of high-energy neutrino beams, especially muon ones :
     High-energy protons from the accelerator are allowed to collide with the nuclei of the target, creating a large number of mesons p (and many other particles - kaons, hyperons, ...) . Charged pions are passed through a vacuum decay tunnel, where they decay during flight (they have a half-life of only about 2.10^-8 sec.) to form muons and muon neutrinos: p^- ® m^- + n'_m , p⁺ ® m⁺ + n_m. These muon neutrinos, arising from high-energy pions, also have high energy and are closely collimated in the direction of the original pion beam (in the direction of the decay tunnel axis) - see " CNGS + OPERA Experiment " below.  
   The production of high-energy electron neutrino beams is more difficult. One possibility could be the acceleration of lighter b- radioactive nuclei with a short half-life (eg ^6,8He, ⁹Li, or the like) on a linear or circular accelerator, which would then be fed to a magnetic storage ring with longer linear sections. Accelerated nuclei would emit electron neutrinos during their b- conversion, which would (in the laboratory reference system) also be "accelerated" to high energies and fly out in beams collimated along said linear sections. It has not been implemented yet.

According their quantum physical nature, three kinds of neutrinos n are observed, according to the type of the associated charged lepton :

• Electron neutrinos
  Neutrinos, operative in beta radioactivity, are just one of three kinds of neutrinos - are neutrino electron n_e accompanying the emission of an electron and a positron in the transformation of beta. However, electron neutrinos (at least in their primary origin) are the predominant type of neutrinos - they are formed during thermonuclear reactions inside stars, during the explosion of supernovae, in natural and artificial radioactivity, in nuclear reactors.
• Muon and tauon neutrinos
  In processes with muons m and tauons t (see §1.5 "Elementary particles"), muon neutrinos n_m are emitted (they are an important part of "atmospheric" neutrinos formed in sprays of secondary cosmic radiation) and tauon neutrinos n_t. Most of their properties are very similar to electron neutrinos, they differ in the way of their interactions with elementary particles - instead of processes with electrons (such as b decays) they are accompanied by weak interactions with the participation of muons and tauons.

We distinguish these individual types of neutrinos according to which type of charged lepton they form from or which lepton is formed during their interaction, whether it is an electron, muon or tauon. In connection with the law of conservation of the lepton number, it is assumed that for each of the three types of neutrinos there is also a corresponding antineutrino n'.
Difference between neutrinos and antineutrinos - helicity of neutrinos. Goldhaber's experiment.
It is discussed whether the neutrinos are Dirac or Majoran particles - whether the antineutrins are different or identical to the neutrinos. The only way to distinguish a neutrino/antineutrino pair from each other is their helicity (rotation, spiral) - the orientation of the spin (internal angular momentum) of a particle with respect to the direction of its motion. Direct measurement of neutrino helicity would be very difficult (beyond the scope of current experimental techniques). The only viable option is the indirect determination of the helicity of the neutrino through the law of conservation of the momentum in the radioactive process electron capture EC (see "Electron capture" below). During electron capture, only neutrino is emitted from the nucleus, which we are essentially unable to detect. However, the daughter nucleus after EC is often in an excited state, during the deexcitation of which a gamma photon is emitted , which in its helicity carries certain information about the angular momentum balance. Under certain circumstances, this information can be decoded to determine the helicity of the flying neutrino.
  This indirect determination of neutrino helicity was achieved in 1958 by an American team led by M.Goldhaber (Brookhaven National Laboratory) by a very sophisticated experiment. They used to measure the helicity of 963keV gamma deexcitation photons emitted from the excited state ¹⁵²Sm generated by electron capture in the nuclear isomer of europium ^152mEu (§1.3, passage "Europium"). This nuclide was chosen because the start and end states have the same spin number 0^-. During electron capture, the neutrino and deexcitation photons are then emitted with opposite spin (due to the law of conservation of angular momentum). If we measure the polarization of the photon, we also find the helicity of the neutrino. The ^152mEu emitter was placed in a ferrite magnet, which filters (selects) the flying deexcitation quantum according to the polarization ...... These gamma photons then fall into the ring from the inactive ¹⁵²Sm, in which they can cause resonant absorption.with deexcitation, whose photons are registered by a scintillation detector... A relatively complex analysis of the results of measured impulses in confrontation with the balance of spins (angular momentums) gave the helicity of electron neutrinos the value Hn_e = -1 ± 0.3 - neutrinos are left-rotatory, while antineutrinos right-rotatory. This is consistent with the finding of parity violation in a weak interaction (see §1.5, passage "CPT symmetry of interactions").

Oscillations of neutrinos
In neutrinos we encounter a surprising and from the classical point of view incomprehensible phenomenon - that there are spontaneous transformations between individual types of neutrinos - the so-called oscillation of neutrinos. Neutrino during their flight while electron n_e, then turns into a muon and taun neutrino and then again on the electron etc. (but see note "physical reincarnation?" at the end of the segment). Metaphorically, it can be said with a bit of exaggeration that neutrinos behave like mythical "ghosts" in a sense: they can go through anything without hindrance (even walls...) and are able to "reincarnate" each into other ...  
  We imagine the phenomenon of neutrino oscillation as a consequence of the quantum-mechanical interference of three quantum states of a neutrino particle, which is an internal superposition of the "1", "2" and "3" neutrino states. These states are described by quantum waves of different wavelengths *), which, when propagated through space, alternately reach the same phases and different phases, which manifests itself as electron, m - or t - neutrinos.
*) In order for this mechanism of interference of different wavelengths to work, it is necessary that the individual quantum states have (in the spirit of corpuscular-wave dualism) different masses - so that the neutrino has a generally non-zero rest mass (at least some of them). In the Standard Model particle interactions, reactions of neutrinos with charged leptons (eg m ^- ® e ^- + n _m + n _e ') are called reactions of so-called weak charged currents and in quantum theory they are described by total Lagrangian or Hamiltonian , including both charged lepton components and neutrino, with coefficients given by the so-called Pontecor-Makai-Nakagawa-Sakat (PMNS) mixing matrix. This matrix, which describes the mixing of neutrino fields, is parameterized by three mixing angles q and three complex phases d . The corresponding Schrödinger equation then provides the overall wave solution as a coherent superposition of "wave clusters" corresponding to the individual eigenvalues of masses. The probability of finding one's own state of mass is then expressed by a periodic function of time , which is reflected in the movement of the neutrino by the periodic dependence of the neutrino species along the path - the oscillation of neutrinos in space and time. The magnitude and time course of the oscillations depends on the degree of "mixing" between the individual pure states "1", "2", "3", which are described by the so-called mixing angles q ₁₂ , q ₂₃ , q ₁₃ , resp. squares of the sinuses of these angles.
  In the simplest case of the motion of a relativistic neutrino with kinetic energy E _n , which is a coherent superposition of two mass components with the difference of quadrates of rest masses D m _n , the probability P finds a certain neutrino state (eg n _e ): P_n®ne » 1 - sin²2q.sin²[(Dm_n²/4hc.E_n).L], where L is the distance from the point of emission of neutrinos and q is the mixing angle parameterizing the PMNS matrix (which is two-dimensional here). For each value of energy E _n , then there are some so-called oscillatory length L_o at which L argument . D m _n ² /4 h C.E. _n in the sine function changed by P and the probability P _{n ®n e} again takes the value 1: L _a = 4 h C.E. _N / D m _n ² . The oscillation length is directly proportional to the neutrino energy E _n and indirectly proportional to the square of the mass difference Dm _n ^{2 of} both species (states) of neutrinos. For commonly used units of length and energy, the oscillation length can be expressed in a simplified form: L _{o [m]} » 2.5 . E _{n [MeV]} / D m _n ² _[eV 2 _] . The value of D m _n ² can be determined experimentally by measuring the dependence of the number of observed neutrinos on the energy E _n for a certain fixed distance L and the known spectrum of energies E _n neutrinos. KamLAND's experiments are based on n _e «n _m oscillationsvalue D m _n ² » 8.10 ^-5 eV ² , in Super-Kamiokande the value D m _n ² » 2.10 ^-3 eV ² is based, which are oscillations of all three types of neutrinos. For common solar and reactor neutrinos with MeV energies, the oscillation length is relatively short, in the order of tens of km. For "atmospheric" neutrinos (which are formed by interactions of high-energy cosmic rays in the Earth's atmosphere) with an energy of tens of GeV or higher, the typical oscillation length reaches hundreds to thousands of kilometers (to test the oscillations, neutrinos detected at great distances from the point of origin must be used; even neutrinos formed in the atmosphere on the opposite side of the globe, as mentioned below in the Super-Kamiokande experiment).
  Neutrino oscillation is a quantum-stochastic process whose probability after neutrino emission is initially low, but increases along its path length. At greater distances from the source emitting neutrinos of a certain species (usually electron), we will register a mixture of neutrinos of all three species, represented roughly homogeneously in a ratio of 1: 3 (it depends on the values of the above-mentioned mixing angles q). The influence of this phenomenon on the detection of individual types of neutrinos will be briefly mentioned below.
Note: Physical reincarnation ?
The phenomenon of oscillations of neutrinos is difficult to understand from the classical point of view, it might seem that it violates the laws of conservation. However, from the point of view of quantum physics, neutrinos do not "physically" transform into each other. Just wave function neutrinos is a superposition of three states (it is parameterized aforementioned mixing angles). Depending on the distance from the point of origin will then show the various probabilities that the neutrino will interact as electron, the muon or tau. In a sense, we can imagine that even the velocity of the neutrino oscillates. In quantum physics these phenomena are not considered to be a violation of energy conservation or symmetry.

"Sterile" neutrinos ?
The nothingness of neutrinos ("ghosts between particles") has led some nuclear physicists and astrophysicists to an even more bizarre idea: that perhaps there could be neutrinos that show not even a weak interaction and do not interact with matter other than through the gravitational force alone. The name sterile neutrinos has been proposed for these hypothetical neutral particles. They could be candidates for explaining the so far mysterious dark matter in the universe (§5.6 "The future of the universe. The arrow of time. Dark matter. Dark energy." monograph "Gravity, black holes..."). They are the product of pure fantasy, there is no evidence for their existence, they could never be directly detected..!..

Interaction of neutrinos with particles and with a matter
Neutrinos do not have an electric charge, they do not exhibit an electromagnetic or strong interaction, but only a weak interaction (we will mention the gravitational one below). From the point of view of the internal mechanism, all processes with neutrinos are mediated by a weak interaction with the virtual participation of heavy intermediate bosons W^± and Z⁰ (within the concept of the so-called electro-weak interaction, this weak interaction is mediated by exchanges of heavy intermediate bosons W and Z according to the Standard Model of particle interactions, see §1.5 "Elementary particles"). A common feature here is a very low effective cross section of neutrino interactions. Depending on the type of particles and energies involved, neutrino interaction includes a wide range of processes - (quasi)elastic scattering, deep inelastic scattering, inverse beta-decay, nuclear capture, hadron production, high-energy interactions with the creation of many other particles. We will briefly mention some of them :
  The simplest neutrino interaction is the (quasi)elastic scattering of neutrinos on leptons (in practice almost always on electrons in the atomic shell) :
n + e^- --> n´ + e^-´.
The value of the effective cross section of the neutrino-lepton interaction of a neutrino of energy E_n with an electron of mass m_e can be expressed as s~ 2m_e.f.(G²/p).E_n , where G is the Fermi coupling constant of the weak interaction (G ~ 1.16x10^–5 GeV^–2) and f is the form factor including additional parameters. The effective cross-section here is approximately s ~ 2x10^-41 cm²/GeV. This small value of the effective cross section is due to the small mass of the target electron.
From a kinematic point of view, a fast-flying neutrino n collides with an e^- electron, bounces off it (mostly at a large angle or even in the opposite direction) as a lower-energy neutrino n´, giving the electron some of its energy. The reflected electron e^-´ moves mostly in the direction of the original (incident) neutrino n and can be detected.
For muon neutrinos, there is also the interaction n_m + e^- --> m^- + n_e (also called inverse muon decay). It has a threshold energy of 10.8 GeV, given the mass of the muon, the effective cross section is approx. s ~ 15x10^-42 cm²/GeV.
At high concentrations and energies in the dense neutrino-electron mixture (in the assumed lepton era during the first tenth of a second after the big bang - "Stages of the Universe's development"), the processes of annihilation and mutual conversion of neutrinos and electrons could take place massively: n_e + n^~_e <--> e^- + e⁺.
  Neutrino-hadron interactions (in practice, interactions of incoming neutrinos with target protons or neutrons in atomic nuclei) :
n_(e,m,t) + nucleon (p⁺,n⁰) --> lepton^-(e,m,t) + hadron.
Neutrino-hadron interactions have a significantly higher effective cross-section than neutrino-electron interactions - in the ratio of approx. 1.8x10³; it is given by the mass ratio of the nucleon to the electron. The effective interaction cross section of a neutrino with energy E_n with a nucleon of mass M_p can be expressed as s ~ f.(G²/4p).M_p.E_n /GeV, where G is the weak interaction factor and f is the form factor depending on the quark structure of the target nucleon. The basic value is s_o ~ (G²/4p).M_p = 1,6x10^-38 cm² /GeV.

Feynman diagrams of some basic interactions of neutrinos with leptons and nucleons.

In general, for most neutrino interactions, the effective cross section is linearly proportional to the energy of the incident neutrinos. The higher the energy of neutrinos, the easier they can be detected through interactions in matter. Only at very high energies (>>~10⁶ GeV) does the effective cross-section cease to be proportional to the energy, it reaches saturation; for neutrino-hadron interactions it already has a constant value of approx. s ~ 10^-38 cm² (for electromagnetic interactions incomparably higher values of up to s ~ 10^-27 cm² are reached).
  These and other types of neutrino interactions are probably applied on a large scale in turbulent astrophysical processes - during the explosion of supernovae, in the very early stages of the evolution of the universe (§5.4 "Standard cosmological model. Big bang. Formation of the structure of the universe.", part "Stages of the evolution of the universe" in the book "Gravity, black holes and space-time physics"). Some of these processes can also be used to detect neutrinos :
 Detection of neutrinos
The detection of different types of radiation will be discussed in detail in Chapter 2 "Detection and spectrometry of ionizing radiation". However, the detection of neutrinos differs considerably in its technique and principles from the more or less "routine" detection of radiation a, b, g, often used in technical practice as well. Neutrinos, which do not have an electromagnetic or strong interaction and hardly affect anything in matter, we can never "see" or detect directly, only secondary products arising from their interactions can be detected. These are (at least so far) rather unique and delicate experiments, trying to prove the very existence of neutrinos and releal some of their basic properties (in this sense, it is somewhat similar to experiments with the detection of gravitational waves). Therefore, we will already mention the neutrino detection methods at this point.
  Neutrinos are generally very difficult to detect - they do not show an electromagnetic or strong interaction, only a weak interaction. The effective cross section of this weak interaction is very small, as it is mediated by exchanges of the heavy intermediate W and Z bosons; this large mass of the exchange particles causes a very small range and strongly suppresses the probability of interactions, unlike the usual electromagnetic processes, mediated by the exchange of zero rest mass photons. In order to be able to detect any neutrinos at all, 4 basic conditions must be fulfilled :
1. A sufficiently intense flow of neutrinos (min approx. 10¹³ neutrinos/cm²/s) falling into the sensitive volume of the detector must be available.
2. The detector must be large - it must contain a large volume of detection substance (mass - usually thousands to tens of thousands of tons) with which the incident neutrinos can interact. Only then will there be some reasonable probability, that some of those billions of neutrinos passing through, will interact and produce detectable pulses.
3. Disturbing background radiation from natural radioactivity, detector material, and cosmic radiation must be reduced to the lowest possible level. In order to shield primarily cosmic radiation, the detectors must be placed deep in the underground or underwater space. It also places high demands on the construction materials used and especially the detection substance, its purity.
4. Considerably long acquisition time (tens of days, months, even several years) in order to register a sufficiently large number of neutrinos, enabling the necessary accurate statistical analysis of the data.
  For neutrino detection, these tend to be large tanks containing many hundreds to thousands of tons of highly pure material (water, liquid scintillator), located at a depth of kilometers underground, or under water or ice in the underwater space. They are equipped with a large number of photomultipliers for the detection of scintillations arising in the scintillating substance or from Cherenkov radiation. It is measured over many days or months.
  Mainly three types of processes can be used to detect neutrinos :

• 1. Interaction of neutrinos with nucleons (reverse beta decay process ; particle production)
  The electron neutrino n_e interacts (weakly interacts) in the atomic nucleus with the neutron n^o and causes a reaction there n_e + n^o ® p⁺ + e^-, or with a proton by the reaction n'_e + p⁺ ® n^o + e⁺. The effective cross section of this interaction is about 10^-47 m².(E_n /1MeV)².
  At high neutrino energies, particle interactions with nucleons can occur to form electrons, muons, or tauons.

The first successful detection of neutrinos
using the process n_e+p⁺ ® n^o+e⁺ was achieved in 1956 by F.Reines and C.Cowan from the laboratories in Los Alamos, who used a powerful nuclear reactor in the Savanah River as a source of neutrinos with an antineutrinos flow of about 10¹³ n/cm²/s. A liquid scintillator (triethylbenzene) with admixture of camium in a large vessel with a volume of 1400 liters was used as a target and at the same time a detector. When a neutrino interacts with a proton contained in a scintillator, a neutron n^o (with a kinetic energy of several keV) and a positron e⁺ (with a kinetic energy of 0 ¸ 8MeV) are formed. Positron e⁺ is braked very rapidly in the liquid (for about 10^-10 s) and then annihilated with one of the electrons (e⁺ + e^- ® g + g ) to form two annihilation photons g, each of which has an energy of 511keV. The ionization energies of the positron together with the annihilation photons (total energy 1 ¸ 8MeV) cause a light flash in the scintillator registered by the photomultipliers. The neutron slows down with collisions with the nuclei (the process of deceleration and diffusion takes up to 30 msec) and is captured by the cadmium nucleus in the reaction n^o + ¹¹³Cd₄₈ ® ¹¹⁴Cd₄₈ + g; the excited isotope cadmium, when deexcited, emits 2-4 quantum gamma with a total energy of 9MeV within a few microseconds and returns to the ground state. These g- quants also produce a flash of light captured by the photomultipliers in the scintillator. The interaction of the neutrino with the proton ( n_e + p⁺ ® n^o + e⁺) is thus revealed by two consecutive electrical signals from the photomultipliers: 1. a pulse of amplitude corresponding to 1-8MeV coming from the positron registration; within about 25 msec, a 2nd pulse with an amplitude of 3-10MeV originating from neutron capture in the cadmium nucleus appears. During measurements lasting more than 100 hours, an average of 36 cases of said reaction (n_e + p⁺ ® n^o + e⁺) neutrinos per hour, which gave an effective cross section of the reaction of about 10^-43 cm².
Radiochemical detection of neutrinos
To measure the interaction with a neutron (n_e + p⁺ ® n^o + e⁺) it is necessary to choose a nucleus where the conversion of a neutron to a proton leads to a radioactive nucleus emitting radiation that can be easily detected. In practice, ³⁷Cl chlorine cores were first used for these measurements- a large tank filled with about 600 tons of tetrachlorethylene C₂C_l4 (otherwise a common chemical cleaner, which had to be specially cleaned) was placed at a depth of about 1.5 km underground in an abandoned gold mine Homestake in South Dakota, USA - to minimize radiation background from cosmic rays and terrestrial sources. The experiments took place under the leadership of R. Davis in the 1960s. Electron neutrinos induce a reverse b- decay reaction in chlorine nuclei : n + ³⁷Cl ® ³⁷Ar + e ^-; the threshold energy of neutrinos here is 814keV. The resulting argon ³⁷Ar decays back to ³⁷Cl with a half-life of 35 days by electron capture. At the same time, Auger electrons with an energy of about 2.6 keV are emitted from the atomic shell of the daughter chlorine (due to the characteristic X-radiation, which is 90% subject to internal conversion), which can be detected by a gas proportional detector. To do this, however, it is necessary to extract the few ³⁷Ar atoms formed from the entire volume of about 400,000 liters of tetrachlorethylene in the tank, which is an extremely difficult technical problem. In 1968, the results of the experiment were evaluated, neutrinos were successfully detected, but their amount represented only about 30% of the neutrinos expected from astrophysical models of thermonuclear reactions inside the Sun.
  Another material suitable for radiochemical detection of neutrinos is gallium ⁷¹Ga, in the nuclei of which electron neutrinos induce the reaction n + ⁷¹Ga ® ⁷¹Ge + e^- with the subsequent decay of germanium ⁷¹Ge by electron capture accompanied by the radiation of Auger electrons, similarly to the decay of ³⁷Ar. The advantage of gallium is a significantly lower threshold energy of 233 keV of detected neutrinos, the disadvantage is the higher price of gallium compared to chlorine. On this basis, the SAGE and GALEX experiments were successfully performed in the early 1990s, which successfully detected low-energy neutrinos, also in lower numbers than expected.
  In this way, neutrinos have been successfully detected both from laboratory sources and from space - especially from the Sun, where huge amounts of neutrinos are formed during thermonuclear reactions. However, one mystery occurred here permanently: all measurements gave approximately 3 times less value of the flow of electron neutrinos than expected from the analysis of thermonuclear reactions on the Sun. This mystery of solar neutrino deficiency has been solved until many years later, when improved neutrino detection methods demonstrated the effect of neutrino oscillation - the spontaneous interconversion of electron, muon and tauon neutrinos, with earlier methods being able to detect only electron neutrinos (1/3).
 CNGS (CERN Neutrinos to Gran Sasso) + OPERA (Oscillation Project with Emulsion Tracking Apparatus)
This is an new interesting measuring system type transmitter ® receiver (detector) neutrinos, which targeted the investigation of neutrino oscillations, especially on taun neutrinos and refinement neutrino masses. It started operating in 2006. The neutrino transmitter is at CERN, the neutrino receiver (detector) is installed in an underground laboratory at a depth of 1400 m below the Gran Sasso mountainin in Italy. The neutrino transmitter is a large proton accelerator, the synchrotron SPS (Super Proton Synchrotron) at CERN, from which protons, accelerated to 400GeV energy, collide with the nuclei of the target to form a large number of mesons p (and a number of other particles - kaons, hyperons, ...). Charged pions are separated by a magnetic field and led to a 1.2 km long vacuum decay tunnel, where they decay during flight (they have a half-life of only about 2.10 ^-8 sec.) to form muons and muon neutrinos : p^- ® m^- + n'_m , p⁺ ® m⁺ + n_m . The average energy of the neutrinos formed is about 17GeV; to register tauon neutrinos using tauons, we need a very high energy of the original muon neutrinos, higher than the resting energy of the tauon (m_0t »1,2GeV/c²). Due to relativistic effects, the neutrino beam is relatively closely collimated approximately in the direction of the original proton and pion beam.
  The whole system [pion beam + decay tube] is directed to the 732 km distant underground laboratory LNGS (Laboratori Nazionali del Gran Sasso) in Italy, where neutrinos arrive through the ground (other particles are quickly absorbed in the shield at the end of the decay tunnel, other muons in rock underground). Here, an OPERA detection system is installed, consisting of 150,000 alternating layers ("sandwiches", bricks) of lead *) 1 mm thick, interspersed with thin sheets of photographic emulsion. Lead serves as a target for the neutrino interaction and a photographic emulsion for registration and visibility of reaction products.
*) To reduce the radiation background, the so-called "Roman lead" from ships carrying lead was used to build a water pipe in Rome and sunk sometime around the 60s BC. At the bottom of the sea, this lead lay intact for 2,000 years, so most of the natural radioactive isotopes decayed in it during that time.
  This "old" technology of nuclear photoemulsions was used because it is the only one that provides a very high spatial resolution »1 mm of registered particle trajectories, needed to capture short tauon trajectories of very short lifetime (of the order of picoseconds). However, the evaluation of photoemulsions is fully automated here (using technologies developed in Japan). Detection of particle trajectories using nuclear photoemulsions, including a technology called ECC (Emulsion Cloud Chamber), a kind of "emulsion fog chamber", is discussed in more detail in §2.2, section "Particle Detectors". The OPERA detection system is very massive, those 150,000 sandwiches together contain about 110,000 m² of film with photoemulsion and more than 100,000 m² lead sheets with a total weight of more than 1200 tonnes. This power is forced by two circumstances: 1. Very low effective cross section of neutrino-substance interactions; 2. The distance of 730km between the transmitter and the detector (corresponding to the flight time of neutrinos 2.43ms) is too short, so only a very small part (approx. 1-2%) of neutrinos can oscillate.
  During the flight from the transmitter to the detector, neutrinos oscillate, so in addition to the original muon ones, also electron and taunine neutrinos arrive here. In the reactions of muon neutrinos in lead, muons are formed, in the reactions of electron neutrinos electrons, in the reactions of tauon neutrinos tauons are formed (which we are mainly looking for here). The resulting tauons decay into pions in 64% of cases, electrons in 18% and muons in 17% (when emitting neutrinos escaping from the detection space). Based on the recording of traces of particles in the photoemulsion, the kinematics of the original interaction are reconstructed by microscopic scanning, which makes it possible to determine the position of the formation of the tauon and the place of its decay. There are also plastic scintillators in the system, the signal of which indicates the moment of interaction and makes it possible to determine in which photoemulsions a useful record can be expected; these are then evaluated. The system also includes electronic particle "trackers" and magnetic spectrometers. In May 2010, a taun neutrino, created by oscillations from an originally muon neutrino, was registered here for the first time.

• 2. Elastic scattering of a neutrino on an electron : n + e ^- ® n ´ + e ^- ´
  (occurs for all types of neutrinos). The fast-flying neutrino n collides with the electron e^-, bouncing off it (usually at a large angle or even in the opposite direction) as a neutrino n´ with lower energy, transferring part of its energy to the electron. The reflected electron e^- mostly moves in the direction of the original (incident) neutrino n and can be detected.
  The effective cross section of this interaction is about 10^-48 m².(E_n/1MeV).

   If this electron e^-´ moves in an optic environment (eg water) at a speed higher than the speed of light in this environment, it emits Cherenkov radiation (mechanism of its origin and properties see §1.6, passage "Cherenkov radiation"), which can be detected by photomultipliers. Although this method of neutrino detection has a higher threshold energy (5MeV), its advantage is its applicability even for other types of neutrinos than electron's.

Detection and spectrometry of neutrinos using various types of their interactions.
Left: Some detection principles. Right: SuperkamiokaNDE photomultiplier system.

Kamioka NDE Neutrinous Detector
A detector of this type, called the Kamioka NDE (Kamioka Neutrino Detection Experiment *), was designed under the leadership M.Koshiba in 1982 in Japan - in the Kamioka tin mine (in the mountains ... called the "Japanese Alps") in at a depth of 820 m, a reservoir containing about 20,000 tons of high-purity water was built. Photons of Cherenkov radiation were registered by almost 1000 large photomultipliers; another 120 photomultipliers involved in anticoincidence surrounded this system in a geometry of 4p. The electronic system processing the pulses from the individual photomultipliers made it possible to locate the place of interaction of the neutrino, determine its energy and approximately the direction of arrival. So this detector was already a spectrometer, working in real time (in contrast to the additional detection of Auger electrons in earlier radiochemical detectors). In addition to refine the results of radiochemical detectors and measuring the high-energy part of the spectra of neutrons from the Sun was in this detector also achieved another major success: on 23 February 1987 was registered glimmer 12 neutrinos coming from the supernova SN 1987A in the Large Magellanic Cloud (a neighboring galaxy 170,000 light years away).
*) Note: The Kamioka NDE detector was originally designed to demonstrate proton decay (NDE stands for "Nucleon Decay Experiment") - according to some versions of the unitary theories of great unification (GUT = Grand Unification Theory, unite strong, weak and electromagnetic interactions) the proton should not be a stable particle, but would decay (eg p⁺ ® p^o + e⁺) with a half-life of T1/2 > 10^30-40 years. This half-life is so long that perhaps not a single proton in the universe may have decayed since its inception! Not surprisingly, the detection of proton decay was not successful. However, the lucky idea of using this device to detect neutrinos was very successful, which gave the acronym NDE a new meaning.
Super Kamioka NDE 
   As a continuation of the KamiokaNDE detector, an even larger Super KamiokaNDE detector was built in 1996, located in an old zinc mine 1700 m below the surface of Mount Iken Yama near the town of Kamioka. The cylindrical tank with a diameter of 34 m and a height of 36 m, on the inner walls of which are placed 11,146 large photomultipliers (photocathode diameter almost 50 cm), is filled with almost 50,000 tons of superpure water. Photomultipliers detect Cherenkov radiation of electrons or muons created by the collision of electron or muon neutrinos with protons and neutrons. Using the ratio of the amount of production of electrons and muons, the system is able to distinguish between electron and muon neutrinos. In 1998, oscillations of atmospheric neutrinos were demonstrated on this apparatus. Atmospheric neutrinos are constantly formed in the upper layers of the atmosphere during the decay of pions and later muons, created by the interaction of hard cosmic radiation with the atmosphere - see §1.6, section "Cosmic radiation", passage "Secondary cosmic radiation". Muon and electron neutrinos are formed (in the ratio 2n_m : 1n_e). Neutrinos of energy E_n coming "from below" pass through the whole Earth (distance L from the place of their origin) and have more time to undergo oscillations, in contrast to neutrinos coming "from above", which passed only a few kilometers of atmosphere and less than 2km of soil. This vertical anisotropy in the relative proportion of muon neutrinos was reliably measured by the detection system. A significant decrease in the detected frequency of muon neutrinos for L/E_n around 500km/GeV was observed and in addition a re-increase was measured - "revival" of the frequency of detection of muon neutrinos for lengths of the order L » 10³-10⁴ km/GeV, caused by oscillating behavior of neutrinos in distances greater than half the oscillation length L_o neutrinos for a given energy E_n (as discussed above in the section "Oscillations of neutrinos").
Neutrin SNO detector
Another significant improvement was implemented in the neutrino SNO spectrometer (Sudbury Neutrino Observatory) located at a depth of 2 km in a mine near Sudbury in Ontario, Canada. Here, inside a vessel with 7000 tonnes of "light" water (¹H₂O), another vessel with 1000 tonnes of heavy water (²H₂O, ie D₂O) is placed. More than 9,500 external photomultipliers monitors the flashes of Cherenkov radiation through light guide tubes. Neutrinos cause three types of reactions in the detector material (water and heavy water) :
a) Absorption of an electron neutrino by a neutron in the deuterium, in which the neutron changes into a proton and an energetic electron. Deuteron, which is a weakly bound nucleus, then decays into two protons and an electron: n_e + ²H ® p + p + e^-. A fast-flying electron causes Cherenkov radiation.
b) A fast-flying neutrino "collides" with a neutron or proton in the deuterium and, in elastic scattering, transfers some of the kinetic energy, causing the deuteron to decay into a proton and a neutron: n + ²H ® n_scattered + p + n^o. The released neutron is then absorbed by another deuteron, emitting a photon of radiation g. This photon g, during a photo effect or Compton scattering in matter, emits an electron that causes Cherenkov radiation.
c) Neutrino "collides" with an electron and, when elastically scattered, accelerates it to such an extent that it causes Cherenkov radiation.
  Process a) is only possible with the electron neutrino n_e, while processes b) and c) can induce by any neutrino. Processes a) and b) occur only in deuterium in heavy water, process c) occurs equally on electrons in light and heavy water. By analyzing these processes, it is possible to measure independently both the flux of electron neutrinos and the flux of all neutrinos (ie electron + muon + tauon) together. The measurement results showed that the lack of solar neutrinos in all previous experiments is due to neutron oscillations.
KamLAND - neutrino scintillation detector from nuclear reactors
Japanese KamLAND detector ( Kamioka Liquid Scintillator Neutrino Detector; originally there was KamiokaNDE, which was redesigned to KamLAND) consists of a spherical vessel with a diameter of 13 m, filled with a liquid scintillation agent detecting positrons formed by the capture of antineutrinos by a proton. Scintillation flashes are registered by a system of more than 18,000 photomultipliers distributed on the inner wall of the vessel. The scintillation vessel is surrounded by an external Cherenkov detector with 3,200 tons of water. Neutrino energy can be determined approximately from positron scintillation. The resulting neutrons are captured by hydrogen nuclei in the path up to about 10 cm, while photons of radiation g are emitted with an energy of about 2MeV, also causing scintillation detected by a photomultiplier system. The device is designed to detect antineutrins from surrounding nuclear reactors, while determining the energy spectrum and the proportion of electron antineutrins depending on the distance traveled. The detector enabled a more detailed study of neutrino oscillations, which confirmed and supplemented the results from both systems mentioned above.
DUNE (Deep Underground Neutrino Experiment)
is built to study the properties of neutrinos, especially in connection with the not yet sufficiently researched and understood phenomenon of neutrino oscillations. This international advanced project is based on the cooperation of two nuclear laboratories in particular :
-> Neutrinos will be "manufactured" at the Fermi National Accelerator Laboratory (Fermilab) in Batavia, Illinois, as part of the Long-Baseline Neutrinos Facility (LBNF) project. Here, the powerful proton accelerator PIP-II (800 MeV) will produce by proton impacts on the carbon target the intense neutron beams (muon (anti)neutrinos in the energy range 1-5 MeV), collimated northwest towards the Sanford Lab. These neutrinos in Fermilab will first pass through a smaller "monitoring" detector of transmitted (non-oscillating) neutrinos.
-> The resulting detection of these neutrinos will be performed at the Sanford Underground Research Facility (Sanford Lab) in Lead, South Dakota, 1,300 km from the source, using a large cryogenic underground detector in depth 1.5-kilometer (in the former Homestake gold mine) containing 70,000 tons of liquid argon cooled to -184 °C, with LArTPC time-projection chambers (these detectors are described in Chapter 2 "Radiation detection and spectrometry", §2.3, passage "Drift and time-projection proportional chambers"), with simultaneous detection of scintillation flashes in argon.
  Neutrinos will oscillate continuously during their 1,300 km underground journey, so all 3 types of neutrinos will fall into the remote detector. By measuring the representation of different types of resulting neutrinos registered in the remote detector, depending on the energy, it will allow a more detailed study of the dynamics of neutron oscillations. One of the goals is also to improve the current low success rate of tauon neutrino detection.
A large cryogenic underground detector in DUNE could also detect neutrinos from a supenova explosions. It is also planned to look for products of possible proton decay ...
  The DUNE experiment can be considered a significant improvement on the previous CNGS + OPERA neutrino experiment (described above "CNGS+OPERA") as well as the famous Kamioka - Super Kamioka NDE neutrino detector. Completion of the large underground detector, start-up of the neutrino beam and start of measurements in DUNE is planned for 2026-27.

• 3. Interaction of high-energy neutrinos with protons to form muons m .
  Charged muons m, then during high-speed movement in the clear optical medium emit Cherenkov radiation which can be detected by a photomultiplier.

Detection of neutrinos in glaciers
An interesting and somewhat curious option for the detection of fast neutrinos is the use of massive masses of natural ice in large glaciers located mainly in Antarctica. When a high-energy neutrino hits a proton (in one of the nuclei of a water-ice molecule), a high-energy muon m is formed, which leaves a bluish light cone of Cherenkov radiation along its path of ice movement. Its direction allows you to determine the direction of the path of the original neutrino. At kilometer depths inside the glacier at high pressures, the ice is highly transparent, compact and bubble-free, so flashes of muons can be detected at distances of tens to hundreds of meters. Geometric placement of the photomultipliers, together with the coincidence analysis of the detected pulses, enables the spatial reconstruction of the cone.
  When optical sensors - photomultipliers - are turned down into the Earth's interior, neutrinos coming from the opposite side, the northern hemisphere, passing through the globe are detected. Interfering muons from secondary cosmic rays are completely shielded from this direction. The system is able to detect not only common neutrinos with energies of several MeV, but also high-energy neutrinos with energies of the order of TeV and higher.
AMANDA
The first system of this kind is the AMANDA (Antarctic Mion And Neutrino Detector Array) built in 1996-2000 at the Amundsen-Scot Polar Station in Antarctica. It consists of more than 700 photomultipliers, housed in pressure-resistant glass spheres, embedded under Antarctic ice in 19 shafts over 2 km deep *). The photomultipliers are powered by electric cables, the detected pulses are led by light cables to the evaluation device. The achieved angular resolution for neutrinos from cosmic rays is around 1°.
*) The ice shafts are "drilled" with a stream of hot water at 80° C, photomultipliers are lowered into them, after which the shaft freezes again after a few hours. However, the photomultipliers frozen in ice will remain electrically connected to the evaluation center.
ICECUBE
A sequel is an even larger system for detecting neutrinos in the Antarctic glacier, called ICECUBE (Ice Cube), completed in December 2010. It consists of 5160 photomultipliers embedded in 86 shafts at various depths of 1450-2450 m under ice. These shafts are arranged horizontally in a hexagonal grid with a spacing of 125 meters. A chain of 60 photomultipliers with vertical distances of 17 meters *) was launched (when the ice melts) on the rope into each these shafts, which then froze in the ice. By detecting light flashes, a cube of 1x1x1 kilometer of ice is covered. All photomultipliers are equipped with digital microprocessors with fast data transfer to remote evaluation computers.
*) Note: In the middle of the field, 8 strings of photomultipliers are distributed more densely, with a horizontal distance of 70 meters and a vertical spacing of 7 meters (so-called "DeepCore"). In addition, a photodetection unit with two photomultipliers facing downwards is placed on the surface above each depth chain of the photomultipliers. This "IceTop" surface field serves as an anticoincidence and calibration detector for the IceCube.
  The IceCube detection system has registered several interesting cases of high-energy neutrinos during its operation. E.g. from September 2017, when a high-energy neutrino was detected, probably coming from the very active blazar TXS 0506+056. There is real hope of successful detection of neutrinos from a supernova ("Supernova explosion. Neutron star. Pulsars."), if it explodes in our Galaxy or in a neighboring one. Or maybe from the fusion of neutron stars ("Collisions and fusion of neutron stars").
Submarine detection of neutrinos
Cherenkov radiation, caused by the passage of muons, can also be detected in water at great depths in the sea (where sunlight no longer penetrates). The first prototype of an underwater neutrino detector was the DUMAND ( Deep Underwater Muon And Neutrino Detector) with 24 photomultipliers off the coast of the Big Island of Hawaii. The first functional neutrinos detector of this type is the BAJKAL with 192 photomultipliers, which successfully works at a depth of 1500 m below the surface of the Siberian lake Baikal.
  The submarine detection system neutrinos ANTARES (Astronomy with a Neutrino Telescope and Abyss environmental RESearch) *) was built in 2006-2007 in the Mediterranean Sea about 40 km from the French coastal city of Toulon. To a depth of 2400 m below sea level (where daylight no longer penetrates), 12 vertical supporting ropes, each 450 m long, carrying a total of 900 photomultipliers was gradually launched. The detection system covers an area of about 200x200m. Flashes of Cherenkov radiation from flying muons cause electrical impulses in the photomultipliers, which is detected in coincidence. This radiation from muons must be distinguished from the background caused by the bioluminescence of submarine organisms and from the Cherenkov radiation of a large number of electrons of energy around 1MeV, arising from the b- decay of radioactive potassium ⁴⁰K.
*) In addition to neutrino detection, the ANTARES experiment is also part of interdisciplinary underwater and oceanographic research, such as monitoring of the underwater environment, mainly bioluminescence; also contains seismographic sensors.
  The ANTARES experiment will continue in the coming years with the NEMO (NEutrino Mediterranean Observatory) projects about 80 km from the coast of Sicily and NESTOR (NEutrinos from Supernova and TeV Sources, Ocean Range) off the coast of Greece, which will detect neutrinos in volume of the order of 1 km³. This will cover a geographical area largely complementary to the aforementioned Antarctic IceCube detector.
Radio detection of neutrinos using Askaryan radiation
Askaryan radiation (see §1.6, passage "Askaryan radiation") is tested for neutrino detection, especially in Antarctica, where high-energy neutrinos pass through a layer of ice. The ANITA (....) antenna, located on a balloon above Antarctica, detects these radio pulses. It works in collaboration with photomultipliers detecting Cherenkov radiation in Antarctic ice in the IceCube system.
  The main task of large ice and submarine detectors is to search for high-energy neutrinos, which could have formed during stormy cosmic events, especially during the explosion of supernovae and during the very formation of the universe, during the Big Bang. Detection of such neutrinos could be a valuable source of information about processes that are otherwise unobservable. The localization of sources of high-energy neutrinos could elucidate the mechanism of proton acceleration and thus answer the question of the origin of high-energy cosmic radiation.

The importance of neutrino detection
In addition to basic (mostly purely theoretical) research into the properties of neutrinos and particle interactions with their participation, neutrino detection can also be important for the study of various processes here on Earth and in space. Neutrinos, due to their extreme penetration, are the only particles that are able to "bring out" information about nuclear and particle processes from the interior of massive, large or compact objects, from which no other radiation absolutely penetrates.
   Here on Earth, an increased number of detected neutrinos in certain places may indicate the presence of deposits of natural radioactive substances (even at great depths underground) - uranium and thorium, during the radioactive decay of which, in decay series, neutrinos (electron antineutrinos) are also formed.
   Detection of the flow of solar neutrinos makes it possible to test the instantaneous intensity of thermonuclear reactions inside the Sun (especially the proton-proton cycle). Even the high density and thickness of the plasma in the solar interior do not prevent neutrinos from leaving the region of their birth almost immediately and thus "bring out" relevant information (unlike photons, which for hundreds of thousands of years "penetrate" plasma, with gradual energy degradation, from interior to surface before they radiate; they can only carry information about the surface layers of the Sun).
   Neutrinos also provide important information about turbulent processes in outer space. They are above all supernova explosions in which a colossal amount of neutrinos (electron n_e) is emitted. Relict neutrinos, originating from the Lepton era, can provide important information about the dynamics of the earliest stages of the universe's evolution and the formation of its structure.
   However, the wider use of the possibilities provided by neutrinos is tied up to the improvement of neutrino detection techniques.

Rest mass of neutrinos
The original Fermi theory assumed that the rest mass of a neutrino was zero. However, in the early 1980s, extensive discussions developed about the rest mass of neutrinos: whether the neutrino has zero rest mass (and is therefore of a wave nature - as a quantum of radiation it propagates at the speed of light c), or a non-zero, albeit very small, rest mass m_0n ( and is therefore a particle moving slower than light). These discussions were fueled by the first successful attempts to detect neutrinos in the 1970s and 1980s, which showed that the flux of solar neutrinos is about 3 times lower than expected based on the analysis of thermonuclear and subsequent reactions inside the Sun. This the solar neutrino deficit was referred to as the "solar neutrino mystery", or even as the "neutrino scandal". In 1985, Miseyev, Smirnov and Wolfstein hypothesized that neutrinos "oscillate" between electron, muon, and tauon neutrino states during their flight, leading to them becoming alternately visible and invisible to detectors capable of detecting only electron neutrinos at the time. However, the mechanism of oscillations can only work if the neutrinos have a non-zero rest mass (at least two species-neutrino states); was discussed above in the section "Neutrino Oscillations". There are several ways to measure, or at least estimate, the rest mass of neutrinos.
   In principle, the mass of the neutrino m_0n could be determined on the basis of the law of conservation of energy in b-decay, if we knew the difference between the masses DM of the parent and daughter nuclei. By measuring the maximum energy of the flying electrons E_bmax, it is possible in principle to determine the rest mass of an electron neutrino on the basis of the law of conservation of energy - the heavier the neutrino, the less kinetic energy remains for the electron b; the rest mass of the neutrino is then m_0n = (DM.c² - E_bmax)/c². The dependence of the end part of the continuous beta spectrum on the rest mass of the neutrino is shown in Fig.1.2.3 on the right, which we will mention here again for clarity :

Fig.1.2.3. Beta radioactivity. Left: Basic scheme of radioactivity b^-. Middle: Continuous energy spectrum of radiation b. Right: Enlarged detail of the end of the spectrum for zero and non-zero rest masses of neutrinos.

However, when direct measuring the difference between the masses DM of the parent and daughter nuclei by mass spectrometry and the energy E_bmax by an electron spectrometer, the measurement errors are significantly larger than the required value m_0n.c² [eV]. Therefore, the linearization of the spectrum by means of the above-mentioned transformation - Fermi-Kurie graph (passage "Shape of the beta radiation spectrum") is used for the energy analysis of radiation b. If the rest mass of the neutrino is zero, the Fermi-Kurie graph will be linear up to the maximum value: the end section will also be linear and will intersect the energy axis at the point of maximum energy b. In the case of a non-zero rest mass of a neutrino, the beta electron will always be deprived of the energy necessary to produce this non-zero mass. In the initial sections of the spectrum, this is only slightly apparent and the linearity of the FK graph is retained here. However, in the final section of the FK-graph, in the case of a non-zero mass of the neutrino on the linear dependence, a small "bend" appears, the spectrum decreases faster and is "prematurely" terminated (reaches zero) at a somewhat lower energy E_bmax - m_0n.c², compare with Fig.1.2.3 on the right. Due to the transformation that must be used to linearize the spectrum b, when analyzing the shape of the Fermi-Kurie spectrum, we find the square of the mass of the neutrino m_0n².
  A suitable b-radionuclide for these measurements is tritium ³H. The measurements are very difficult because we are looking for effects much smaller than the "blur" of energy caused by the recoil of nuclei (according to the law of action and reaction at emission b, the nucleus is reflected in the opposite direction) and by thermal motion; measurements were performed at temperatures close to absolute zero and the investigated b -radioactive nuclei ³H was bound in a high molecular weight substance so that the recoil converted to the whole molecule was small. In some of the new planned experiments, a gaseous radioactive source of ³H will be used to minimize the energy losses of electrons in the spectrum.
   Initial measurement based on a detailed analysis of the shape of the end portion of the continuous spectrum of radiation b, giving initially a relatively high value of m_on » 40 eV, later however, the value decreased to 5 eV, which during the measuring error greater than ⁺5 eV admit even a zero value. Only recently have experiments leaned towards a non-zero rest mass of neutrinos - the so-called oscillation of neutrinos has been proven (as previously described experiments Super-Kamiokande, SNO, KamLAND) - spontaneous conversion between electron neutrino n_e , muon n_m and taun n_t , which can occur only when the nonzero rest mass. However, these neutrino oscillation measurements do not provide any absolute range of neutrino masses; they only say that at least two of the three neutrinos have a non-zero rest mass and for the most heavy of them give an estimate of the lower limit > 0.05 eV.
  The latest results of measuring the shape of the ³H tritium b spectrum on special electrostatic spectrometers with magnetic collimation (in the laboratories in Troick and Mainz) show the upper limit m_on < 2.3 eV. New planned experiments and possibly analysis of neutrino-free double beta decay should further reduce and refine this limit. One of these forthcoming experiments is KATRIN (Karlsruhe Tritium Neutrino Experiment), built in international collaboration in a special Tritium Laboratory in Karlsruhe. It will consist of a gaseous tritium source, one smaller "filtration" spectrometer and a giant main spectrometer of particles b (diameter 10m, length 23m). Another planned independent experiment is called MARE (Microcalorimeter Arrays for a Rhenium Experiment), which will measure the radiation b of the radionuclide ¹⁸⁷Re, which has the lowest energy of all only 2.5keV, but an extremely long half-life T1/2 = 4,3.10¹⁰ years; the specific activity and intensity of the radiation is therefore very low. Instead of the usual spectrometric methods, a large number of cryogenic microcalorimeters will be used (their principle is briefly outlined in §2.5 "Semiconductor detectors"), in which a slight increase in temperature caused by complete absorption of particle b in the sample Re will be electronically detected. These future experiments are expected to have a neutrino mass sensitivity of about 0.2 eV.
  Astronomical observations provide other possibilities for determining (or estimating) the rest mass of neutrinos. One of the possibilities, unfortunately very rare, is the observation of a supernova explosion: in the initial phase, it produces an intense flash of light and a massive outburst of neutrinos. If we could observe a flash of light (or a flash of harder photon radiation - X, g) and at the same time detect a "flash" of neutrinos from the same supernova, then we can determine from the time difference between the arrival of a photon and a neutrino flash, how much slower than light the neutrinos moved through space travel. From this, according to the laws of the special theory of relativity, it would be possible to determine the rest mass of neutrinos *)
*) Purely theoretically: a zero time difference would correspond to a zero rest mass; the greater the time difference, the greater the resting mass of neutrinos. Unfortunately, the reality is more complicated. During the initial phase of a supernova explosion - the formation of a neutron star - a huge amount of neutrinos is quickly emitted, which fly almost unobstructed and immediately fly into space. However, a flash of light (and electromagnetic radiation in general) forms for a long time and "laboriously penetrates" the dense mass and the gas envelope. Therefore, the neutrino from the supernova usually arrives at a distant observer a little earlier than a flash of light. The neutrino flash is fast - it lasts only a few tens of seconds, the light flash is delayed, it gradually increases and reaches its maximum only after a few hours. Measurements during the supernova explosion in the Large Magellanic Cloud in 1987 did not show (with regard to the mentioned facts) a difference in the speed of light and neutrinos and thus showed a very small rest mass of neutrinos.
   Indirect (and unfortunately model-dependent) estimates of the rest mass of neutrinos can be derived in cosmology from the measurement of relic radiation anisotropy and from the analysis of the mechanisms of formation of large-scale structures in the early stage of universe.

The cosmic significance of neutrinos
An unbiased person may be surprised, "what are the physicists' worries about?" - if almost nothing like neutrino has a negligibly small or completely zero rest mass! - depends on the? However, interest in this issue was also stimulated by a completely opposite side of scientific research than the microworld - by relativistic astrophysics and cosmology - see Chapter 5 "Relativistic Cosmology" of the book "Gravity, Black Holes and the Physics of Spacetime". The standard cosmological model of the origin and evolution of the universe shows, that shortly after the Big Bang - in the so-called lepton era - such a huge amount of neutrinos was formed in the universe that if their rest mass was greater than about 5 eV, it would be able to "close the universe" by its gravitational action - the current expansion of the universe would stop (in the distant future), the universe would begin to shrink and end up in the "fiery furnace" of large crash. Otherwise, the universe would expand constantly (and the end state would be a kind of "thermal death" - stopping all the processes that release energy, dropping the temperature to absolute zero...); details in §5.6 "The Future of the Universe. The Arrow of Time.". Such a gnoseological situation is characteristic of contemporary fundamental physics, astrophysics and cosmology - that also the tiniest particles we know (almost "nothing" like neutrinos) can, with their ephemeral properties, "have or do not have a rest mass" decide the fate of the largest thing - the whole universe. One of the paradoxes of microworld physics is also that we need to have the largest instruments for research the smallest particles - see §1.5 "Elementary particles".
  Here we briefly touched on evolution of space in connection with neutrinos. However, the situation is much more complicated - neutrinos are only one of the "candidates" for dark matter in the universe, there are also a number of scenarios for the evolution of the universe, just as there may be "more universes" (see the work "Anthropic Principle or Cosmic God " and "Existence of multiple universes?"). In any case, the now determined resting mass of neutrinos shows that neutrinos would probably not be enough to close the universe, or metagalaxy. However, there has been speculation that a suitable "candidate" for dark matter could be neutralines - boson superpartners to neutrinos, the existence of which is predicted by so-called supergravity theories (see §1.5 "Elementary Particles" and §B.6 "Unification of Fundamental Interactions. Supergravity. Superstrings" in book "Gravity, Black Holes...."). In addition, recent observations of the distant universe suggest that in addition to dark matter, the universe is filled with a kind of "dark energy" causing the accelerating expansion of the universe - see the conclusion of the already mentioned chapter "The Future of the Universe. Time arrow.", section "Accelerated expansion of the universe? Dark energy?".
  In stellar astrophysics, neutrinos are shown to play an important role in the final stage of the evolution of massive stars during gravitational collapse and supernova explosion, where they carry away a substantial part of the enormous released energy from the interior of the collapsing star - §4.2, "Supernova explosion. Neutron star. Pulsars.".

1.1. Atoms and nuclei		1.3. Nuclear reactions and nuclear energy

Vojtech Ullmann

A courious report - mystery: Superlight speed neutrinos?

In september 2011, a report appeared in the press that in the CNGS + OPERA experiment , the slightly superluminal velocity of muon neutrinos emitted from the accelerator at CERN and detected in the Gran Sasso underground laboratory was measured . Based on synchronization of send and receive times (using GPS) and statistical evaluation of the detection of about 16,000 muon neutrinos, CNGS experimenters measured that the neutrino traveled a distance of 732km about 60 nanoseconds before flying at the speed of light (the velocity of these neutrinos would be about 2 , 5 thousandths of a percent higher than the speed of light). And immediately bombastic speculations about the invalidity of the special theory of relativity were deduced from this ("Einstein was refuted", "Physics textbooks must be rewritten", etc.). All physicists hoped it was a "false alarm", that some systematic error will be found (probably in the synchronization of the time of sending and receiving). Otherwise it would be a big "trouble"! This can be compared to a situation where you build a house and just before completion a laboratory tells you to demolish it, because a certain hidden defect was found in the bricks used. At the same time, hundreds of houses were built from exactly the same bricks, which have been standing for many decades ..! .. The special theory of relativity (STR) is verified with high accuracy for all known phenomena, for all other particles. It is based on the existence of a maximum velocity of propagation of interactions , which is equal to the speed of propagation of electromagnetic waves (and therefore also light) in a vacuum. Particles with zero rest mass , which are mainly photons , move at this speed . And since neutrinos have been shown to have a non-zero rest mass (albeit indirectly), they should move slightly slower than light. If no error could be found, I would suggest exploring, for example, the following speculative possibility of explanation : Some supersymmetric unitary field theories contain tachyons - hypothetical particles moving only at superluminal speeds (see §1.5, section " Hypothetical and model particles ", passage " Tachyons ", or in more detail §1.6 "Four- dimensional spacetime and special theory of relativity ", passage " Tachyons " in the book "Gravity, black holes and physics of spacetime"). These particles do not formally violate the special theory of relativity      , but due to some of their "pathological" properties, they probably cannot exist as real. However, they can "exist" as virtual tachyons . There could then be a quantum "mixing" of wave functions of real neutrinos with a slight contribution of the wave functions of virtual tachyons. This mix of quantum states could then effectively cause slightly superluminal neutrino velocities as a quantum effect against the STR background. In quantum physics, it is common for real particle states to be affected by virtual particles without violating the laws of physics. But it would remain to explain There would certainly be more possibilities of "explanation", but all of them would probably also be "pulled by the hair" (eg to declare the measured rate of neutrinos as the new maximum rate of propagation of interactions; or the manifestation of hidden extra-dimensions of multidimensional microstructure of spacetime). .) . However, we are ahead of that. In any case, if a systematic error cannot be found, the effect must be verified by a completely independent experiment . Only then can we take it seriously and it will be justified to draw some far-reaching conclusions. So far, it is only about scientific-physical "folklore" ...

Note 1: After all, there is a contradiction with the astronomical observation of the supernova explosion in the Large Magellanic Cloud (a neighboring galaxy 170,000 light-years away) in 1987, from which a 12-neutrino spray was registered (see below " KamiokaNDE Neutrine Detector "), which arrived about 3 hours before the flash of light was astronomically registered. This time difference does not mean that perhaps neutrinos are slightly faster than light, but it is explained by the mechanism of the supernova explosion (below in the section " Resting mass of neutrinos ") and suggests that neutrinos move at the speed of light.with an accuracy of the order of billionths of a percent. If the neutrino moved at the speed as "measured" in the above experiment, a flash of light from this supernova would reach us a few years later (about 4 years) than the neutrino spray! So this is a strong argument against the superluminal speed of neutrinos. It should be noted, however, that these are mainly lower-energy electron (anti) neutrinos; however, we do not see any reason yet why muon neutrinos (which also have a rest mass perhaps higher than electrons) should behave differently ... Note 2: R. van Elburg recently investigated the effect of time dilation (according to a special theory of relativity) between the Earth's reference systems and the moving GPS satellite. The relativistic dilation of time caused by the movement of the clock on board the GPS relative to the Earth's reference system would lead to a time difference of 32ns in CERN and 32ns in Gran Sasso. That might explain the difference 60ns ..? ..

A technical error has been found ! - the "bubble burst" At the end of February 2012, the CNGS + OPERA experimenters themselves found two technical errors: incorrect connection of the optical cable connecting the computer to the signal from the GPS satellite and an error in the oscillator used to synchronize the external GPS signal with the OPERA experiment control clock. These problems could skew the measurements and cause a false result that the neutrino beam covered a distance of 732km from CERN to the Gran Sasso detector 60 nanoseconds before it corresponds to the speed of light ...