In a number of experiments, when detecting particles emitted in beta decays, periodic oscillations of count rate with an amplitude up to tenths of a percent and short bursts vastly exceeding the usual count rate are found. At the same time, several experiments did not detect any differences from the “normal” course of beta decays greater than 0.01%. The article shows that the inconsistency of the experimental results is due to different measurement technique. The assumption is made of the possible participation in the beta decay processes of cosmic slow neutrinos, which makes it possible to explain in a comprehensive manner not only periodic and sporadic changes in the beta decay rate, but also a number of other incomprehensible phenomena associated with beta radioactivity. On the basis of the experiments carried out, an estimate is made of the flux density of slow cosmic neutrinos.
Until recently, the strictly exponential nature of radioactive nuclides decay rate was considered unquestionable. But recently many articles have been published with the results of measurements of radioactivity, which give rise to doubts about the inviolability of this property of radioactivity. Both periodic (first of all, with a period of 1 year) [
Let us assume that the anomalies in the beta decay rate are associated with the action of neutrinos or antineutrinos in accordance with nuclear reactions
ν e + ( A , Z ) → ( A , Z + 1 ) + e −
or
ν ˜ e + ( A , Z ) → ( A , Z − 1 ) + e + (1)
This occurs against the backdrop of spontaneous decays
( A , Z ) → ( A , Z + 1 ) + e − + ν ˜ e
or
( A , Z ) → ( A , Z − 1 ) + e + + ν e (2)
The problem is to detect a small number of reaction acts (1) against the background of a large number of reaction acts (2). Solution of this problem is possible due to the fact that in the reactions (2) there are electrons or positrons with energies from zero to the upper boundary Emax, characteristic for each nuclide. In the case of reaction (1), the emerging electrons or positrons have an energy exceeding Emax on the energy of the absorbed neutrino or antineutrinos. If neutrinos (antineutrinos) appear in nuclear reactions, for example, in the interior of the Sun, the excess reaches several MeV. If relic neutrinos with very low energy are registered, the electrons have energy close to Emax.
If the number of induced reactions is much less than the number of spontaneous decays, in order to detect effects associated with the action of neutrinos (antineutrinos), it is necessary to have detectors that can selectively register electrons (positrons) with an energy exceeding Emax. Geiger counters, proportional counters, ionization chambers, semiconductor and scintillation detectors allow you to directly register beta particles. Moreover, these detectors allow partially to solve the problem of high-energy particles separation by placing a layer between the source and the detector of a substance that absorbs the bulk of the particles that arise during spontaneous beta decays and which transmits most of the particles of higher energy.
It is tempting to use gamma spectrometers to register beta decays. The use of such detectors is based on the fact that in most cases, as a result of beta decays, nuclei are formed in an excited state, which remove excitation by emitting gamma quanta. But the energy of the emerging gamma rays does not depend on the energy of the emerging electrons. Therefore, by detecting gamma quanta, it is practically impossible to isolate the events of interest related to the action of neutrinos (antineutrinos).
Thus, to detect variations in the rate of beta decays, if they are associated with the action of neutrinos (antineutrinos), it is necessary to use beta spectrometers or beta particle detectors in combination with the optimum absorbers of particles formed during spontaneous decays. The registration of gamma quanta [
Some works, for example [
An attempt was made in [
With a lot of experiments in which anomalies in the beta-decay process are discovered, one can get acquainted in [
To detect anomalies in the course of radioactive decay, it was necessary to create a set of facilities that made it possible to obtain and continuously record, over the years, various information [
The testing of various detectors has shown that the most suitable for long-term detection of beta particles are halogen Geiger counters, and for alpha particles―semiconductor detectors. To reduce the influence of temperature changes, not only detectors with signal amplifiers were thermostated, but also power supplies.
Counter located in the air cavity detects the radiation of both radionuclides, and the second, separated from the source by a layer of matter absorbing strontium radiation, registers radiation only of yttrium.
three different detectors from two different beta sources on average vary throughout the year almost identically. At the same time, the main environmental parameters that can be suspected as a source of instability of the recording equipment are radiation background, temperature, atmospheric pressure, humidity, behave differently. This indicates that there is a phenomenon associated with the beta sources, rather than the influence of variations in the parameters of the external environment.
In addition to beta radioactivity, long-term studies of the alpha decay process were carried out. To do this, the alpha source 239Pu, located near to the silicon detector, was placed with the amplifier in a thermostat at a temperature of 18˚C. The results obtained for more than three years are shown in
A large amount of accumulated data makes it possible to apply frequency analysis, which allows us not only to clarify the parameters of the observed annual rhythms, but also to reveal other periodicity, imperceptible against the background of statistical fluctuations and interference acting at random times. For analysis of the results of 90Sr90Y beta particle count rate measurements fast Fourier transformation was applied, followed by recalculation of the frequency in the periods [
The question arises, which of the known rhythms can be related to the observed near-monthly periodicity? With the period of the change of the lunar phases, the period of the Moon’s rotation relative to the stars, the period of the change in the distance to the Moon, and perhaps with the period of solar activity
change associated with the rotation of the Sun-which is also close to 1 month? Analysis [
In the range of shorter periods, the peak of the solar-diurnal period is clearly visible, near which peaks corresponding to the star-day and moon-diurnal periods are visible [
Summarizing the results of this section, taking into account the results obtained with the use of other detectors and radionuclides [
Strong outbursts of beta particles count rate are detected with the continuous scanning of the celestial sphere by peculiar telescopes in which the beta source is located in the focus of the parabolic mirror. One of these types telescopes, with which the most striking results are obtained, has a steel mirror with a concave parabolic surface 22 cm in diameter with a focal length of 10 cm. A small beta 60Co source connected to a miniature Geiger counter is located in the focus. Like astronomical telescopes, the telescope has two axes of rotation. One is parallel to the Earth’s axis. The other axis is perpendicular to the earth’s axis. This design allows you to determine which area of the celestial sphere the telescope is pointing to. More detailed description of the methodology of these experiments and the results obtained can be found in [
At the first stage of the researches, the telescope was oriented in a direction close to the east, with a fixed inclination above the horizon. Rotating with the Earth, the telescope “viewed” a strip of the celestial sphere about 1˚ wide. The count rate was continuously recorded by the computer. The astronomical coordinates of the celestial sphere place, to which the telescope is currently directed (declination and right ascension), were determined with an error of about 1˚ on the basis of observations of the movement of the image of the Sun. Sometimes, at intervals of several months, bursts of counting counts from a few seconds to an hour were recorded, at which the count rate many times exceeded the background count (
The effectiveness of observations has increased to several bursts per day in the transition from one-dimensional scanning to two-dimensional. For this purpose, the telescope was given an oscillatory motion perpendicular to the scanning line associated with the daily rotation of the Earth. The amplitude of the oscillations is up to 40˚, the “forward stroke” is about 10 minutes, the “reverse” is about 1 minute, the time of the beginning and the end of the backward movement was recorded by a computer with an exact time reference, which made it possible to determine to what points of the celestial sphere the telescope “looks” when the bursts are discovered.
The conducted investigations give grounds for the following generalizations [
Important results were obtained using detector that allows the extraction of beta particles with energy close to the maximum energy of the beta spectrum [
the channel, where particles with an energy close to the boundary value are recorded, is approximately equal to the magnitudes of the bursts in the channel, where the particles of the whole spectrum are recorded. This indicates that the emerging particles have energy close to the boundary energy, and not the “smeared out” spectrum inherent in the usual beta decay. Thus, during the outbursts, there is no intensification of the usual “direct” beta decay, but a nuclear reaction of the “reverse” beta decay occurs, as a result of which neutrinos and nuclei interact with the same daughter nuclei as in “direct” beta decay, But the emerging electrons are not distributed over the spectrum, but have a fixed energy.
The hypothesis of the connection between the variations of beta sources decay rate with neutrinos arising in nuclear processes on the Sun [
σ = λ 3 / T V (3)
where σ is the reaction cross section, λ is the de Broglie wavelength of the neutrino, T is the mean lifetime of radioactive nuclei, and V is the neutrino velocity.
In the case of relativistic neutrinos, which are dealt with in nuclear physics, λ = h c / E (h is the Planck constant, c is the speed of light, E is the neutrino energy), relation (3) goes over into formula
σ = h 3 c 2 / E 3 T (4)
Substituting in Equation (4) typical for nuclear physics values E = 1 MeV (1.6∙10−13 J), T = 1000 s, we obtain the value of σ ~ 6∙10−48 m2, which is confirmed by experiments [
It follows from (4) that
n = N φ σ = N φ h 3 c 2 / E 3 T = A φ h 3 c 2 / E 3 (5)
where n is the number of acts of inverse beta decays per second, A = N/T is the number of direct beta decays per second (activity of the source), N is the total number of radioactive nuclei, and ϕ is the neutrino flux density.
Let us find the ratio of the rate of reverse beta decays to the rate of spontaneous beta radioactivity К = n/A, using the relation (5):
K = φ h 3 c 2 / E 3 (6)
Substituting into (6) the flux density of solar neutrinos ϕ ~ 6∙1014 m−2∙s−1 [
In the case of neutrinos of very low energies (relic neutrinos) V ≪ c , λ = h / m V (m is the neutrino mass), the ratio (3) goes over into formula
σ = h 3 / m 3 V 4 T (7)
Since neutrinos, which have very small kinetic energy and mass, cannot make a significant contribution to the energy of nuclear reactions, they can react only with nuclei that do not have an energy threshold. Such nuclei have beta radioactivity
It should be noted that the term “relic neutrinos” arose in connection with the fact that initially the presence in the universe of a huge number of neutrinos with very low energies was predicted by the “big bang” theory. But it cannot be ruled out that there may be other sources of such neutrinos. For us it is important that these particles have a rest mass and the speed of motion is so low that they are kept by the gravitational fields of the Galaxy, stars and other massive objects. Therefore, it is better to call such particles “slow neutrinos”. It cannot be ruled out that the anomalies in beta decays are associated not only with neutrinos, but also with other electrically neutral particles, capable of participate into weak interactions. But we are only considering neutrinos, since the initial assumption of equal probability of direct and inverse beta decays implies the identity of the decayed particles emitted from spontaneous decays and absorbed upon inverse beta decays.
It follows from (7) that in the case of neutrinos of very low energies
n = N φ σ = A φ h 3 / m 3 V 4 (8)
Let us find the ratio of the rate of reverse beta decays to the rate of spontaneous beta radioactivity K = n / A using the relation (8):
K = φ h 3 / m 3 V 4 . (9)
Taking into account that φ = ρ V / m , where ρ is the mass neutrino density, we obtain
K = ρ h 3 / m 4 V 3 (10)
An important feature of relations (9) and (10) is independence from the half-life of the nuclei. Any beta radioactive sources, being in the same stream of slow neutrinos, acquire the same relative increase in activity. If during its motion the Earth passes regions with different velocities or neutrinos flux density, the same relative changes in the activity of different beta sources should occur.
These calculations do not pretend to be accurate, but clearly show that neutrino fluxes can be a tangible cosmic agent. In what follows we will assume that the agent that causes additional beta decays is neutrinos moving in the gravitational field of the Galaxy. In addition to galactic neutrinos, neutrino fluxes moving in near-solar and near-Earth gravitational fields can influence beta-radioactivity [
Combining the results of astronomical observations with relations (9, 10), we can estimate neutrino flux density, based on the strong dependence of the magnitude of the effect on velocity. Suppose that the main reason for variations in activity with a period of 1 year is that the velocity of the neutrino flux coming to the solar system is summed with the speed of the Earth’s orbital motion around the Sun.
According to [
increase due to the reverse beta decay changes on Δ K = ρ h 3 m 4 ( V min − 3 − V max − 3 ) = 2 a ,
where a is the amplitude of the relative activity change, ρ is neutrino mass density, and m is neutrino mass. Therefore
ρ = 2 a m 4 h 3 ( V min − 3 − V max − 3 ) . (11)
In [
At present, there is no exact data on the mass of the electron neutrino (antineutrinos). A variety of experiments and astronomical observations indicate that it does not exceed 1 eV [
Note that the de Broglie wavelength λ = h / m V of slow neutrinos with a mass of 1 eV moving in the Galaxy with a velocity of about 4∙105 m/s relative to the terrestrial observer has a value near 1 mm. This means that the interaction region of these particles covers an enormous number of atoms (~1020 in a condensed matter), in contrast to relativistic neutrinos, which interact with only one particle. This is the main reason for a radical increase in the efficiency of neutrino interaction with matter at very low energies. Another reason is that the speed of movement is small, as a result of which the duration of neutrino contact with each particle of matter becomes much greater than in the case of “nuclear” neutrinos moving at a speed close to the speed of light. The interaction of slow neutrinos with matter is similar to the interaction of light with a transparent medium: refraction, reflection, and scattering on inhomogeneities occur practically without exchange of energy. Capture is possible only when interacting with beta radioactive nuclei. In addition, interference and diffraction are possible in slow neutrino fluxes.
If surface is sufficiently smooth (unevenness is less than the wavelength), refraction and reflection occur according to the laws of geometric optics, which makes it possible to focus by means of lenses or mirrors. This circumstance makes it possible to create telescopes for slow neutrinos, using mirrors with a concave parabolic surface with a beta source located in the focus [
For telescopes with a diameter D and a focal length f under the action of a monodirectional agent having wavelength λ , excess of the flux density in the focus above the unfocused flux density χ = 0.14 k D 4 / f 2 λ 2 , where k is the coefficient that takes into account reflection losses from the mirrors or as a result of absorption in the lenses [
Telescopes can only be used if the active agent is narrowly directed. The presence of narrowly directed beams in slow neutrino fluxes is associated with another important feature of them: the influence of gravitational fields on their motion. Slow neutrinos trajectories, as well as other objects of dark matter, is not different from any other space objects (stars, planets, asteroids, cosmic dust, etc.) and can be calculated by conventional methods of celestial mechanics [
Intent of this experiment was based on the idea of gravitational focusing of slow neutrino fluxes by a certain star and secondary focusing by the Sun. This effect can be observed if the star, the center of the Sun and the observer located on the Earth are on the same straight line. Close connections of the Sun with the near-by stars are rather rare events, the time of which is easy to determine using astronomical atlases. For example, on August 19 of each year the star v Leo
passes at a distance of 5 angular minutes from the center of the Sun. On this day of 1994, the telescope was directed in such a way that the scanning path of the celestial sphere passed through the Sun. When the telescope was aimed at a region near the Sun, a strong burst of count rate was recorded. A similar burst was registered exactly one year later (
In a variety of experiments, periodic changes in beta particles count rate with amplitude up to tenths of percent were observed. However, such variations can be detected only with the predominant detection of particles with energies close to the maximum energy of the beta spectrum. This indicates that the observed oscillations in the count rate are associated with the action of neutrino fluxes. This is also indicated by the absence of such anomalies in alpha decays, in which the neutrino does not participate. Experiments in which most particles of beta spectrum are detected do not show periodic deviations from the usual beta decay process of more than 0.01%. This indicates that the periodic anomalies do not exceed 1/10,000 of the average beta decay rate.
Short-term irregular bursts of count rate of beta particles can be observed by placing a radioactive source in the focus of a concave parabolic mirror. These bursts can highly exceed the normal counting rate. The energy of the detected particles, as in the case of periodic anomalies, is close to the maximum energy of the spectrum of spontaneous beta decays.
In contrast to the hypothesis about the effects on beta radioactivity of solar neutrinos, the assumption of the possible involvement of space slow neutrinos in the process of beta decay allows, without departing from the scope of existing scientific knowledge, complex to explain not only the periodic and sporadic changes in the beta decay rate, but also a number of other phenomena associated with beta radioactivity, for example, inexplicable effects observed in the measurement of the neutrino mass by tritium decay beta studies [
Parkhomov, A.G. (2018) Rhythmic and Spоradic Changes in the Rate of Beta Decays: Possible Reasons. Journal of Modern Physics, 9, 1617-1632. https://doi.org/10.4236/jmp.2018.98101