Full Text
From Current Literature
Attempts at the Experimental Detection of Double Beta Decay
If the masses of two isobaric nuclei with a charge difference of \(\Delta Z = 2\) differ by more than twice the rest mass of the electron, then a transition of a nucleus with the larger mass into a nucleus of smaller mass with the emission of two electrons or positrons is energetically possible. Such a transition is called double \(\beta\)-decay.
Two different ways of describing this phenomenon are possible within the framework of the presently existing theory of elementary particles, depending on assumptions about the properties of the neutrino.
One may start from the assumption that, in double \(\beta\)-decay, four particles are emitted by the nucleus—two electrons and two neutrinos (or antineutrinos); in this case the neutrino and the antineutrino are regarded as physically distinct particles.
Alternatively, in contrast to the preceding case, one may suppose that double \(\beta\)-decay is accompanied by the emission only of electrons, since in order to satisfy the laws of conservation of energy and momentum in the process under consideration the participation of the neutrino as a decay product is not obligatory (unlike in ordinary \(\beta\)-processes). In this case the neutrino and antineutrino must be identical particles, and as a consequence the charge of the neutrino must be taken to be zero.
Experimental establishment of the validity of one of the indicated variants would provide important information for the modern theory of elementary particles. Which of the two theories is correct can be checked experimentally on the basis of the following facts.
Calculations\(^1\) lead to a sharp difference in the half-life periods for the double \(\beta\)-process in passing from one variant to the other. Thus, for a transition energy of about \(1\) MeV, in the case of double \(\beta\)-decay accompanied by the emission of four particles, the half-life is of the order of \(10^{22}\)—\(10^{23}\) years, whereas in the case of a process with the emission of two particles it is of the order of \(10^{17}\)—\(10^{18}\) years.
In addition, in the latter case the sum of the energies of the electrons emitted from the nucleus is constant and equal to the total transition energy, in contrast to the process with the emission of four particles. The probability of double \(\beta\)-decay with the emission of two electrons and two neutrinos is so small that the corresponding effect is impossible to observe with the present state of experiment. Consequently, in experiment one can detect only the process with the emission of two electrons with constant total energy.
Most of the published experimental work on the study of double \(\beta\)-decay has been carried out with tin \(\mathrm{Sn}^{124}_{50}\). Recently\(^2\), with the aid of mass-
of the spectrograph, the mass difference of the atoms \(\mathrm{Sn}_{50}^{124}\) and \(\mathrm{Te}_{52}^{124}\) was measured. It was found to be \(1.5 \pm 0.4\) MeV. Consequently, the transition
\[ \mathrm{Sn}_{50}^{124} \xrightarrow{2\beta} \mathrm{Te}_{52}^{124} \]
is theoretically possible, with a maximum value of the total kinetic energy of the electrons of about \(1.5\) MeV. Fajerman was the first to attempt to detect this effect experimentally. He placed a tin sample enriched to \(54\%\) in the isotope \(\mathrm{Sn}^{123}\) between two thin-walled counters and registered coincidences of discharges in these counters. When the enriched sample was replaced by a plate of the same dimensions made from the natural mixture of tin isotopes (with a content of the isotope \(\mathrm{Sn}^{124}\) of \(0.4\%\)), the number of coincidences per hour decreased from \(16.4 \pm 0.3\) to \(14.4 \pm 0.3\). The author explained the decrease in the number of coincidences by the occurrence of double \(\beta\)-decay of \(\mathrm{Sn}_{50}^{124}\), and, proceeding from this, for the half-life obtained a value within the limits from \(4 \cdot 10^{15}\) to \(9 \cdot 10^{15}\) years.
However, the value obtained by Fajerman was not confirmed by subsequent work.
Lawson\(^{4}\), having obtained 8794 photographs with an ionization chamber inside which a tin sample enriched to \(83\%\) in the isotope \(\mathrm{Sn}^{124}\) was placed, did not find a single pair of electron tracks caused by double \(\beta\)-decay of tin, and concluded that the half-life of \(\mathrm{Sn}_{50}^{124}\) must be considerably greater than \(10^{16}\) years.
By a coincidence-counting method analogous to that used in work\(^{3}\), Kalkstein and Libby obtained, for the minimum value of the half-life of tin, a value of the order of \(2 \cdot 10^{17}\) years\(^{5}\).
In the work of Pearce and Derby\(^{6}\), to detect double \(\beta\)-decay in tin \(\mathrm{Sn}_{50}^{124}\), an apparatus was used that made it possible to register not only the number of coincidences but also the energy of the particles that produced the coincidences. In this work, tin foil \(100\ \mathrm{mg/cm^2}\) thick, containing \(95\%\) of the isotope \(\mathrm{Sn}^{124}\), was used. The foil was placed between two crystalline counters, by means of which coincidences were registered. The electronic selector circuit was arranged so that the amplitudes of the coincident pulses were added, and the total amplitude was selected by the corresponding channel of an 18-channel discriminator. Since the amplitudes of the pulses in the counters were proportional to the electron energy, with the help of this apparatus it was possible to obtain a curve of the dependence of the number of coincidences per unit time on the total energy of the electrons that produced the coincidences. The presence of double \(\beta\)-decay in the sample under study would have led to the appearance of a peak on this curve.
To reduce the background, the counters were protected by a layer of lead and were connected in anticoincidence with a third counter placed above them, which mainly registered cosmic particles and showers. The background of coincidences was measured when the tin foil was replaced by aluminum of equivalent thickness and amounted to approximately \(0.5\) pulse per hour per channel.
In the authors’ opinion, their apparatus could have registered an excess in the number of coincidences caused by double \(\beta\)-decay over the background of \(0.2\) pulse per hour. Since they were unable to detect an effect under these conditions, they concluded that the lower value of the half-life lies within the limits from \(3 \cdot 10^{16}\) to \(6 \cdot 10^{16}\) years.
Finally, Fajerman, together with Schwarzschild, again tested the experiment for detecting double \(\beta\)-decay of \(\mathrm{Sn}_{50}^{124}\), this time with the aid of a Wilson cloud chamber controlled from within by the investigated sample\(^{7}\). The chamber was controlled by the coincidence of pulses in thin-walled counters also placed inside the chamber. Samples of tin of natural isotopic composition and enriched to \(95\%\) in the isotope were used.
with Sn\(^{124}\). With the enriched sample, 2754 photographs were obtained. Only in three of them could the electron tracks be explained by double \(\beta\)-decay. However, in the opinion of the authors of the work, they could also have been caused by other effects associated with multiple scattering of electrons in the Wilson chamber gas and in the chamber window plate, as well as with possible radioactive contamination of the sample. The total energy of the electrons in these three cases, measured from the radius of curvature in the magnetic field, turned out to be, respectively, 750 keV, 785 keV, and 330 keV.
If these three photographs are interpreted as cases of manifestation of double \(\beta\)-decay, then for the half-life one obtains the value \(2 \div 5 \cdot 10^{17}\) years. The authors attempt to explain their previous result\(^3\) by the insignificant fraction of impurities that may have been present in the sample they used.
Double \(\beta\)-decay in palladium\(^8\) has also been investigated. It is known\(^9\) that Ag\(_{47}^{110}\) goes by \(\beta\)-decay with maximum energy 2.79 MeV into the ground state Cd\(_{48}^{110}\). At the same time, the transition\(^ {10}\)
\[ \mathrm{Ag}_{47}^{110} \xrightarrow{\beta^{+},K} \mathrm{Pd}_{46}^{110}. \]
has not been observed.
From this one may conclude that the mass difference of the isobaric nuclei Ag\(_{47}^{110}\) and Pd\(_{46}^{110}\) is not greater than the rest mass of the electron. Consequently, the double \(\beta\)-decay
\[ \mathrm{Pd}_{46}^{110} \xrightarrow{2\beta^-} \mathrm{Cd}_{48}^{110} \]
is energetically possible, with a maximum total kinetic energy of the electrons between 1.77 MeV and 2.28 MeV. The transition
\[ \mathrm{Pd}_{46}^{108} \xrightarrow{2\beta^-} \mathrm{Cd}_{48}^{108} \]
is apparently also energetically possible. The author of the work\(^8\) placed in a Wilson chamber a plate of natural palladium (26.7% Pd\(^{108}\) and 13.5% Pd\(^{110}\)) and obtained more than 10,000 photographs. One of the photographs contained two electron tracks emerging from one point of the sample. The electron energies turned out to be, respectively, \(0.8 \div 1.1\) MeV and \(1.4 \div 2.1\) MeV. These tracks could have arisen from double \(\beta\)-decay, as well as from background caused by cosmic radiation and by other extraneous sources. If these traces are attributed to double \(\beta\)-decay, then for the half-life one obtains the value \(6 \cdot 10^{17}\) years for Pd\(^{110}\) and \(1.1 \cdot 10^{18}\) years for Pd\(^{108}\).
Attempts to detect double \(\beta\)-decay in the isotopes of tellurium Te\(_{52}^{128}\) and uranium U\(_{92}^{238}\) by determining the content, respectively, of xenon in tellurite\(^ {11}\) and plutonium in uranium\(^ {12}\) were unsuccessful and led to a lower value of the half-life of the order of \(10^{19}\) years.
Thus, the experimental works on double \(\beta\)-decay published up to the present time have not led to any reliable conclusions regarding the nature of this phenomenon. In most cases there is only a lower limit on the half-life, which varies in different works within the range from \(10^{15}\) to \(10^{19}\) years.
P. Sh.
CITED LITERATURE
- L. A. Sliv, ZhETF 20, 1035 (1951).
- B. G. Hogg, H. E. Duckworth, Phys. Rev. 86, 567 (1952).
- E. L. Fireman, Phys. Rev. 75, 323 (1949).
- J. S. Lawson, Phys. Rev. 81, 299 (1951).
- M. L. Kalkstein, W. F. Libby, Phys. Rev. 85, 368 (1952).
- R. M. Pearce, E. K. Darby, Phys. Rev. 86, 1049 (1952).
- Fireman, Schwarzer, Phys. Rev. 86, 451 (1952).
- R. G. Winter, Phys. Rev. 85, 687 (1952).
- Siegbahn, Phys. Rev. 77, 233 (1950).
- Deutsch, Phys. Rev. 72, 527 (1947).
- M. G. Inghram, J. H. Reynolds, Phys. Rev. 76, 1265 (1949).
- C. A. Levine, A. Giorso, G. T. Seaborg, Phys. Rev. 77, 296 (1950).