THE NEUTRINO HYPOTHESIS AND NEW EXPERIMENTAL DATA SUPPORTING IT

A. P. Grinberg

It would hardly be possible to name another hypothesis that has occupied so peculiar a position in science as the hypothesis of the existence of the neutrino. Proposed by Pauli more than 12 years ago to explain the puzzle of β-decay, it, owing to its simplicity and convincing character, won universal recognition and at present remains the only one that gives an acceptable interpretation of the facts observed in β-decay. In the course of time, ever new experimental data from various fields of nuclear physics, as well as theoretical questions, on the one hand required for their explanation the invocation of the same hypothesis of the existence of the neutrino, and on the other hand provided additional evidence in its favor. It is therefore not surprising that physicists have already become accustomed to speaking of the neutrino as of a real particle. At the same time, up to now no one has succeeded in proving by direct experiments that the neutrino actually exists in nature. Moreover, at present it is not even possible to indicate a method by which one might try to discover the neutrino in the free state. All the greater significance, therefore, in the question of the experimental confirmation of the neutrino hypothesis is acquired by indirect proofs of the reality of the neutrino. Among such proofs the most direct and convincing may be obtained by studying the recoil of nuclei in radioactive decay. Several works of this kind were carried out long ago, but they led to no definite results. Only in 1941 did the American physicist James Allen, having carried out his remarkable investigation, provide that last and most weighty argument in favor of the existence of the neutrino which experimenters had so long been seeking. This work can undoubtedly be regarded as proof of the existence of the neutrino.

Before presenting Allen’s work, it is necessary to dwell on the essence of the problem of β-decay, on the premises that compelled the proposal of the neutrino hypothesis, and on those attempts to prove it experimentally which were made before Allen.

1. THE PROBLEM OF β-DECAY AND VARIOUS ATTEMPTS AT ITS SOLUTION

β-radioactivity, as is known, consists in the spontaneous emission of fast electrons by the nuclei of certain radioactive elements; in this process an element with atomic number \(Z\) is transformed into an element with number \(Z+1\). Examples of β-active substances may be RaB, RaC, ThB, and others.

In the early period of the study of β-radioactivity, the primary nuclear radiation was considered to be those groups of electrons homogeneous in energy into which β-radiation is split in a magnetic spectrograph (the experiments of Baeyer and Hahn^1, 1910).

The work of Rutherford and his school showed that this line spectrum of electrons arises as a result of secondary processes taking place in the atom; that these electrons are not primary and are not emitted from the nucleus in β-decay. At about the same time the radiation that could be regarded as primary, nuclear radiation was discovered: in 1914 Chadwick^2 found that electrons with homogeneous energies constitute only a very small fraction of all the electronic radiation of a β-active substance; besides these groups there is a much larger number of electrons whose velocities are distributed continuously over a very wide region. A whole series of subsequent experiments provided information about the form of this distribution—the form of the continuous spectrum of β-particles—and also showed that for each β-active substance there exists a quite definite upper limit to the velocity of the β-particles (the latter question was long disputed and was finally resolved only in 1933, thanks to the work of Sargent). In Fig. 1 are shown, as examples,

Fig. 1. Distribution of β-particles by energy for RaE and Al^28

typical forms of the β-spectrum^3: one for a substance with a large atomic number—for radium E \((\mathrm{RaE}=\mathrm{Bi}_{83}^{210})\), the other for a substance with a small atomic number—for one of the artificially radioactive isotopes of aluminum \((\mathrm{Al}_{13}^{28})\).

At first the presence of a continuous spectrum of β-particles did not cause any particular perplexity among physicists—the knowledge of β-decay was in general too scanty. Gradually, however, it became increasingly clear that here we were encountering quite unusual circumstances requiring explanation. The problem of β-decay arose.

All the data that had accumulated in the study of α- and γ-emission indicated that the atomic nucleus is a quantum system having strictly definite energy levels. For example, it is well known that α-particles emitted by the nuclei of a given radioactive substance all possess exactly the same energy^1).

^1) As regards the so-called long-range α-particles and the fine structure of the α-spectrum, these phenomena are also excellently interpreted on the basis of the conception of discrete levels of excited nuclei.

This means that all nuclei of an α-active substance before decay are in a definite, one and the same energy state; then, upon decay, exactly the same amount of energy is released in the form of the mass of the α-particle and its kinetic energy, and the final nuclei again are all in one and the same definite energy state.

Data on the strict monochromaticity of nuclear γ-rays lead to the same conceptions of definite quantum states in which the nucleus is found.

The energy conditions observed in β-decay differ fundamentally from those enumerated above. First of all, the energies of different β-particles are different; but this is not merely a question of the presence of a large number of discrete groups of electrons with identical energies within each group, but of a continuous set of energies. The conclusion suggests itself that the emission of β-particles corresponds to transitions between arbitrarily and continuously arranged energy levels of nuclei. However, such a conclusion, contradicting both quantum-mechanical conceptions and experiment, seemed so implausible that it was immediately rejected, and attempts were made to find the solution of the question in the supposition that the energy inhomogeneity of β-particles is the result of certain secondary processes. According to Meitner’s hypothesis, proposed by her in 1922, all electrons fly out of the nuclei of a given substance with one and the same energy, but then lose one or another fraction of it while passing through the electron shell surrounding the nucleus. There are a number of general considerations that constitute strong arguments against such an assumption. Let us consider, for example, the data on the β-decay of RaE. The greatest energy of the β-particles of RaE is approximately 1.2 MeV, while the maximum of the curve of their continuous spectrum lies in the range from 0 to 30 keV (see Fig. 1). From Meitner’s point of view this means that there is a large number of electrons which, possessing an initial energy of 1–2 MeV, as a result of certain processes have reduced their energy, for example, to values below 0.1 MeV. What, however, are the processes that could account for such a considerable loss of energy? We cannot name any such processes. A β-particle may, for example, lose its energy in a collision with one of the orbital electrons of the given atom, transferring all its energy to this electron. But to knock out even the most strongly bound orbital electron—the electron of the K-shell—in the case of a RaD atom requires only 90 keV, so that the ejected electron will have a very large energy (1200 − 90 = 1110 keV). Thus the continuity of the β-spectrum of RaE cannot be explained by an exchange of energy between the β-particle and an orbital electron. Another assumption that might be advanced also falls away: the supposition that β-particles spend part of their energy in order to excite the emission of γ-rays; it is known that RaE emits no γ-rays at all.

Finally, a decisive refutation of Meitner’s hypothesis was provided by a direct experiment of Ellis and Wooster, carried out by them in 1927[^4a]. Its idea is as follows. If the initial energy of the β-electrons is the same and changes only as a result of certain processes of transfer of it to oth—

these particles or atoms, then, when a definite quantity of a β-active substance is placed in a calorimeter, there should be observed a thermal effect corresponding to the product of the number of decayed atoms by the maximum energy of the β-particles, because both the kinetic energy of the β-particles and that fraction of their energy which is lost inside the electronic shell of the atom must ultimately be converted into heat and will be registered by the calorimeter. Ellis and Wooster showed that this is not the case. The total thermal energy liberated in the decay of the substance they took (RaE) proved to be exactly equal to the product of the number of decayed atoms by the average energy of the electrons of the continuous spectrum. This undoubtedly indicates that the energetic inhomogeneity of β-particles is of a primary character: already upon emission from the nucleus the electrons have the same velocity distribution that we know from the form of the continuous β-spectrum.

The experiment of Ellis and Wooster was repeated with great care in 1930 by Meitner and Orthmann^4b, who obtained the same result.

Thus, the energetic inhomogeneity of β-particles is not due to secondary effects. It was therefore necessary to return to the former conclusion: consequently, in β-decay the amount of energy emitted is indeterminate, not quantized, and varies continuously over wide limits. This obviously means that either the initial β-active nuclei, or the final nuclei formed as a result of β-decay, or, finally, both the former and the latter have unequal energies, i.e. are in a completely indeterminate energy state. In other words, two nuclei of the same kind must differ measurably in mass. We have already said above that such a state of affairs contradicts both theoretical conceptions and experimental facts relating to neighboring domains of nuclear physics. To this one may add still a number of arguments. Experimental data on molecular spectra give convincing evidence that nuclei of the same kind obey a definite statistics and, consequently, must be regarded not merely as approximately alike, but as essentially identical particles. From the hyperfine structure of atomic spectra it follows in exactly the same way that the nucleus is a quantized system with a completely definite mass and angular momentum. These observations concern nonradioactive substances, but obviously there is no reason to doubt that the same is true also for radioactive nuclei, in particular for β-radioactive ones. Further, there are no facts whatever that would indicate that, before β-decay or after it, the nuclei of a given substance differ in energy. For example, if there is a chain of radioactive transformations of the type α-β-α, experience shows that all the α-particles in the first link possess one and the same energy, and the α-particles in the third link are likewise all identical in energy among themselves, despite the fact that in the second link of this chain β-decay occurs, with its characteristic emission of energetically heterogeneous particles. Finally, convincing experimental proof that all initial β-active nuclei of a definite substance possess one and the same intrinsic energy, i.e. mass (the same also applies to the final nuclei), can be obtained for artificially radioactive substances.

nuclei with very great accuracy by measuring the transformation energy in the corresponding nuclear reactions or with the aid of a mass spectrograph.

Thus, any assumptions about an energetic inhomogeneity of nuclei of one kind must be recognized as entirely untenable.

After the failure of the first hypotheses put forward to solve the problem of β-decay, physicists found a number of other possible assumptions. These are various versions of the hypothesis of the emission of a pair of particles. The basic idea of this hypothesis is as follows: it is assumed that in β-decay the nucleus emits not only an electron, but also some other particle simultaneously with it. The total energy, obtained by the two particles, is the same for all decay events of nuclei of the given substance, but it is distributed differently between these two particles; this distribution is governed by the laws of statistics, and it is the cause of the fact that the electrons are energetically inhomogeneous, i.e. that a continuous β-spectrum occurs.

At first, two electrons were named as the pair of simultaneously emitted particles. However, such an assumption is clearly erroneous, since it is known from experiment that as a result of β-decay the positive charge of the nucleus increases by one unit (i.e. by one electron charge), and not by two units. Therefore a certain modification of this hypothesis was proposed: it was assumed that in a chain decay of the type α—β—β—α there is a definite correlation between the energies of the two β-particles emitted successively one after the other; if, for example, in the second link of the chain an electron with relatively small energy is emitted, then in the third link of the chain an electron with greater energy will be emitted, so that the sum of the energies for each pair of such successive β-decays is the same⁵. This hypothesis, obviously, could have only limited application—it does not give a general solution of the problem of the continuous β-spectrum, concerning only special cases of chain radioactive decay. However, in analyzing the experimental data it is easy to be convinced that in these cases as well it does not correspond to reality⁶.

Another proposal, also belonging to the very earliest attempts to interpret the energetic inhomogeneity of β-particles, consists in the assertion that, when a nucleus decays, a γ-quantum is emitted simultaneously with the electron⁷. A continuous spectrum of β-particles, of course, should correspond also to a continuous spectrum of γ-rays.

This hypothesis is easily refuted by experiment. First of all, a number of β-radioactive substances are known that do not emit γ-rays. A classic example of such substances has long been RaE. Its β-spectrum has also long been studied, and it is well known that it is just as continuous as in other cases of β-radioactivity. On the other hand, in those cases where β-decay is accompanied by the emission of γ-rays, it is well known that the spectrum of γ-quanta is not continuous: one or several γ-lines of strictly definite energy are always emitted.

One more hypothesis of the same type was proposed—the theory of β-decay developed in 1933 by Beck and Sitte⁸. It consists in—

that in $\beta$-decay the nucleus emits a pair of particles—an electron and a positron, the positron being in some way recaptured by the nucleus, so that as a result the charge of the nucleus increases by one unit. This theory can explain the energetic inhomogeneity of the $\beta$-electrons, but obviously gives no answer to the question why the energy of all the final nuclei remains the same, despite the capture of positrons of different energies. In this sense Beck and Sitte’s theory leaves the problem of $\beta$-decay altogether open.

Finally, one should mention one more attempt to solve this problem. It was made considerably later than the preceding ones—in 1937; however, so as not to return to the question of the various unsuccessful assumptions concerning $\beta$-decay, we shall speak of it here. Crane and others$^{9}$, as well as Jones$^{10}$, proposed that the energy received by the $\beta$-particle from the nucleus is the same for all $\beta$-particles of a given substance, but that the masses of these electrons (rest masses) are different, and correspondingly their kinetic energy is different: an electron with a larger mass has a smaller kinetic energy, and conversely. A careful analysis of the $\beta$-particles of RaE and other substances showed that this assumption is erroneous—there are no “heavy” $\beta$-electrons, the masses of all $\beta$-particles are the same, so that the inequality of their kinetic energies means also that the total energy acquired by them on leaving the nuclei is unequal.

So far we have not emphasized one circumstance. The phenomenon of $\beta$-decay appears unusual and incomprehensible only because we consider it from the standpoint of the law of conservation of energy, regarding this law as inviolable and valid in all phenomena of nature. In that case, in $\beta$-decay we do indeed encounter contradictory, enigmatic facts: nuclei with energy $A$ emit an electron and are transformed into nuclei with energy $B$, but the energy of the electrons is equal neither to the difference $(A-B)$ nor to any other constant quantity. Thus, what we know about $\beta$-decay indicates a violation here of the law of conservation of energy. Two points of view on this matter are possible, however: either there are aspects of the phenomenon of $\beta$-decay which we do not yet know, and only as a consequence of this do we state an apparent nonconservation of energy, or else this nonconservation of energy is a real fact, and we must acknowledge that we have encountered a phenomenon in which the law of conservation of energy does not operate. All the attempts described above to solve the problem of $\beta$-decay evidently proceeded from the first point of view and sought to describe the phenomenon in such a way that the law of conservation of energy would be restored to its rights. As we have seen, all these attempts were unsuccessful; this is what led Bohr, as early as 1930,$^{12}$ to point out that the second point of view is possible, namely, that the law of conservation of energy is in fact not obeyed in $\beta$-decay. It is hardly necessary to point out what fundamental significance for all of physics confirmation of this supposition would have. Experimental data, however, completely refute it.

A purely logical argument against the hypothesis of nonconservation of energy in $\beta$-decay is the experimentally established fact that the law of conservation of energy is obeyed in all nuclear phenomena,

in reactions both with light and with heavy particles, and $\beta$-decay would be the sole and inexplicable exception. There are also weighty theoretical considerations against this hypothesis. We shall not dwell on them here, and shall turn to objections of an experimental character.

The first of these arguments is the fact that there exists a quite definite upper limit of the $\beta$-spectrum. If energy is not conserved in $\beta$-decay, it is difficult to understand why $\beta$-particles with arbitrarily large energy are not observed.

Next, it is necessary to clarify what is meant by the assumption of nonconservation of energy in $\beta$-decay. Obviously it would be absurd to suppose that energy is not conserved at all in this process; this would imply macroscopic nonconservation of energy and the possibility of realizing “perpetual motion” by means of $\beta$-decay or of the processes inverse to it. Consequently, one can speak only of energy not being conserved in the elementary act of $\beta$-decay, but being conserved statistically, on the average, for a large number of $\beta$-decays. However, the assumption of statistical conservation of energy in $\beta$-decay is completely refuted by experimental data. Indeed, mathematically this assumption may be written in the form of the following equality:

\[ \Delta E = \overline{E} + mc^2, \]

where $\Delta E$ is the decay energy, i.e. the difference between the energies of the initial nucleus emitting the $\beta$-particle and the final nucleus (we assume $\Delta E=\mathrm{const.}$ for all nuclei of a given kind; only such an assumption corresponds to all experimental data and to quantum-mechanical concepts); $\overline{E}$ is the mean kinetic energy of the $\beta$-particle, and $mc^2$ is its rest energy. Thus, under the assumption of statistical conservation of energy, the measure of the decay energy must be the mean energy of the $\beta$-particles. Experiment, however, shows that the measure of the decay energy is not the mean but the maximum energy of the $\beta$-particles, i.e. the upper limit of the $\beta$-spectrum. Consider, for example, the data on the branched decay of ThC. The so-called thorium fork was studied in detail by Ellis and Mott in 1933–1934.^13 ThC is transformed into ThD by two routes: either through the formation of ThC$'$, or through the formation of ThC$''$. The complete scheme of transitions is very complicated, including many groups of $\alpha$-particles and $\gamma$-rays. The principal transitions may be represented as follows (the figures below the isotope name give its atomic number $Z$):

\[ \begin{array}{ccccc} & & \mathrm{ThC}'_{84} & & \\ & \nearrow_{\beta,\gamma} & & \searrow^{\alpha} & \\ \mathrm{ThC}_{83} & & & & \mathrm{ThD(Pb)}_{82} \\ & \searrow_{\alpha,\gamma} & & \nearrow_{\beta,\gamma} & \\ & & \mathrm{ThC}''_{81} & & \end{array} \]

The difference between the energies of the nuclei ThC and ThD is a certain constant quantity which can be calculated, knowing from experiment the energies of the $\beta$- and $\alpha$-particles in the corresponding transitions. Obviously, calculation along either of the branches—

via \( \mathrm{ThC}' \) or \( \mathrm{ThC}'' \)—must give one and the same value. Such equality of the values is indeed obtained if the upper limit of the \(\beta\)-spectrum is taken as the measure of the \(\beta\)-decay energy. The figures for each of the branches are as follows:

\[ \begin{aligned} \mathrm{ThC}\to \mathrm{ThC}' : E_{\max}(\beta) &= 2.25\ \mathrm{MeV} &\qquad \mathrm{ThC}\to \mathrm{ThC}'' : E_{\max}(\alpha) &= 6.2\ \mathrm{MeV} \\ \mathrm{ThC}'\to \mathrm{ThD} : E_{\max}(\alpha) &= 8.947\ \mathrm{MeV} &\qquad \mathrm{ThC}''\to \mathrm{ThD}^{*} : E_{\max}(\beta) &= 1.79\ \mathrm{MeV} \\ \cline{1-2} && \mathrm{ThD}^{*}\to \mathrm{ThD} : E(\gamma) &= 3.202\ \mathrm{MeV} \\ 11.197\ \mathrm{MeV} && \cline{3-4} 11.192\ \mathrm{MeV} \end{aligned} \]

If, however, one assumes that the difference of the nuclear energies before and after \(\beta\)-decay is determined by the mean energy of the \(\beta\)-particles, then the energy balance along the different branches of the thorium fork gives completely different values.

Another example is the production and decay of radioactive \(\mathrm{N}^{13}\). This isotope of nitrogen is formed when carbon is bombarded with protons in the reaction

\[ \mathrm{C}^{13}+p+Q=\mathrm{N}^{13}+n, \tag{1} \]

where \(Q\) is the energy that must be expended for such a reaction to take place. \(\mathrm{N}^{13}\) decays, emitting positrons, and thus is transformed into the original stable nucleus \(\mathrm{C}^{13}\). The value of \(Q\) can be calculated with very great accuracy by measuring the so-called threshold of the reaction, i.e. the smallest kinetic energy of the protons at which the indicated reaction still occurs. An excellently performed determination in 1940 by Haxby et al. of the threshold of this reaction gave for \(Q\) the value \(2.97 \pm 0.03\ \mathrm{MeV}\). Knowing \(Q\) and the mass difference of the proton and neutron (which, in energy units, amounts to \(0.730 \pm 0.056\ \mathrm{MeV}\)), one can, on the basis of equation (1), calculate the difference of the energies of the atoms \(\mathrm{N}^{13}\) and \(\mathrm{C}^{13}\), and thence also the difference of the energies of the nuclei \(\mathrm{N}^{13}\) and \(\mathrm{C}^{13}\). This difference is found to be \(1.71 \pm 0.04\ \mathrm{MeV}\). Such, therefore, is the energy that must be released in the transition \(\mathrm{N}^{13}\) and \(\mathrm{C}^{13}\). Subtracting from this \(mc^2\)—the rest energy of the positron—one readily establishes what the kinetic energy of the positrons emitted in this transition must be. The calculation gives the value \(1.20 \pm 0.04\ \mathrm{MeV}\). Experiment, however, shows that the upper limit of the positron spectrum of \(\mathrm{N}^{13}\) is equal to \(1.198 \pm 0.006\ \mathrm{MeV}\). The agreement, as we see, is excellent.

The examples cited are sufficient to convince us that it is not the mean but the maximum energy of the \(\beta\)-particles that is the measure of the decay energy. Thus, the assumption of a statistical character of the conservation of energy in \(\beta\)-decay must be rejected. Apparently, energy is conserved in each individual act of \(\beta\)-decay, while the observed nonconservation is only apparent, as a result of the incompleteness of our knowledge of the course of the phenomenon.

2. PAULI’S HYPOTHESIS OF THE NEUTRINO

We have seen how, on the basis of an ever-widening circle of experimental data, one after another all the numerous attempts to solve the problem of \(\beta\)-decay had to be rejected. The question of \(\beta\)-decay comes to such a state that there remains only a single possibility

of its solution; this possibility had been pointed out by Pauli as early as 1931, although at that time many of the experimental arguments cited above were not yet known with the same certainty as they are now.

Pauli, as many had done before him, assumed that \(\beta\)-decay is indeed a process in which not one particle—an electron—flies out of the nucleus, but two particles simultaneously. But as the partner of the electron Pauli postulates not a second electron, not a \(\gamma\)-quantum, but a new particle, not yet encountered in other phenomena, which he calls the neutrino1. One must recall that in 1931 physics knew only two elementary particles—the electron and the proton—in order to understand how bold and revolutionary at that time was the proposal that one more elementary particle exists.

As we have already said above, the assumption that in \(\beta\)-decay two particles are emitted simultaneously can fully explain the energetic non-uniformity of the \(\beta\)-electrons: the total decay energy, which is constant for nuclei of a given kind, is distributed between the two particles differently in each elementary act. The upper limit of the continuous \(\beta\)-spectrum acquires a clear physical meaning: in those cases where the fraction of energy received by the neutrino is practically zero, the nucleus emits the fastest electrons, whose energy is equal to the total decay energy.

What properties, then, must be ascribed to the neutrino so that, while assuming its participation in the act of \(\beta\)-decay, one does not fall into contradiction with the accumulated rich experimental material concerning this phenomenon? First of all, this new particle must have no charge—it must be electrically neutral (hence also its name; the name “ergon” was also proposed, but did not become widespread). The basis for this requirement is the firmly established fact that in \(\beta\)-decay the charge of the nucleus changes only by one unit, i.e. by the amount of charge carried away by the \(\beta\)-particle. Further, the mass of the neutrino must be small in comparison with the mass of the proton, since it is known that in \(\beta\)-decay the mass number of the nucleus does not change; the final nucleus is an isobar of the original one.

These two properties of the neutrino—the absence of charge and the smallness of its mass—make comprehensible both the fact that neutrinos have not been detected by ordinary means as part of radioactive radiation, and the results of calorimetric experiments. Particles of this kind pass unhindered through the walls of the calorimeter, and, consequently, the energy carried away by neutrinos cannot be taken into account by this instrument; therefore the observed thermal effect is connected only with the \(\beta\)-electrons and turns out to be equal to their mean energy.

In 1932 the neutron was discovered, and soon thereafter the only correct theory of nuclear structure came to be recognized as the theory according

in which all nuclei consist only of neutrons and protons, and there are no electrons in the nucleus. It follows directly from this that it is necessary to assume that β-particles are produced at the moment of β-decay of the nucleus. But there remains another difficulty in the question of β-decay, arising in connection with the proton-neutron scheme of nuclear structure. A firmly established empirical law states that nuclei with an even mass number possess an integral spin (i.e. the mechanical moment of momentum, or spin, of the nucleus

\[ i = 0, 1, 2 \ldots \text{ in units of } \frac{h}{2\pi}), \]

whereas nuclei with an odd mass number possess a half-integral spin \((i = 1/2, 3/2 \ldots)\). This law is quite understandable from the point of view of the indicated theory of nuclear structure and the vector model of nuclear spin, if one takes into account that the spin of the neutron, like the spin of the proton, is equal to one half, while the orbital moment of momentum of particles inside the nucleus is always expressed by an integer.

The law indicated was, of course, established for stable nuclei, but there are no grounds whatever not to extend it also to β-active nuclei. In β-decay the mass number does not change, so that if the initial nucleus had an even mass number, then the mass number of the final nucleus also remains even. Consequently, if the spin of the initial nucleus was an integer, then the spin of the final nucleus will also remain an integer. Meanwhile, the spin of the β-particle, i.e. of the electron, as is known, is equal to one half, and its orbital moment can be only an integer. Therefore in β-decay an integral nuclear spin would have to pass into a half-integral one and conversely. Thus, in β-decay there is an evident violation of the law of conservation of moments, and this nonconservation of spin “stands in almost as sharp a contradiction with firmly established laws of nature as would the nonconservation of energy” (Bethe).

The adoption of the hypothesis of the emission, simultaneously with the β-electron, of a second particle—the neutrino—completely removes this difficulty; for this it is sufficient to ascribe to the neutrino half-integral spin, i.e. to assume that the spin of the neutrino is equal to \(1/2\) or \(3/2\), etc. It is most rational to suppose that the neutrino, like all other elementary particles, possesses spin equal to one half.

Thus, consideration of nuclear spins, quite independently of the preceding considerations, also compels us to assume the existence of the neutrino. The functions assigned to the neutrino are broadened. This particle makes it possible to keep in force not only the law of conservation of energy, but also the law of conservation of moments. On the other hand, the list of properties that must be ascribed to the neutrino is supplemented: it is necessary to assume that this particle has a definite spin. By analogy with other elementary particles one might suppose that the neutrino also has a magnetic moment associated with the spin. However, nothing can be said in advance about this property of the neutrino; whether the neutrino has a magnetic moment or not—this must be decided by experiment.

Without going into details, let us point out one more phenomenon whose interpretation cannot do without the hypothesis of the existence of the neutrino. This is—

decay of the meson. Considerations analogous to those that arise in the question of β-decay compel one to suppose that the meson, in transforming into an electron, simultaneously emits a neutrino.

3. ATTEMPTS TO DETECT THE NEUTRINO EXPERIMENTALLY

There is no doubt that the assumption of the existence of a third elementary particle (in addition to the two known at that time—the electron and the proton) was a bold and ingenious conjecture. On a superficial consideration of the question it seemed not only implausible, but also logically defective: one cannot regard as satisfactory a method by which the solution of a problem is achieved by introducing an elusive and unobservable particle. Curious in this connection is the following remark by Ellis concerning the fact that Fermi’s theory of β-decay is based on accepting the neutrino hypothesis: “The neutrino in Fermi’s theory either may be a real particle, or else represents merely a convenient form of stating the discrepancy between theory and facts.”

Subsequently, however, a whole series of experimental data gave new evidence in favor of the neutrino hypothesis. Comparison of the energy balance in the branched decay of the thorium-fork type, or in the closed cycle of transformations \(C^{13} \to N^{13} \to C^{13}\), the question of conservation of spin in β-decay, and so forth—all this led to the point that essentially almost nothing hypothetical remained in the idea of the neutrino. With full justification it could already be regarded not as an assumption but as an assertion based on a large body of experimental data; no other possibility remained for interpreting the fact, already established beyond doubt, that in β-decay each time a quite definite energy is released, which very often is transferred only in part to the β-particle, while in such cases the remaining part goes to something else.

Nevertheless, the indicated evidence for the reality of the neutrino, for all its persuasiveness, is indirect, and the desire of physicists to prove the existence of the neutrino by a direct experiment is understandable. The difficulties of solving this problem are obvious from the very outset. In what way can one detect the neutrino—this uncharged particle with a very small mass? All existing methods and instruments for observing elementary particles—the Wilson chamber, the Geiger–Müller counter, the ionization chamber, the photographic plate—are in the final analysis based on the ionization produced in the surrounding medium by the electric charge carried by the particle.

A neutron, which has no charge, is much more difficult to detect than a charged particle, but it is still quite possible to do so thanks to the fact that the neutron, first, has a large mass and, second, interacts strongly with matter; as a result of this interaction fast charged particles arise: protons—in the elastic collision of neutrons or in the reaction of neutron absorption with emission of a proton (reactions of the \(n,p\) type), electrons or positrons—when β-active isotopes arise as a result of the capture of a neutron by a nucleus

(reactions of the type \(n,\ \gamma\) or the same reactions of the type \(n,\ p\)). There can be no question, in the case of the neutrino, of any such secondary effects that would help to detect the particle; a light uncharged particle passes through matter practically without interaction, as through empty space. The only kind of interaction of the neutrino with matter that can be predicted with certainty is the “inverse \(\beta\)-process,” i.e. capture of a neutrino by a nucleus with simultaneous emission of an electron or positron. However, the probability of such a process is negligibly small: as was shown by a calculation carried out by Bethe and Peierls\(^{15}\), a neutrino must travel on the average \(10^{16}\) km in a solid before it is captured by a nucleus.

There remains one further hypothetical possibility: it is possible that the neutrino possesses a magnetic moment, and in that case, by virtue of the interaction of this moment with the electron shells of atoms, a neutrino flying, for example, through a gas should ionize it; such an effect would make it possible to detect this particle.

The first experimental works aimed at finding the neutrino were precisely attempts to measure the ionization of a gas caused by the neutrino.

Chadwick and Lea\(^{16}\), in 1933, using an ionization chamber filled with nitrogen at a pressure of 75 atm, tried to find the ionization caused by the radiation of RaE (\(100\ mC\)) after absorption of all its \(\beta\)-particles in a layer of lead 58 mm thick. It turned out that under these conditions no more than two pairs of ions in \(1\ \text{cm}^3\) of gas per second could be ascribed to neutrinos, from which it followed that a neutrino produces less than one ion pair in 150 km of its path in gas at normal pressure. Nahmias\(^{17}\), in 1934, carried out similar experiments much more carefully. In order to reduce to a minimum the chamber background associated with cosmic radiation, the experiments were performed deep underground, in the London Underground. In addition, an extraordinarily strong radioactive preparation was used—5 g of radium. The radioactive radiations were filtered by a large quantity of lead—the thickness of its layer reaching 1 m. No additional ionization (above the background due to cosmic rays) that could be attributed to the ionizing action of neutrinos could be detected. As a calculation made by Bethe\(^{15}\) showed, the results of Nahmias’s experiments indicate that the ionizing power of the neutrino is no more than one ion approximately in 500,000 km of path in air. This means that if the neutrino has a magnetic moment, it is less than \(1/7000\) of the Bohr magneton. Most probably the neutrino has no magnetic moment at all.

This conclusion renders finally hopeless the attempts to detect the neutrino in the free state by means of the ionization it produces. One must state the following: unless some special properties of the neutrino are discovered, some special kind of interaction of the neutrino with matter, or unless entirely new methods are found for observing particles that carry no electric charge, there is no basis for expecting that it will be possible to detect the neutrino in the free state. But this means that at the present time no way is seen for a direct experimental proof of the existence

neutrino. In fact, how does a physicist understand the discovery of a new particle? In all cases, particles discovered up to now meant that some action produced by it could be detected not only at the place where its emergence is presumed, but also somewhere else, where this particle flies.

In the case of the neutrino, we repeat, this is still hopeless. One has to confine oneself to the narrower task of obtaining certain additional indirect proofs of the reality of the neutrino. Here the circumstances are more encouraging. Not having means for detecting the neutrino in its motion through matter, one may try to investigate the initial point of the neutrino trajectory, to find an effect connected with the departure of the neutrino from the nucleus. The thought of the experimenter turns first of all to the phenomenon of β-decay itself—to the act in which the birth of the neutrino is presumed. Is it not possible, for example, to extract some information about the neutrino by studying the shape of the β-spectrum, i.e. the form of the curve of distribution of β-particles by energies? Existing theories of β-decay, proceeding from the neutrino hypothesis (Fermi’s theory and its various modifications), predict different shapes of this curve near the upper limit of the spectrum, depending on whether the mass of the neutrino differs from zero or is exactly equal to zero. By comparing the experimental curves with the requirements of theory, it would be possible to draw conclusions concerning the mass of the neutrino. Unfortunately, their reliability is very small, since it is unknown to what degree these theories correctly reflect reality; not one of the variants of the theory of β-decay gives complete agreement with experiment with respect to the shape of the β-spectrum. In any case, it may be noted that the conclusions are as follows: the mass of the neutrino is possibly different from zero, but does not exceed \(1/5\) of the electron mass\(^{18}\) (this agrees with the much more reliable conclusion that can be made on the basis of an analysis of the energy balance in nuclear transformations and especially in the formation and decay of N\(^{13}\)). This case, already mentioned above, is remarkable in that in the detailed balance equation only one unknown remains—the mass of the neutrino; from the experimental data\(^{14}\) it follows that the neutrino mass is \(0.001 \pm 0.056\) MeV, i.e. does not exceed \(1/10\) of the electron mass.

Another aspect of the process of β-decay makes it possible to obtain much more convincing information about the neutrino. It is necessary to study the elementary process of β-decay, to investigate the so-called recoil of the nucleus. When a fast particle flies out of the nucleus, the nucleus receives a push in the opposite direction, acquires a certain velocity, and remains in motion until it dissipates the energy received by it in collisions with other particles. Such a moving nucleus (more precisely—atom or ion) is quite accessible to modern methods of observation, and thus there is the possibility of studying experimentally the properties of recoil nuclei. Of course, the very fact of the occurrence of recoil nuclei in β-decay as yet says nothing about the neutrino: even if the emission of an electron is not accompanied by the simultaneous emission of another particle, recoil nuclei must certainly be observed, since a fast electron flies out of the nucleus. However, the kinetic energy and the direction of motion of the recoil nuclei will depend on whether only an electron flies out of the nucleus

or a neutrino may also have flown out, and analysis of the corresponding experimental data on recoil nuclei in $\beta$-decay may lead to definite conclusions about the existence of the neutrino.

One may indicate three possible types of experiments for studying recoil in $\beta$-decay. Experiments of the first type should consist in measuring, for each act of $\beta$-decay, the momentum of the $\beta$-particle, the momentum of the recoil nucleus, and the angle between them, i.e., in establishing the complete vector diagram of the elementary act. Such experiments may provide decisive arguments on the question of accepting or rejecting the neutrino scheme of $\beta$-decay. The law of conservation of energy in the nucleus—$\beta$-particle system, as we have seen, is manifestly not obeyed. But what will be the situation in this system with respect to the conservation of momentum? If it turns out that the vector sum of the momentum of the recoil nucleus and the momentum of the $\beta$-particle is always equal to zero, this will mean the complete collapse of the hypothesis of neutrino emission in $\beta$-decay, since then it is obvious that only two particles—the nucleus and the electron, flying off in opposite directions—participate in the elementary act. If, however, it turns out that in a number of cases the indicated vector sum differs from zero, i.e., that the law of conservation of momentum in the nucleus—$\beta$-particle system is not obeyed, then, for testing the neutrino hypothesis, the question of how exactly this law is not obeyed becomes of the greatest importance. Is it in an arbitrary manner, or in such a way that the introduction of a third particle immediately restores it to its rights, leading to results in complete agreement with one another? Let us explain what has been said. In those cases when an appropriately performed experiment shows that the momentum of the recoil nucleus and the momentum of the $\beta$-particle do not constitute two equal and oppositely directed vectors, we can, assuming the participation of a third particle in the act of $\beta$-emission, determine precisely its momentum $p$ (since the vector sum of all three momenta must be equal to zero). On the other hand, knowing the energy of the given $\beta$-particle and the value of the upper limit of the $\beta$-spectrum, we determine, from the difference of these two quantities, the neutrino energy $E$. If it now turns out that the values of $p$ and $E$ found in this way satisfy the relativistic relation between the momentum and the kinetic energy of one particle:

\[ (E+\mu c^2)^2=p^2c^2+\mu^2c^4, \]

where $\mu$ is the mass of this particle, and if this relation proves to be valid for all observed recoil cases at one and the same value of $\mu$, then this will be an extremely convincing testimony in favor of the hypothesis of the existence of the neutrino. At the same time these experiments would also give a direct determination of the neutrino mass and the distribution of the angles of emission of the neutrino and the electron. The latter would represent very valuable experimental material for choosing between different variants of the theory of $\beta$-decay, since different variants predict different distributions of the emission angles2.

The realization of such experiments is, however, connected with great difficulties. The Wilson chamber method is unsuitable, since the tracks of recoil nuclei cannot be observed; the energy of the latter is too small (up to $50$—

100 eV), their range even in the rarefied gas in a Wilson chamber is very small, so that the tracks of recoil nuclei have a length of small fractions of a millimeter.

Another method may be proposed for obtaining a vector diagram of an elementary act of β-decay (we shall say a few words about it below), but so far experiments of this kind have not been carried out, and thus measurements of the first type have not yet been realized.

Less complete, but nevertheless still sufficiently convincing, may be experiments of the second type. One may confine oneself to measuring the kinetic energy of the recoil nuclei, without considering the question of the direction of their motion. By comparing, for a number of individual acts of β-decay, the value of the energy of the recoil nucleus with the value of the momentum of the corresponding β-particle, one can establish whether it is necessary to assume the participation of a third particle in order that both the law of conservation of energy and the law of conservation of momentum be satisfied, or whether this second law is satisfied even without the neutrino hypothesis. Attempts at investigations of this kind have been undertaken, but, for reasons which we shall set forth later, they have not led to any substantial results.

Finally, experiments of the third type, the least complete, giving only the most indirect evidence of the reality of the neutrino, consist in obtaining the distribution of recoil nuclei with respect to energies. Here, therefore, the experimenter completely departs from the study of the elementary act of β-decay, confining himself only to establishing the general statistical characteristic of the aggregate of recoil nuclei.

It is precisely to this type of experiment that the first work on the investigation of recoil in β-decay, connected with the question of the existence of the neutrino, belongs; it was carried out by A. I. Leipunskii \(^{20}\) in 1936. This work has rather the character of a preliminary experiment than of a thorough investigation; blunders were allowed in the experiment, and the result obtained was clearly erroneous. Nevertheless, thanks to the ingenious use of the ideas employed in it, it has fundamental significance and in many respects is the prototype of subsequent works of this kind. We shall therefore briefly describe it. A metallic surface \(B\) (Fig. 2), cooled by liquid air, adsorbs molecules of carbon dioxide, some of which contain the radioactive isotope of carbon \(C^{11}\). This isotope is obtained in the reaction

\[ B^{10} + d = C^{11} + n \]

or, in abbreviated notation, \(B^{10}(d, n)C^{11}\); it is positron-active, the maximum energy of the positrons being equal to 0.95 MeV. The choice of the radioactive substance for the investigation is very important. If one were to use a natural radioactive substance—and such are elements with very large atomic weights—then the energy of the recoil nucleus would be extremely small. It is determined by the following formula, which is easily obtained from the laws

Fig. 2. Diagram of Leipunskii’s experiment.

\(A\)—liquid air, \(B\)—radioactive source, \(C\)—grid, \(D\)—secondary electron emitter, \(E\)—Geiger counter.

conservation of energy and momentum:

\[ E_{r(\max)}=\frac{540E_0}{A}(E_0+1)\ \mathrm{eV}, \]

where \(E_0\) is the upper limit of the \(\beta\)-spectrum in MeV, \(A\) is the atomic weight. It is easy to calculate that, at ordinary energies of \(\beta\)-particles, in the case of large \(A\) the energy of the recoil nuclei is of the order of \(1\ \mathrm{eV}\), i.e., quite comparable with the energy of adsorption of atoms on the surface of a solid. Therefore the energy distribution of ions torn from such a surface as a result of recoil would be completely distorted and would by no means reflect the distribution of the recoil energy. In order to avoid this difficulty, one must deal with a light atom; at small values of the atomic weight \(A\) the energy of the recoil nucleus may reach values tens of times larger. Consequently, it is necessary to take for investigation an artificial \(\beta\)-active substance, choosing an element with a small atomic weight. This was done in Leipunsky’s work.

A variable negative potential is applied to the metallic surface \(B\), which, owing to strong cooling, retains on itself an approximately monomolecular layer of carbon dioxide. The grid \(C\) is at zero potential, the cathode \(D\) at a negative potential of \(5\ \mathrm{kV}\). The entire electrode system is, of course, in a vacuum chamber, since the energy of the recoil ions is nevertheless so small that in air at atmospheric pressure their range would be negligibly small.

By varying the retarding electric field between the grid \(C\) and the source \(B\), it is possible to allow through the grid only those positive recoil ions flying from the surface \(B\) whose energy exceeds some assigned value. If it is possible to measure the number of ions that have passed through the grid, then in this way, evidently, one can obtain the integral curve of the energy distribution of the recoil ions. The number of ions that have penetrated into the space between \(C\) and \(D\) is counted in the following manner: ions accelerated by a potential of \(5\ \mathrm{kV}\), applied to the cathode \(D\), upon striking the surface of the latter knock secondary electrons out of it; these electrons are accelerated by the electric field applied between the cathode and the counter \(E\), enter the counter and are recorded by it (the counter is of the needle type, with a very thin window). Thus the counting intensity of secondary electrons gives a measure of the intensity of the flux of positive ions of a definite energy leaving the surface \(B\).

What experimental results could speak in favor of the neutrino hypothesis? One can draw the curve of the distribution of recoil nuclei by energies for the case in which the recoil were caused only by the emission of \(\beta\)-particles from the nucleus. In this case the form of the distribution curve is entirely determined by the form of the \(\beta\)-spectrum: from the energy distribution of the \(\beta\)-particles it is easy to calculate for them the distribution curve by momenta; this same curve also gives the distribution by momenta for the recoil nuclei, since, under the initial assumption that the recoil of the nucleus is connected only with the emission of a \(\beta\)-particle, the momentum of the recoil nucleus must be equal (in absolute value) to the momentum of the \(\beta\)-particle. Finally, from the distribution

of impulses of the recoil nucleus one can again pass to their energy distribution, and thence to the expected curve of the number of counts of the counter registering the recoil ions, as a function of the retarding potential. If, in addition to the β-particle, the nucleus in β-decay simultaneously emits also a neutrino, this should be reflected in the fact that there will be almost no slow recoil nuclei, since at a small velocity of the β-particle the neutrino, on the contrary, must have a relatively large momentum, and because of this the recoil of the nucleus will not be small1. Consequently, if a third particle participates in the act of β-decay, the experimental curve of the number of recoil nuclei as a function of the retarding potential should, on the whole, pass above the theoretical curve calculated in the manner indicated.

Of course, as we have already said above, the data on the neutrino that can be obtained in experiments of this kind are very scanty and indirect. As for the results obtained directly in this work, they are, in general, erroneous, and no conclusions can be drawn on their basis. From the author’s experimental points it follows that the energy of the recoil nuclei in the β-decay of \(C^{11}\) reaches \(250\ \mathrm{eV}\) and more. Meanwhile, using the formula given above, it is easy to see that the maximum energy of the recoil nuclei in this case cannot be more than \(91\ \mathrm{eV}\). This discrepancy is in all probability connected with an error in the measurements of the retarding field; the true retarding field between \(B\) and \(C\), because of the “sagging” (through the cells of grid \(C\)) of the large field existing between \(C\) and \(D\), has a much smaller magnitude than follows from the potential difference imposed between \(B\) and \(C\).

The next attempt to investigate recoil in β-decay with the aim of testing the neutrino hypothesis was carried out in 1938 by Crane and Halpern[^21]. The authors set as their aim to measure, for each individual act of β-decay, the kinetic energy of the recoil nucleus and the momentum of the β-particle. Thus, according to the classification given above, this work belongs to the second type of investigation of recoil in β-decay.

How, on the basis of results of experiments of this type, can one judge the validity of the neutrino scheme of β-decay? The curve representing the dependence of the kinetic energy of the recoil nucleus on the momentum of the β-particle emitted by the nucleus can be calculated theoretically, if one starts from the law of conservation of momentum and adopts one or another assumption concerning the number and mutual motion of the particles emitted from the nucleus in β-decay. In Fig. 3 three theoretical curves of this dependence are shown. The first curve \(a\) corresponds to the assumption that the neutrino does not exist and that in β-decay only an electron is emitted from the nucleus; this means, by virtue of the law of conservation of momentum, that the momentum of the recoil nucleus must be equal (in magnitude) to the momentum of the β-particle.

\[ p = E/c. \]

The second curve \(b\) corresponds to the following assumptions: 1) in \(\beta\)-decay the nucleus emits an electron and a neutrino simultaneously; 2) these two particles always fly out of the nucleus in one and the same direction. Finally, the third curve \(c\) refers to the assumption that the nucleus emits an electron and a neutrino simultaneously, but these two particles always fly out of the nucleus in opposite directions (all three curves are calculated for the case in which the maximum momentum of the \(\beta\)-particle is \(p_{\max}=11\) in units \(mc\); this corresponds to the upper limit of the \(\beta\)-spectrum \(E_{\max}(\beta)\simeq 5 \text{ MeV}\)).

Fig. 3. Kinetic energy of the recoil nucleus as a function of the momentum of the \(\beta\)-particle

In reality, any angles between the directions of emission of the neutrino and the \(\beta\)-particle are possible, differing for different acts of \(\beta\)-decay. The statistical distribution of the angles of divergence of these two particles can be calculated theoretically, and its form will depend on the variant of the theory of \(\beta\)-decay adopted in the calculation2. In any case one may assert that, if statistically all angles of divergence occur, from 0 to \(180^\circ\), then the experimental points in experiments of the indicated type should not lie on a smooth curve of the form \(b\) or \(c\), but will fall in the region of the drawing between the curves \(b\) and \(c\). Thus, two results of the experiments are possible: either the experimental points form a smooth curve of type \(a\)—and then the hypothesis of neutrino emission in \(\beta\)-decay must be rejected—or these points will fill the region between the curves \(b\) and \(c\). If, in the left part of the diagram, i.e. at small momenta of the \(\beta\)-particles, all the points obtained lie above curve \(a\), then this means that the momentum acquired by the nucleus at the moment of \(\beta\)-decay is, as a rule, much greater than the momentum that the nucleus could receive from the \(\beta\)-particle alone, and such a result would be an undoubted indication that in \(\beta\)-decay some other particle also flies out of the nucleus in addition to the electron.

Crane and Halpern, in their work, used the following method. A gaseous compound of radiochlorine \(\mathrm{Cl}^{38}\) is introduced into a Wilson chamber. This artificially radioactive isotope of chlorine emits \(\beta\)-particles with a maximum energy of about \(5 \text{ MeV}\); its half-life is 37 min. Under the normal operating regime of the chamber, only the tracks of the chlorine \(\beta\)-particles can be observed in it. If, however, the electric field in the chamber, which is switched on to clear its volume, is switched on approximately 0.5 sec before the moment of expansion, then at the initial point of each \(\beta\)-track there appears a more or less dense spherical cloud of fog droplets. The authors believe that its appearance is connected with recoil nuclei. The range of the recoil nucleus in the atmosphere of the chamber is extremely small, and therefore the track of the recoil nucleus cannot be seen under the ordinary operating regime of the chamber. If, however, the regime is modified as indicated, then, in the opinion of Crane and Halpern, the ions formed by the recoil nucleus diffuse from the point of their origin in all directions and, because of this, at the corresponding point

a cloud of droplets appears. By determining with a microscope the number of droplets, the authors estimate from this quantity the kinetic energy of the recoil nucleus (taking this energy, in a first approximation, to be proportional to the number of droplets), and from the curvature of the β-track emerging from the same point they determine the momentum of the β-particle. Obviously, the method of determining the energy of the recoil nuclei is an extremely doubtful element of these experiments. It should be emphasized that, in order to obtain the desired conclusions from the experiment, there is no need to know the absolute value of the energy of the recoil nuclei—it is sufficient to be able to measure it in an arbitrary relative measure. However, even such data apparently cannot be obtained by the method of Crane and Halpern. One cannot agree with their interpretation of the mechanism by which fog droplets arise in their experiments. It is known that slow ions practically do not ionize a gas, expending their energy on elastic collisions with atoms as a whole, and not on tearing electrons away from them. In their second paper\(^{22}\), Crane and Halpern showed that the formation of fog droplets by the recoil nucleus is partly associated with dissociation of gas molecules. It is also possible that the appearance of these droplets is connected with Auger processes, by means of which the orbital electrons of gas atoms excited by collisions with the recoil nucleus return to the normal state. In any case, the question of the connection between the number of fog droplets in the experiments of Crane and Halpern and the magnitude of the kinetic energy of the recoil nucleus remains open, and therefore the arrangement of the experimental points obtained by them cannot in any degree be regarded as reliable.

Let us note that if, in experiments of this type, it were possible to determine the absolute value of the kinetic energy of the recoil nuclei, then by means of a simple calculation one could find also the distribution of the angles at which the β-particle and the neutrino fly apart in the β-decay of the given substance.

In summary, we may say that the few works on the study of recoil in β-decay connected with the question of the existence of the neutrino have encountered considerable experimental difficulties and in fact have yielded no results. Undoubtedly, valuable conclusions could be obtained in experiments of the first type, i.e. those which would give the complete vector diagram of the elementary act of β-decay. The best arrangement of such an experiment would probably be the use of a beam of β-active atoms in vacuum and two groups of counters capable of registering the simultaneous motion of the electron and the recoil nucleus in prescribed directions. The difficulties of such experiments are obvious, and so far they have not been carried out.

In nuclear physics, however, comparatively recently (in 1938) a phenomenon was discovered which gives the experimenter far greater convenience for studying recoil nuclei and for drawing conclusions about the existence of the neutrino than does the phenomenon of β-decay. This is the so-called \(K\)-capture, one of the types of radioactive decay, which takes place in the following manner: an unstable atomic nucleus captures an orbital electron from the \(K\)-shell of the electronic envelope surrounding this nucleus and, in this way, is transformed into a nucleus with atomic number smaller by one ...

… earlier3. Analysis of this phenomenon immediately leads to the necessity of assuming, as in the case of β-decay, the participation of the neutrino, namely the emission of a neutrino by the nucleus at the moment of capture of the \(K\)-electron. This is required, as before, by both the law of conservation of energy and the law of conservation of angular momentum (spin). The neutrino, in the form of its kinetic energy, carries away that difference of energies which is liberated in such a process of radioactive transformation of the nucleus. If one were to abandon the idea of neutrino emission, one would have to assume the traceless disappearance of this energy.

The essential difference between the neutrinos emitted in \(K\)-capture and the neutrinos emitted in β-decay lies in their complete energetic homogeneity: in \(K\)-capture the decay energy is not distributed between two particles; the only particle flying out of the nucleus is the neutrino, and in every event it receives one and the same energy—the full decay energy.

It is evident that if nuclei in \(K\)-decay really emit neutrinos, then in each such decay a recoil nucleus must arise, and the kinetic energies of all recoil nuclei of a given \(K\)-active substance must likewise be the same.

The scheme of a study of recoil aimed at testing the neutrino hypothesis in \(K\)-decay is considerably simpler than in β-decay. Capturing a \(K\)-electron, the nucleus emits no other particles except the neutrino. Therefore, if an experiment shows that recoil nuclei are observed in \(K\)-decay, then this fact by itself, in contrast to the situation in β-decay, is clear evidence that neutrinos fly out of the nucleus. However, of course, such evidence acquires full force only after a quantitative investigation. The latter is comparatively not difficult.

It is sufficient to measure the kinetic energy of the recoil nucleus in order, on the basis of the law of conservation of momenta—that is, taking the momentum of the recoil nucleus to be equal to the momentum of the neutrino—to calculate the energy of the neutrino. On the other hand, the latter can be calculated—on the basis of the law of conservation of energy—from the experimental data on the energy liberated in the radioactive transformation of the given \(K\)-active nucleus. If these two entirely independent methods give one and the same figure, this may be regarded as experimental proof, to the highest degree convincing, of the existence of the neutrino.

The idea of using the phenomenon of \(K\)-capture for the investigation of phenomena connected with the question of the reality of the neutrino was first proposed by A. I. Alikhanov and A. I. Alikhanyan at the end of 1938, very soon after the possibility of radioactive transformations by means of \(K\)-capture had been finally proved experimentally. Alikhanov and Alikhanyan proposed in their experiments to use \(K\)-active \(\mathrm{Be}^7\), about whose properties a detailed investigation had just been published by that time4. This substance, by virtue of a number of features, is indeed extremely suitable for experiments of this kind. First of all, because its atomic weight is very small, recoil nuclei possessing a considerable kinetic energy should be obtained. Further

Unlike many other $K$-active substances, in $\mathrm{Be}^7$ $K$-capture occurs in pure form—it is not accompanied by a parallel positron or electron decay. Therefore all secondary phenomena are absent, for example, electron recoil. Finally, $\mathrm{Be}^7$ has a rather long half-life—it is equal to 43 days, which is a considerable convenience in measurements.

The radioactive decay of $\mathrm{Be}^7$ manifests itself only in the emission of $\gamma$-quanta with an energy of 485 keV ^25. It is known that these $\gamma$-quanta are emitted only in approximately 10% of all acts of $K$-decay of $\mathrm{Be}^7$ and correspond to those cases when, as a result of $K$-capture, the final nucleus, i.e. the $\mathrm{Li}^7$ nucleus, is formed in an excited state ^24. In the remaining 90% of all decays the transition occurs to the ground level of $\mathrm{Li}^7$, and in this case no radiation is emitted by the $\mathrm{Be}^7$ nucleus during decay, apart from the presumed emission of a neutrino. Let us note that the emission of $\gamma$-rays in some of the decays of $\mathrm{Be}^7$ is a very fortunate circumstance: without it, it is unlikely that by the present time it would have been discovered that in certain nuclear reactions $\mathrm{Be}^7$ is formed, undergoing $K$-decay. The characteristic X-rays, whose emission is usually the only comparatively easily observable external effect in $K$-capture, in the case of beryllium consist of such soft quanta (the energy of the characteristic $K$-quanta of lithium is less than 100 eV) that it is almost impossible to detect them; moreover, for lithium the fluorescence yield is extremely small, and the emission of X-ray quanta is almost completely replaced by the emission of Auger electrons, likewise very soft ($E \sim 50 \text{ eV}$) and difficult to observe.

On the basis of data on the corresponding nuclear reactions, the difference of the intrinsic energies (masses) of the atoms $\mathrm{Be}^7$ and $\mathrm{Li}^7$ is known. It amounts to about 1 MeV (more accurate data were later obtained; we shall indicate them below). Such, consequently, is the presumed kinetic energy of the neutrinos emitted in the $K$-decay of $\mathrm{Be}^7$. From this it is easy to calculate that the kinetic energy of the recoil nuclei should amount to only about 80 eV. Therefore, measurements with them must be carried out under vacuum conditions.

Alikhanov and Alikhanyan proposed determining the energy of the recoil ions by means of the retarding-field method, as had also been done in Leipunsky’s work. The scheme of the experiment is as follows. $\mathrm{Be}^7$ is deposited in an extremely thin layer on a metal plate. As a result of radioactive $K$-decay, beryllium is transformed into lithium. The lithium nuclei, owing to the momentum acquired when the neutrino is emitted, must tear themselves away from the surface of the metal, which they leave in the form of ions. Some of these recoil ions, overcoming the retarding field, pass through a mesh electrode, after which they are accelerated by a potential difference of $\sim 6 \text{ kV}$ and strike a metal plate coated with beryllium oxide; the latter, under the impacts of the ions, emits secondary electrons, which are counted by a Geiger–Müller counter. In order to increase the effective area of the secondary emitter from which electrons can still enter the counter, focusing of the electrons by means of an appropriate transverse magnetic field was provided.

The main difficulty encountered in the work begun by Alikhanov and Alikhanyan in 1940 consisted in the difficulty of obtaining a sufficiently thin and at the same time very intense preparation of Be\(^7\). The work was interrupted in June 1941.

Some experimental work devoted to the investigation of the recoil of nuclei in \(K\)-capture was carried out by Alvarez et al.\(^{26}\) in 1941. It had the character of preliminary experiments. It was shown that a transfer of ions takes place from the surface of a radioactive source to another surface located nearby. Since, however, the energy of the ions was not measured, it could not be asserted that the cause of the transfer was the emission of a neutrino by the nucleus in \(K\)-capture and the associated recoil of the nucleus. Other causes may also be assumed, for example, a change in the binding force of the atom with the surface of the metallic backing occurring at the moment of \(K\)-decay. Thus, with respect to solving the problem of the reality of the neutrino, these works yielded nothing essential.

The first detailed and successful investigation of recoil nuclei arising in \(K\)-decay was carried out in 1942 by the American physicist James Allen\(^{27}\). For the first time, the results of the experiment gave an undoubtedly positive answer to the question of the existence of the neutrino. We shall now turn to an account of this work.

4. ALLEN’S WORK. PROOF OF THE EXISTENCE OF THE NEUTRINO

As the initial \(K\)-active substance Allen likewise chose Be\(^7\). The measurement of the kinetic energy of the recoil nuclei was again carried out by means of the retarding-field method. In Fig. 4 Allen’s apparatus is shown schematically. Between the radioactive source and the ion counter there are two copper grids, one of which—the grid \(B\)—is insulated from the body and has a separate lead, whereas the other is in contact with the body and, together with the latter, is grounded. Positively charged recoil ions, breaking away from the surface of the source, first enter the accelerating electric field, which is produced by applying to grid \(B\) a potential \(U\) (100–200 V), negative with respect to the source \(A\). Ions which have passed through the first grid enter the retarding field produced by applying to grid \(C\) a certain variable potential, positive with respect to \(B\) and equal to \(U+\Delta U\). As long as the energy of the ions is greater than that required to overcome the retarding potential difference \(\Delta U\), some fraction of the ions passes through grid \(C\), again enters the accelerating field created between it and the ion counter, and is recorded by the counter. By taking the curve of the dependence of the number of ions reaching the counter on the magnitude of the retarding potential, it is easy to determine the maximum energy of the recoil ions. A typical curve of this kind,

Fig. 4. Schematic of Allen’s experiment.

\(A\) — radioactive source, \(B\) and \(C\) — grids, \(D\) — receiving electrode of the ion counter, \(E\) — tube to the vacuum pump.

obtained by Allen, is shown in Fig. 5. From this curve it is evident that the maximum energy of the recoil ions is about 50 eV. At first glance it may seem that the form of the curve contradicts what we said above, namely, that in \(K\)-capture all recoil nuclei should have one and the same energy, in accordance with the monochromaticity of the neutrino. The form of the curve shown in Fig. 5 indicates that the recoil nuclei have various energies from zero to a maximum energy equal to approximately 50 eV. However, the contradiction here is only apparent. The recoil nuclei are indeed homogeneous in energy, but they differ in that the normal component of their velocity is different, since the recoil ions leave the surface of the source at different angles to the normal. If, in order to retard an ion flying directly along the normal, it is necessary to apply a certain electric field, then ions flying at an angle to the normal will be retarded by fields of smaller magnitude. Thus, the form of the curve obtained is determined by the very nature of that variant of the retarding-field method which is used in the present case. In addition, some of the ions are slowed down by gas molecules adhering to the surface of the source, which also affects the shape of the curve, since it leads to the appearance of ions that do not possess the full amount of recoil energy1.

Fig. 5. Number of ion-counter counts (per 1 min.) as a function of the magnitude of the retarding potential. The dashed line is the spontaneous counts of the counter.

The figure for the maximum energy of the recoil ions obtained by Allen is sufficiently high to allow one at once to reject the supposition of any secondary causes for the tearing off of ions from the surface of the source. It agrees well with the calculated value corresponding to the hypothesis of neutrino emission in the \(K\)-decay of \(\mathrm{Be}^7\), and the conclusion appears fully justified that the ions counted by the counter are torn from the surface of the source in fact as a result of the recoil arising upon neutrino emission. We shall say further below what measurements Allen made in order to obtain as accurate a value as possible for the energy of the recoil nuclei. For the moment we shall dwell on some details of Allen’s experiments.

We have already indicated that the energy of recoil nuclei is comparatively very small, and that recoil nuclei therefore have an insignificant range in matter and an insignificant penetrating power. Hence it is clear that a very essential requirement for the radioactive source in experiments of this kind is that its surface should contain no extraneous substances, so that the recoil nuclei should not be covered over by anything from above and could freely break away from the surface of the metallic backing, overcoming only the adsorption forces holding them on this surface. Ideally, one should strive to obtain a monatomic layer of the radioactive substance on the surface of the backing. Further, the choice of the backing material plays a by no means unimportant role. It is essential that the recoil atoms leave the surface of the source precisely in the form most convenient for subsequent measurements: in the form of positively charged ions with unit charge.

The success of Allen’s experiments is to a considerable extent due to the fact that he succeeded in obtaining a sufficiently thin layer of Be⁷ on a metal (although, as we shall see, his source was still far from ideal). He used platinum as the backing. The lithium atoms formed from beryllium atoms as a result of the latter’s K-capture, breaking away from the platinum surface as a result of recoil, are thereby ionized and leave it in the form of positive ions. This occurs because the work function of an electron from platinum is greater than the first ionization potential of lithium. Therefore the electron “common” to the platinum atom and to the lithium atom adhering to it remains on the platinum when the lithium is torn away from it.

The procedure for obtaining a thin-layer Be⁷ source is essentially as follows. Lithium fluoride is irradiated with deuterons in a cyclotron. As a result of the reaction Li⁶ \((d, n)\), K-active Be⁷ is formed. The activated salt is fused onto a platinum ribbon and then evaporated in vacuum at a temperature of \(800^\circ\)C. In this process all inactive material is removed, whereas almost all the radioactive beryllium remains on the platinum and within the platinum, where it enters by diffusion. After this the platinum ribbon is subjected to brief, intense heating by passing through it so large a current that it melts in the center. As a result, a sufficient surface concentration of radioactive Be⁷ atoms is obtained on the platinum. A piece of such a ribbon is welded to a strip of tantalum, and this entire radioactive source is mounted in a vacuum chamber between two clamps through which current can be passed.

The second experimental detail on which it is necessary to dwell is the ion counter. The problem of counting comparatively very slow ions is far from simple. In Leipunsky’s work it was solved with the aid of the effect of secondary-electron emission: recoil ions, accelerated by an electric field, struck a metallic surface and knocked secondary electrons out of it, which were then counted by a Geiger counter. A similar method, but in a much more refined form, was also used by Allen. As the ion counter, the latter uses a secondary-electron multiplier tube, developed

designed by him in 1939 and improved (by him) in 1941. In the tube there is purely electrostatic focusing of the secondary electrons; the tube contains 11 electrodes coated with beryllium oxide, and gives an overall multiplication factor of \(\sim 18\,000\). The great advantages of Allen’s multiplier are: 1) a very small number of spontaneous counts (low background); 2) the possibility of attaching it directly to a vacuum apparatus without any window, which is especially important when working with slow ions; 3) the possibility of admitting air into the apparatus without any harm to the tube electrodes. The multiplier is connected to a valve amplifier, at the output of which there is an electromagnetic counter registering the number of pulses. Specially performed experiments showed that this entire counting device counts practically every ion that reaches the first electrode of the multiplying tube.

It is interesting that Allen at first obtained a negative result: the ion counter gave no counts even at zero value of the retarding potential, which testified to the fact that no ions were being torn off from the surface of the source. However, it was sufficient to heat the source for several minutes to \(1\,000^\circ\mathrm{C}\), by passing a current through the tantalum strip (and then to cool it to room temperature), for an intense counting of ions to begin. Immediately after such temperature treatment of the source Allen obtained up to \(5\,000\) counts per minute. With time the intensity of the ion count decreased appreciably; its decrease proceeded approximately according to a linear law, and the initial intensity fell by half in 40 min. Repeated heating of the source returned everything to the initial state—the number of recoil ions increased to its former value. These effects receive a completely natural and plausible explanation: the surface of the source, despite the high vacuum in the apparatus (maintained by a three-stage oil diffusion pump), gradually becomes contaminated by adhering gas molecules, which in the end form a layer impenetrable to recoil ions. Heating the tantalum strip degasses the surface of the source, and then the recoil ions freely leave it. This kind of locking-in of ions by a gas layer once again shows how clean the experimental conditions here must be in order to obtain a positive result.

By means of control experiments Allen showed that the true value of the retarding potential is somewhat smaller than the actually applied potential difference between the grids \(B\) and \(C\), evidently on account of the so-called “sagging” of the strong electric field (acting between \(C\) and the ion counter) through the cells of grid \(C\). If, in the data obtained from the curve of Fig. 5, a correction is introduced for field penetration, it is found that the maximum energy of the recoil ions is approximately \(42\ \mathrm{eV}\). This may be regarded as quite satisfactory agreement with the value \(58\ \mathrm{eV}\), which is obtained by calculation for the tritium atom, if one assumes that the neutrino energy in the \(K\)-decay of \(\mathrm{Be}^7\) is \(870\ \mathrm{keV}\), and the neutrino rest mass is zero. The indicated figure—\(870\ \mathrm{keV}\)—was obtained in 1940\({}^{14}\) with great accuracy by means of

determination of the threshold of the reaction \(Li^7(p,n)Be^7\). These measurements showed that the difference of the proper energies (masses) of the atoms \(Be^7\) and \(Li^7\) is \(0.87 \pm 0.03\) MeV; consequently, such should be the kinetic energy of the neutrino emitted at the moment of the transformation of \(Be^7\) into \(Li^7\).

If one takes the rest mass of the neutrino to be not zero, but \(0.2m\) (where \(m\) is the electron mass), the calculation gives, for the recoil energy of the lithium ion, the figure 57 eV. This shows that it would have been necessary to measure the maximum energy of the recoil ions with very great accuracy in order to make it possible, on the basis of these data, to judge the mass of the neutrino. Allen’s results show that further refinement of the measurements is not easy and requires substantial improvement of the method. The discrepancy of his data with the theoretically expected value, although it has no fundamental significance and does not diminish the value of the results obtained, reaches, as we have seen, 15–16 eV. The reason for this discrepancy, as Allen believes, lies partly in the fact that the lithium ions expend some energy in overcoming the adsorption forces holding them on the surface of the platinum, and partly in the fact that, apparently, on heating the source its surface is still not completely degassed, so that the ions are somewhat slowed down by adsorbed molecules of air. To this it must be added that if one carefully analyzes the possible trajectories of the recoil ions for the electric fields and the experimental geometry that occur in Allen’s apparatus, it becomes evident that the limiting value of the energy of the ions entering the counter cannot be determined with great accuracy. This is confirmed by the character of the curve shown in Fig. 5: it does not pass sharply into a line parallel to the axis of abscissas; on the contrary, this transition is very smooth.

Let us point out in conclusion that Allen carried out one more control experiment with the aim of proving that the recoil ions registered by the counter cannot be interpreted as recoil ions from \(\gamma\)-quanta emitted in the \(K\)-decay of \(Be^7\). As we have already mentioned above, these \(\gamma\)-quanta are emitted in only approximately \(10\%\) of all acts of \(Be^7\) decay and have an energy of 485 keV. As is easy to calculate, the recoil energy which such a \(\gamma\)-quantum, at the moment of emission, imparts to the lithium atom amounts to only 18.1 eV. Since the maximum energy of the recoil ions measured in the experiment is almost three times greater than this value, the carrying out of the indicated control experiments may in essence be considered unnecessary rigor. The experiments consisted in an attempt to establish coincidences in time between the emission of the \(\gamma\)-quantum and the appearance of the recoil nucleus. For this purpose, near the source, outside the vacuum chamber, a Geiger–Müller counter was placed, which counted the \(\gamma\)-rays of beryllium, and, by means of well-known radio-engineering methods, coincidences in time were recorded between pulses in this counter and pulses in the ion counter. The result obtained was completely negative—no coincidences of this kind are observed.

We may summarize the results obtained by Allen as follows.

1. In setting as his goal to give, albeit not direct, but at the present time apparently the only possible experimental proof of the existence of the neutrino, Allen devised an experiment whose idea is extremely simple and clear.

of the existence of the neutrino, Allen investigates the phenomenon of nuclear recoil, which must occur in \(K\)-decay if the latter is accompanied by the emission of a neutrino. For this purpose he takes radioactive \(\mathrm{Be}^7\), which decays, emitting only \(\gamma\)-rays and emitting neither electrons nor positrons. A series of data obtained by many investigators convincingly indicates that \(\mathrm{Be}^7\) decays by \(K\)-capture, transforming into \(\mathrm{Li}^7\). The difference between the masses of the atoms \(\mathrm{Be}^7 - \mathrm{Li}^7\), i.e. the energy released in this transition, is equal to \(0.87 \pm 0.03\) MeV. It is assumed that this energy is received by the neutrino. Without the neutrino hypothesis one would have to assume that this energy is lost without a trace and that the law of conservation of energy is not obeyed.

1. Allen established in his experiments that, in the decay of \(\mathrm{Be}^7\), atoms are torn from the surface of the metal on which they had been held up to the moment of decay, and that the maximum kinetic energy which they acquire agrees sufficiently well with the recoil energy that the lithium atom should receive upon the emission from the nucleus of some particle with an energy of \(0.87\) MeV and a small mass.

2. If one does not make any entirely new assumptions concerning the mechanism by which the energy of \(0.87\) MeV released in the \(K\)-decay of the \(\mathrm{Be}^7\) atom can be carried away, and by which the nucleus at that moment experiences recoil, acquiring an energy of approximately \(58\) eV, we must conclude that Allen’s experimental results indicate that neutrinos are indeed emitted in the decay of \(\mathrm{Be}^7\).

Thus, it will not be an exaggeration if, summing up all that has been set forth, we say that in Allen’s excellently performed work the experimental discovery of the neutrino has been accomplished. Henceforth the neutrino—this particle which for 11 years was not recognized as really existing and remained in the position of a hypothetical one—becomes a full-fledged member of the family of elementary particles, alongside the neutron, positron, meson, and others.

It remains for us to say a few more words about the desirable direction of further investigations. First of all, Allen’s work did not reflect the fact that the recoil nuclei in the decay of \(\mathrm{Be}^7\) possess one and the same energy—in accordance with the monochromatic character of the neutrinos arising in \(K\)-capture. To verify these ideas it would be very important to obtain a curve from which the equality of the recoil-nucleus energies would be evident. Such a curve can undoubtedly be obtained if the method for determining the energy of recoil ions is considerably improved, by applying, instead of the primitive version of the retarding-field method, a rationally chosen electron-optical system of electrodes. At the same time this would make it possible to increase substantially the accuracy of determining the absolute value of the recoil-ion energy, owing to which it would probably be possible to establish with great accuracy whether the mass of the neutrino differs from zero. For this same purpose it would be very important to obtain an even thinner layer of \(\mathrm{Be}^7\) preparation than Allen’s, and an even better degassing of the active surface (which, as Allen also indicates, could probably have been ...

be achieved by heating the radioactive source during the measurements).

Finally, let us note that, despite the much greater complexity, it would also be of great interest to carry through to completion experiments on the recoil of nuclei in beta decay—not in order once again to prove the reality of the neutrino, but in order to obtain information on the distribution of the angles of emission of the electron and the neutrino in beta decay. We have already mentioned that such information would be very interesting from the point of view of testing various variants of the theory of beta decay.

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1. Strictly speaking, in the case of \(K\)-decay of \(\mathrm{Be}^7\) one should speak not of complete homogeneity of all neutrinos in energy, but of the presence of two groups of neutrinos: in one group—the principal one—the neutrinos possess the full energy released in the transformation of \(\mathrm{Be}^7\) into \(\mathrm{Li}^7\); in the other group, which in number amounts to approximately \(1/9\) of the first, the neutrino energy is 485 keV less than the full decay energy of \(\mathrm{Be}^7\), in accordance with the energy of the \(\gamma\)-quanta emitted in these cases following the emission of the neutrino. ↩↩↩

2. visible footnote/reference marker in the source text. ↩↩