NEW DATA ON THE POSITRON

E. V. Shpolsky, Moscow

Chadwick, Blackett, and Occhialini,^1 as well as Meitner and Philipp,^2 published reports on the production of positrons by bombarding lead with neutrons. Earlier, similar observations had been made by I. Curie and F. Joliot, who, however, having detected particles deflected in the direction opposite to the usual deflection of negative electrons, regarded the particles they found as negative electrons directed toward the source of the neutrons. Anderson and Neddermeyer succeeded in obtaining positrons when hard $\gamma$-rays passed through lead. For this purpose radium was used together with its products

of disintegration; moreover, in order to obtain a sharply outlined beam the rays were passed through a series of diaphragms, made in thick pieces of lead, so that the total thickness of the diaphragm was 18 cm. This beam of rays went vertically downward and entered a Wilson chamber, across which there was placed a lead plate 2 mm thick, and below it a layer of aluminum 0.5 mm thick. A uniform magnetic field (with an accuracy of up to 10%) was directed perpendicular to the bases of the Wilson chamber and had an intensity of 430 gauss. In the photograph reproduced here (Fig. 1) the path of a positron is shown, emerging from the lead plate and penetrating the layer of aluminum. Owing to the decrease in speed in passing through the aluminum, the curvature of the path after leaving the plate increases, and from this it is possible to establish the direction of motion, which, together with the direction of deflection in the magnetic field, makes it possible to determine the sign of the charge. The most remarkable phenomenon observed in such observations consists in the fact that most often paired tracks appear, emerging from a single point, with one track belonging to a negative particle and the other to a positive one. The production of electron pairs under the action of ThC″ γ-rays was also observed by I. Curie and F. Joliot. Fig. 2 is a striking photograph in which the production of a positron–electron pair in a volume of gas (a rare case) is visible. In Fig. 3 a photograph is shown in which the trajectories of a positron and an electron are visible, as well as the trajectory of a proton (the heavy track at the right), produced under the action of a neutron impact. The last photograph was obtained from a source consisting of a radium preparation surrounded by beryllium. Contrary to the original opinion of Chadwick, Blackett and Occhialini, and also of Meitner and Philipp, Curie and Joliot (as well as Anderson and Neddermeyer) believe that the production of positron–electron pairs is caused by the action of penetrating radiation of the γ-ray type, accompanying the emission of neutrons, but not by the neutrons themselves. This is confirmed by the results of the following experiment. If a layer of lead is placed

Fig. 1.

Fig. 2.

Fig. 3.

in \(2\ \mathrm{cm}\) thickness between the source \((\mathrm{Po}+\mathrm{Be})\) and the lead emitting positrons, then the number of the latter decreases by about \(40\%\). This is fully consistent with the absorption of the penetrating \(\gamma\)-radiation accompanying the emission of neutrons \((h\nu=5\cdot 10^{6}\ \mathrm{V})\), whereas the neutrons are absorbed by such a layer of lead by only \(10\)—\(12\%\).

The energies of the particles obtained, both by the American and by the French investigators, were found to be the same. Namely, Anderson and Neddermeyer found that each pair receives from \(1.6\cdot 10^{6}\) to \(10^{6}\), equal in sign, V; for Curie and Joliot the maximum energy of each particle did not exceed \(0.8\cdot 10^{6}\ \mathrm{V}\). An explanation of these results may be given as follows. Blackett and Occhialini had already indicated that the occurrence of a positron should apparently be regarded as a consequence of the “birth” of a positron–electron pair at the expense of some quantum \(h\nu\). Since for the mass of an electron an equivalent amount of energy \(m_{0}c^{2}\) is \(0.5\cdot 10^{6}\ \mathrm{V}\), for the creation of a pair the minimum necessary energy will be \(2m_{0}c^{2}=1\cdot 10^{6}\ \mathrm{V}\). Thus radiation with a quantum smaller than \(10^{6}\ \mathrm{V}\) cannot in general create a positron; for quanta of greater magnitude the excess \(h\nu-1\cdot 10^{6}\) goes into imparting kinetic energy to the particles formed. In the case of \(\mathrm{ThC}^{\prime\prime}\) the magnitude of the quantum is \(2.6\cdot 10^{6}\). Consequently, the kinetic energy of each of the particles of the arising pair should not exceed

\[ \frac{2.6\cdot 10^{6}-1\cdot 10^{6}}{2}=0.8\cdot 10^{6}, \]

which agrees with the experimental results. In the experiments of Curie and Joliot, where positron–electron pairs arose at the expense of the \(\gamma\)-radiation of beryllium, the maximum energy of each particle was \(1.8\cdot 10^{6}\); the magnitude of the quantum here is \(5\cdot 10^{6}\). But

\[ \frac{5\cdot 10^{6}-1\cdot 10^{6}}{2}=2\cdot 10^{6}. \]

Consequently, in this case as well the maximum energy agrees with the expected value.

The picture outlined above of the origin of the positron was developed into a quantitative theory by a number of investigators—first by Oppenheimer and Plesset, who made use for this purpose of the theory of the positron developed by Dirac. As is known, according to this theory, positrons are regarded as unoccupied levels in the region of electrons with negative energy. In such a case the occurrence of a positron must be viewed as a kind of “photoelectric effect,” in which, in the presence of a nucleus, an electron from the region of negative energies is transferred into the region of positive energies. As a result, a free electron with positive energy is obtained, and an unoccupied place in the region of negative energies, i.e. a positron. The presence of a nucleus is necessary for the following considerations. On considerations based on the law of conservation of momentum, the process of annihilation of a positron and an electron must lead to the appearance of at least two light quanta. One may imagine, however, also such a case when the entire annihilation energy \(2m_{0}c^{2}\) is emitted in the form of a single light quantum, but for this there must be a “third body,” for example in the form of some nucleus, which must take upon itself the excess momentum. In such a case, conversely, one light quantum of sufficient energy, in the presence of a nucleus, can cause a “photoeffect,” i.e. transfer an electron from the region of negative energies into the region of positive energies—or, in other words, create a pair of particles—a positron and an electron. If the energy of the incident quantum is \(h\nu\), then, obviously, the excess \(h\nu-2m_{0}c^{2}\) will appear in the form of kinetic energy of the pair. Such pairs were in fact observed by Anderson and Neddermeyer in the work reviewed above. But if such a “birth”

“generation” of pairs under the influence of γ-rays takes place, then hard γ-rays should exhibit excess absorption in comparison with the absorption leading to the creation of Compton electrons. Such excess absorption had already been found by Chao and studied in detail by Gray and Tarrant³. Gray and Tarrant showed, moreover, that part of the excessively absorbed energy is emitted again in the form of a peculiar “fluorescence” radiation of the nucleus, consisting, independently of the nature of the scattering nucleus, of a monochromatic band at \(0.5\cdot 10^6\) V and, in addition, in some cases, of a weaker band at \(1\cdot 10^6\) V. The origin of the first band is readily understood from the point of view set forth: if one assumes that the radiation is the result of annihilation of part of the pairs born, then in each annihilation two quanta of energy \(m_0c^2=0.5\cdot 10^6\) V each must arise. To explain the second, harder band, one must assume that the entire annihilation energy \(2m_0c^2=1\cdot 10^6\), in some cases, can be emitted at once in the form of a single quantum, the excess momentum then being taken up by the scattering nucleus. Thus the process of scattering of hard γ-rays may be represented in the following way. Some of the quanta undergo ordinary scattering by electrons, producing Compton recoil electrons and scattered radiation in accordance with the Klein–Nishina formula; another part of the quanta, upon absorption, goes into the creation of positron–electron pairs. The positron formed in this way travels a comparatively short path after collisions and, at the end of its path, acquires a considerable probability of annihilation; as a result of the annihilation, part of the absorbed quanta is emitted again, as was indicated above.

Quantitative calculations based on these ideas were published by Oppenheimer and Plesset and by Fermi and Uhlenbeck⁴. The former obtained formulae according to which, for γ-quantum energies substantially exceeding the minimum (\(10^6\) V), the probability of anomalous absorption increases proportionally to the square of the atomic number. This conclusion agrees well with the experimental results obtained for ThC″. Further, for the same case ThC″ (quantum energy \(2.6\cdot 10^6\) V), according to the formulae of Oppenheimer and Plesset, it is found that for lead the excess absorption should amount to 25% of the absorption calculated by the Klein–Nishina formula, and for tin—15%, which also satisfies the experimental data well. Thus the theory gives a satisfactory result insofar as it concerns the dependence of the excess absorption on the energy of the γ-quantum and on the atomic number, and also on the absolute magnitude of the excess absorption. However, the explanation of the hard component of anomalous scattering (\(h\nu=10^6\) V) encounters considerable difficulties. Calculations carried out by Fermi and Uhlenbeck led to values of the rate of annihilation with emission of two quanta (the soft band) that agree well with the experimental data; the same calculations for the process with emission of one quantum lead to values differing from the experimental data by a factor of \(10^{13}\), in the case when the annihilation occurs after the positron has lost its velocity. If one assumes that the annihilation process already occurs at high velocities of the positron, then the results are somewhat improved, although even for a positron velocity of \(10^6\) V the resulting probability of annihilation with one quantum is still 100 times smaller than the observed one. The authors consider it unlikely that the introduction of relativistic corrections into the theory could substantially improve the situation. Thus the explanation of the hard component of anomalous γ-ray scattering still encounters serious difficulties.

References

1. Chadwick J., Blackett P. M. S. and Occhialini, Nature, 131, 473, 1933; cf. UFN, 13, 511, 1933.
2. Meitner L. und Philipp K., Naturwiss., 21, 286, 1933.
3. Anderson C. and Neddermeyer S. H., Phys. Rev., 43, 1034, 1933.
4. Curie J. et Joliot E., Journ. de Physique, 4 (Serie VII), 494, 1933.
5. Oppenheimer J. R. and Plesset M. S., Phys. Rev., 44, 53, 1933.
6. Dirac P. B. M., Proc. Roy. Society; cf. UFN.
7. See Bronstein M.’s review, UFN, 1932.
8. Fermi F. E. and Uhlenbeck, Phys. Rev., 44, 510, 1933.
9. Anderson C., Phys. Rev., 44, 406, 1933.