Bibliography

G. Gamow. Constitution of Atomic Nuclei and Radioactivity. Pp. VIII + 114, Oxford University Press, Oxford 1931, 10 s. 6 d. (The International Series of Monographs on Physics, edited by R. H. Fowler and P. Kapitza).

Gamow. Structure of the Atomic Nucleus and Radioactivity

Until 1928, wave mechanics was applied exclusively to phenomena occurring in the shells of atoms; the processes taking place in the atomic nucleus were entirely incomprehensible, and, despite the astonishing successes achieved by wave mechanics in explaining atomic phenomena, no one had been able to apply it to the nucleus. This achievement belongs to the Soviet physicist G. A. Gamow. Gamow showed that atomic nuclei are surrounded by barriers of potential energy; owing to the peculiar properties of the laws of wave mechanics, α-particles seep out of nuclei through these barriers, despite the fact that the height of the barriers exceeds the energy of the particles. Thus the phenomenon of radioactive α-decay received a theoretical explanation. The empirical Geiger–Nuttall relation, which gives the connection between the velocity of an α-particle and the probability of decay, was derived theoretically and, moreover, in a more exact form; at the same time, for the first time, it became possible to calculate reliably the sizes of radioactive nuclei. Continuing these investigations, Gamow discovered a previously unknown connection between γ-rays and the fine structure of α-rays and constructed the first scheme of the energy levels of the nucleus. To him also belongs the theory of the artificial disintegration of elements. It is noteworthy that all these results concern only the heavy particles that make up the nucleus (protons and α-particles); the properties of intranuclear electrons are still, from the theoretical side, very mysterious, since the behavior of these electrons lies beyond the limits of applicability of wave mechanics. An explanation of the behavior of intranuclear electrons requires a fusion of wave mechanics with the theory of relativity—a fusion that has not yet been achieved and apparently presents enormous difficulties.

One cannot but welcome the appearance of a book that presents a survey of everything that is at present known about the atomic nucleus, and that comes from the pen of the Soviet theorist to whom we owe all the theoretical achievements relating to this field. The book contains not only a connected exposition of these theoretical results, but also

a complete survey of the experimental facts on which they are based. The first chapter is devoted to a description of the material accumulated by experimental investigations concerning such properties of nuclei as the number of protons, the magnitude of the “packing” effect, and the moments of nuclei. The second chapter is devoted to spontaneous disintegration; its principal content is an exposition of Gamow’s theory of $\alpha$-decay. It should be noted that the exposition of this theory given by Gamow in his works led to a great many misunderstandings connected with the “complex values of the energy”: statements even appeared in the literature (for example, by Lauer) that the mathematical side of the theory contains defects. In reality, the misunderstanding is explained quite simply if one recalls that in wave mechanics only stationary states possess a definite value of the energy, and these energy values are, of course, always real. Nonstationary states (including the state of the $\alpha$-particle corresponding to leakage through the barrier) possess no energy values; those complex eigenvalues of Schrödinger’s equation for the amplitudes which play a role in the theory of $\alpha$-decay are not energy values at all, although Gamow, through carelessness, calls them such. From a pedagogical point of view, it would seem to me that the only correct exposition of the theory would be one in which the starting point were an initial state with probability density equal to zero outside the barrier; by “continuing” such a state in time with the aid of Schrödinger’s equation containing time, one could obtain exponential damping in a wholly natural way, whereas the search for the complex eigenvalues of the amplitude Schrödinger equation, as is done in Gamow’s book, corresponds to the exponential character of the decay—that is, one of the most essential features of radioactivity—being, as it were, postulated in advance rather than derived.

The third chapter is devoted to $\gamma$-rays and the energy levels of radioactive nuclei. In this chapter an explanation is given of the fine structure of $\alpha$-rays: when an $\alpha$-particle is emitted accompanied by excitation of the nucleus, an $\alpha$-particle of lower energy is obtained, while when emission occurs from an excited level an $\alpha$-particle of higher energy than usual is obtained. The nuclear levels are connected with the frequencies of the $\gamma$-rays. The exposition of the question is given somewhat more complicated than it ought to be, since the author uses such concepts as the level of an $\alpha$-particle and the level of a proton in the nucleus (only nuclear levels have physical meaning). In the same chapter questions concerning the probability of emission of $\gamma$-rays are considered. The exposition is very brief, and the final results are given almost without derivation. In conclusion the anomalous absorption of $\gamma$-rays, still not explained theoretically, is considered.

The last, fourth, chapter treats the interaction of nuclei with high-energy particles incident upon them, which can penetrate inside the barrier of potential energy surrounding the nuclei.

This includes the case of elastic collision with penetration beyond the barrier (anomalous scattering) and inelastic collision, leading to excitation or artificial disintegration of the nucleus. Let us note that the theoretical analysis of these phenomena given in the book requires of the reader a far greater acquaintance with wave mechanics than is needed for understanding the second chapter. In conclusion, a survey is given of the experimental material relating to artificial excitation and disintegration.

Gamow’s book has already appeared in German translation; the Russian translation is in press. We wish it the speediest possible appearance. Let us note that the Soviet reader has the right to demand that, in compensation for the delayed appearance of the Russian edition as compared with the English and German ones, the book include a survey of new experimental facts discovered in the time that has elapsed since the appearance of the foreign editions. Some of these facts (Chadwick’s discovery of neutrons and Curie-Joliot’s discovery of the isotope of hydrogen) are very interesting, and it would be regrettable if they were absent from the survey appearing in the summer of 1932. It is also necessary to eliminate from the Russian edition the misprints that mar the English and especially the German edition of the book.

M. Bronshtein