H. A. Bethe. Elementary nuclear theory. John Wiley, New York; Chapman-Hall, London, 1947.

H. Bethe. Introduction to the Theory of the Atomic Nucleus. (New York, 1947.)

The appearance of Bethe’s new book on the theory of the atomic nucleus was awaited with understandable interest by theoretical physicists and experimentalists. In fact, up to the present time Bethe’s monograph of 1936–1937, in three parts, on nuclear theory (republished several years ago) has been the most complete presentation of these problems and has acquired the significance of a standard book, to which all subsequent authors refer (the first part is available in Russian translation; for unclear reasons the publication of the remaining ...

BIBLIOGRAPHY

...of two parts). Although over the past ten years nuclear physics has advanced far, Bethe’s monograph has nevertheless retained its importance, since the basic concepts and facts had already been clarified at that time. In Bethe’s new book there are also many references to his monograph. The author himself, now professor at Cornell University, is one of the most eminent specialists in nuclear theory, having produced a considerable number of results, chiefly in the application of theory to the calculation of various physical effects.

Let us note at once that the book to a certain extent justifies expectations, giving a clear, though concise, exposition of the deuteron problem, nucleon scattering, beta decay, and other questions. At the same time, the reader of Bethe’s new book experiences a certain disappointment, since in this work there is no discussion of a systematic presentation of the whole of nuclear theory, i.e., of a corrected and modernized edition of the earlier monograph.

The small book under review (121 pages of small-format text) is based on lectures delivered to staff members of research laboratories and engineers of the General Electric Company in Schenectady, New York, and is an exposition of selected chapters of nuclear theory. The first chapter (22 pages) contains a general description of the basic properties of nuclei, the determination of their sizes, data on spin, statistics, and a brief introduction to the physics of beta decay. Here one would naturally include part of § 7 of the following chapter, devoted to the basic properties of the proton, neutron, and deuteron. The concise exposition is very clear and fresh. In this chapter, as especially in the next two, essentially not only the basic facts of nuclear physics are assumed to be known, but also such sections of theory as, for example, alpha decay, not to mention quantum mechanics. Therefore, in all likelihood, Bethe’s book is not so much an introduction that can be read and studied, for example, after F. Rasetti (Elements of Nuclear Physics) or the last chapters of E. V. Shpolsky’s course (Introduction to Atomic Physics), as a supplement to the basic monographs, containing, alongside a summary of basic points, also the latest information from the last 10 years.

The conciseness of the exposition is often vexing when, for example, Bethe confines himself to a single phrase, unintelligible without explanation for nonspecialists, about the radioactive family of type \(4n + 1\) (i.e., neptunium). Further, Bethe writes nothing about the newest, so promising and already yielding remarkable results, Bloch method of measuring the nuclear paramagnetic moment.

The second chapter, which is the main part of the book (pp. 23–96), is devoted to nuclear forces, considered through examples of the deuteron problem and nucleon scattering. Bethe rightly emphasizes in the preface that the problem of forces and, at the same time, the two-body problem should now occupy the central place in the physics of the atomic nucleus and should take precedence over the study of preliminary and, in the final analysis, approximate models, including the compound-nucleus theory applied to complex nuclei, despite its well-known successes, in particular in the direction of the use of atomic energy.

If significant efforts are concentrated on the fundamental problem of nuclear forces between nucleons, then after its solution an enormous number of results concerning the abundance of elements, nuclear reactions, beta decay, etc., etc., will undoubtedly be obtained in the shortest possible time with the aid of the powerful computational apparatus of modern physics and will, so to speak, fall into our hands of their own accord.

However, Bethe makes, in our view, a mistake by adhering in the book to a purely empirical approach to the theory of nuclear forces. In our view, one should proceed as follows: first list all the basic arguments in favor of the nucleon model of the nucleus and formulate the problem of nuclear forces, then, briefly indicating the first model of pair forces, set forth the foundations of the various versions of the field meson theory of nuclear forces (scalar, pseudoscalar, vector, with charged and neutral fields). As is known, field theory

nuclear forces naturally leads to all the required types of exchange forces, to short-range forces, to spin forces, and to noncentral forces, and makes it possible to satisfy the requirement of charge independence. At the same time, of course, one must emphasize the principal additional difficulty in the theory of nuclear forces connected with the appearance of a quasi-magnetron member of the type \(r^{-3}\), which makes it impossible to obtain stable states. All the other approaches to the problem of nuclear forces are, in one way or another, semi-empirical preparations and still make use of one or another result of the field theory of forces, as Bethe himself arrives at, for example, in § 14 on p. 88 of his book.

As an illustration let us recall that, as is well known, for example, the Heisenberg direction, although it could explain various types of exchange forces, could not obtain noncentral forces.

Instead of the indicated deductive method, Bethe prefers to employ an empirical approach. The model of the atomic nucleus is presented by him fragmentarily, in four separate paragraphs, in connection with the sizes of nuclei, spin, statistics, which does not give any integral impression and diminishes the cogency of the arguments. Further, in analyzing the deuteron, he first confines himself to ordinary central forces, then introduces spin forces. The scattering of protons by protons leads to charge independence of the forces, i.e. to equality of the forces \(n—p\), \(p—p\), \(n—n\). Further, to explain the quadrupole moment of the deuteron, noncentral forces are introduced. Finally, to explain saturation and the approximate constancy of the average binding energy per nucleon, exchange forces are introduced. The field meson theory of forces, however, is set forth at the end of the chapter very briefly, in three pages.

If one adopts the point of view of such an inductive construction of the theory, then Bethe’s exposition must be acknowledged as successful. The abstract foundations of the theory of noncentral and exchange forces, including the formalism of isotopic spin, are communicated in a clear form. Bethe everywhere uses the most recent material, explaining, for example, the magnetic moment of the deuteron on the basis of the latest measurements of the magnetic moment of the neutron \((\mu_n = 1.9103\,\mu_0)\) by Arnold and Roberts (pp. 25–28), citing the experimental proof of the presence of a substantial admixture of exchange forces in the nuclear field from experiments on the scattering of fast neutrons (100 MeV) by protons (p. 93), etc.

We find § 10, devoted to the scattering of neutrons bound with protons in molecules, very valuable; this had not yet been the subject of exposition in monographs. Here the significance is clarified of experiments that showed the predominant scattering of neutrons by ortho-hydrogen as compared with parahydrogen \((\sigma_o : \sigma_p \simeq 30)\).

The third small chapter (pp. 97–120) is devoted, above all, to a good exposition of Fermi’s theory of beta decay, in particular of the selection rules; unfortunately, however, this is not connected with Yukawa’s hypothesis of the intermediate role of the meson. In the last paragraph 17 the Bohr model of the compound nucleus is set forth, along with questions of nuclear temperature, resonance, and the dispersion formula.

At the end a list of isotopes is appended.

In conclusion to our review, it must be noted that Bethe’s book is very “Americanized” in the sense of the mention of authors of both fundamental and secondary results. For example, on p. 84, in the exposition of Bartlett’s force, it is not mentioned that the spin-exchange operator \(\frac{1}{2}(1 + \vec{\sigma}_1 \cdot \vec{\sigma}_2)\) was derived by Dirac (see his Principles of Quantum Mechanics, 2nd ed., M.–L., 1937, p. 241). In the exposition of beta decay (p. 98 ff.) it is not indicated that the statistical factor determining, to a considerable extent, the form of the spectrum was established by F. Perrin and then already used in Fermi’s theory. In Bethe’s book there is a complete absence of references to Soviet authors, despite the use of their results, and even the references that were present in the principal monograph in the devel-

matters, which are being repeated now. In particular, references to Frenkel and Landau and others in the theory of the compound nucleus are ignored. Further, although Bethe repeatedly emphasizes the importance and nontriviality of arguments in favor of the nucleon model of the nucleus (pp. 8, 14, 18, etc.), he never once refers in this connection to our works. We would not consider it possible, in any exposition of the field theory of nuclear forces, to pass over in silence at least the well-known Soviet works that laid the foundation of this theory.

We consider ourselves obliged to note that the rapid translation of Bethe’s book, which will be useful both for students and for scientific workers, is justified. The Russian edition should be supplemented by a clarification of the literature and by brief orienting notes on the state of the theory of nuclear forces.

D. Ivanenko