L. PAULING and S. GOUDSMIT. The Structure of Line Spectra. (International Series in Physics). McGraw Hill Book Co. New-York, 1930. Pp. X + 263.

PAULING and GOUDSMIT. The Structure of Linear Spectra.

The development of the new quantum mechanics has led to very substantial successes in the field of theoretical spectroscopy. However, the complexity of the mathematical apparatus and the abstractness characteristic of the new quantum mechanics, and the absence of a visual model, make its method, for all its power, rather cumbersome and inconvenient as a working tool for the experimenter—in particular, the spectroscopist. Fortunately, there is another path, although also formal to a considerable degree, but highly convenient, simple, and visual. This path proceeds from the so-called “vector model” of the atom, developed almost simultaneously with the new quantum mechanics, chiefly by Hund on the basis of the work of Sommerfeld, Goudsmit, Uhlenbeck, and others. The essence of this method reduces approximately to the following. The energy state of the electrons forming an atom is characterized by a set of quantum numbers. These quantum numbers are the following: the principal quantum number \(n\), determining the principal part of the electron’s energy; the quantum number \(l\), characterizing the angular momentum due to its orbital motion; the quantum number \(s\), characterizing the mechanical moment of the electron’s intrinsic rotation (spin); and the magnetic quantum number \(m\), characterizing the orientation of the orbit in an external, for example magnetic, field. A visual description of the motion of each electron in the atom by means of orbits, owing to the complexity of this motion—especially sharply expressed in those cases when the atom is in an external field—is possible only in the simplest cases. There is, however, no need for such a detailed description of the motion. The spectroscopic properties of an atom can be described when its mechanical and magnetic moment are known. The mechanical moment of the atom is known when the orbital moments \(l_i\) and the moments of intrinsic rotation \(s_i\) of the individual electrons are given. All these moments are vectors and are summed according to the rules of vector addition, forming the resultant moment of the atom, characterized by the vector \(J\). The vector of the magnetic moment is determined, on the basis of the known laws of electrodynamics, from the mechanical moment of the atom. Thus the vector model of atoms consists of only two vectors \(L\) and \(S\) and their resultant vector \(J\), about which the vectors \(L\) and \(S\) execute a rapid precessional motion. Such a simple model is already sufficient to give not only the known doublet or, in general, mul-

...triplet splitting of lines, but from it there immediately follow all cases of the simple and complex Zeeman effect, the Stark effect—in short, all the spectral properties of the alkali metals. The addition of the “Pauli prohibition,” by virtue of which there cannot be two electrons in an atom having the same four quantum numbers, leads to the construction of a completely unambiguous theory of the periodic system of the elements.

Although in some complicated cases the vector model leads to inexact formulae, its usefulness and significance are very great. For it not only performs an essential mnemonic service, permitting a very graphic classification of the already known spectral terms, but also suggests new experiments, facilitates the theoretical interpretation of new facts, and makes it possible, by an elementary and simple geometrical route, to obtain equations whose quantum-mechanical derivation is often very difficult.

Three years ago there appeared the well-known monograph by Hund, Linienspektren und Periodisches System der Elemente, in which for the first time a completed development of the vector scheme of atoms was given. The scientific significance of this book is, of course, very great. However, by its nature it is hardly suitable for beginners—and this was not its purpose. The authors of the book under review, Pauling and Goudsmit, on the contrary, set themselves a pedagogical task: to write a book that could serve as a textbook-like guide for all those beginning the study of atomic physics and spectroscopy. “In the present book,” the authors write in the preface, “we have attempted to describe the vector model of the atom and to give an account of the interpretation of line spectra from the point of view of this model. We prefer a clear and intelligible presentation to an encyclopedic one. In doing so we have in mind the reader who is completely unfamiliar with the subject, or who is familiar with the empirical side of the doctrine of spectra but not familiar with their interpretation.” The authors have unquestionably solved this extremely difficult task. As far as the subject permits, the book is indeed written quite elementarily, although in places it may perhaps be somewhat overly dogmatic.

A simple enumeration of the chapters shows how broadly Pauling and Goudsmit’s book covers the subject. I. Atomic theories and atomic models. II. Stationary states of the hydrogen atom. III. Term values of the alkali atoms. IV. The rotating electron and the fine structure of the spectra of alkali atoms. V. Vector model of alkali atoms. VI. Vector model for atoms with two valence electrons. VII. Vector model for atoms with several valence electrons. VIII. Intensity and polarization of spectral lines. IX. Pauli’s exclusion principle and the periodic system of elements. X. X-ray spectra. XI. Hyperfine structure and the rotational moment of the nucleus. XII. Magnetic phenomena other than the Zeeman effect.

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BIBLIOGRAPHY

Concerning individual chapters and the general character of the book, we can make the following remarks. Chs. I and II are intended for persons already well acquainted with atomic theory and quantum mechanics, and are meant to serve as a reminder of already familiar matters. Taking into account the elementary character of the book, one may regret that these chapters are not set forth somewhat more fully, since in their present form they are of little use precisely for those readers whom the authors have in mind. In Chs. III–VI, as in the whole book, factual material is given only to illustrate the theoretical propositions being developed. Such a didactic device is quite proper; however, it seems to us that in places the authors have bent the stick in the opposite direction. In particular, Ch. VI, in which practically not a single concrete example of complex spectra is analyzed to the end, has, as a result, proved to be a dry formal scheme, devoid of living content. Here it may be appropriate to note that, proceeding from the same considerations of the elementary nature of the exposition, the derivation of Larmor’s theorem should have been given somewhere, since it is naturally necessary to refer to it constantly in expounding the vector model. Ch. VIII treats the question from the point of view of Einstein transition probabilities and the correspondence principle. Ch. XI, devoted to the question of the influence of the nucleus on line spectra, is extremely fresh and interesting. As is known, the work of one of the authors—Goudsmit—played a decisive role in the development of this problem. In Ch. XII are considered: the Stern–Gerlach experiment, paramagnetism, magneto-mechanical effects, and the polarization of resonance radiation in a magnetic field.

In conclusion, we should like to emphasize that the book under review fills a very substantial gap in the literature. The distinctive language of modern spectroscopy and its symbolism must be firmly mastered not only by those who intend to devote themselves specially to the study of spectra, but also by all physicists and chemists wishing to keep abreast of the modern development of atomic theory. From this point of view one cannot but acknowledge that the authors have accomplished work deserving gratitude.

E. Shpolsky