FROM CURRENT LITERATURE

ON THE HISTORY OF THE EXCLUSION PRINCIPLE (PAULI PRINCIPLE)

In a speech delivered at the Institute for Advanced Study on the occasion of Pauli’s celebration upon his receiving the Nobel Prize,*) Pauli recounts the history of the establishment of the principle that bears his name. He points out that the beginning of this history goes back to his student years, when he studied under Sommerfeld in Munich. While still in secondary school Pauli had acquired knowledge of classical physics and the new theory of relativity. When, at the university, he became acquainted with the theory of atomic structure, the basic postulates of Bohr—as to all physicists at that time—seemed very strange to him. Pauli recalls that in this period of the development of quantum theory there existed two trends. One—headed by N. Bohr—sought to bring order into the new ideas by finding a key for translating classical mechanics and electrodynamics into the quantum language by means of the correspondence principle. Sommerfeld, however, was a representative of another trend, which attempted to overcome the difficulties of using kinematic models by a direct interpretation of the laws of spectra in terms of integers, following—much as Kepler had done in establishing the laws of planetary motions—“an inner sense of harmony.” “Both of these methods, which did not seem to me incompatible, influenced me,” writes Pauli. At that time, among Sommerfeld’s students, there was heated discussion of the significance of a series of integers 2, 8, 18, 32 ..., which give the lengths of the periods of the periodic system. Rydberg’s indication was also discussed, namely that these numbers have the simple form \(2n^2\), where \(n\) is an integer. Sommerfeld, however, attached special significance to the number 8 and tried to connect it with the number of vertices of a cube.

Pauli associates a new stage in his scientific development with his personal acquaintance with N. Bohr. In 1922 Bohr gave lectures in Göttingen; in these lectures he presented the results of his work on the theory of the periodic system. Already in his earlier works Bohr pointed to the fundamental problem in this field: to the explanation of the reason why, in the ground state of an atom, all the electrons of the atom are not bound in its innermost shell. In his Göttingen lectures Bohr dwelt in particular detail on the completion of this very innermost \(K\)-shell of helium and on the connection of this completion with two simple features of the spectra of helium—the spectra of parahelium and orthohelium. No explanation of this feature on the basis of classical mechanics had been given. Pauli, however, was most struck by the fact that, unlike Sommerfeld, Bohr ascribed to the number 2 the same significance as to the number 8.

Pauli describes his personal acquaintance with Bohr, which took place at that time, in comic terms. Once, he relates, Bohr came to me together with his assistant Oskar Klein and asked me—not

*) W. Pauli, Science 103, 213, 1946 (No. 2639, 22 Febr.).

agree to go to him in Copenhagen for a year... I was very much struck and, after thinking a little, answered as only a young man can answer: “I think that the scientific requirements which you will make of me present no difficulty for me, but learning a new language, like Danish, surpasses my abilities.” Bohr and Kramers laughed, and I arrived in Copenhagen at the end of 1922. In this, both of my assertions proved false. The first Danish words that I learned were the names of whole numbers. The way in which such simple numbers as 50, 70, 90 are expressed in Danish—in a complicated manner, as half multiples of 20 (50 = 20·3/2, etc.)—especially struck me. However, I soon easily learned them. But the half-integral numbers that Landé used as magnetic quantum numbers to explain the anomalous Zeeman effect presented much greater difficulties for me”... At that time Pauli was working on the theory of the anomalous Zeeman effect, and his attention was drawn to the fact that, on the one hand, in this phenomenon simple regularities are found, while, on the other, the most general assumptions about the properties of the electron both in classical and in quantum theory lead only to a simple Lorentz triplet, and not to complex types of splitting. The problem seemed insoluble to Pauli. Nevertheless, he succeeded in generalizing Landé’s analysis for the simpler case of strong fields (the Paschen–Back effect).

In 1923 Pauli devoted his inaugural lecture as a Privatdozent, delivered in Hamburg, to the theory of the periodic system. The content of this lecture now seems to him highly unsatisfactory, since the problem of the closing of electron shells had not been explained. The only essential point was the indication of the connection of this problem with the multiplet structure of atomic spectra. Taking this into account, Pauli again critically examined the simplest case of the alkali metals and came to the conclusion that the orthodox point of view at that time—according to which the doublet structure of the spectra of these atoms is explained by the angular momentum of the “atomic residue,” consisting of the nucleus and \(Z-1\) inner electrons—was not correct. In his 1924 paper Pauli put forward considerations by virtue of which, in order to explain the doublet structure, one must ascribe to the electron a new quantum property, which he called “a two-valuedness not accessible to classical description.”

It was precisely at this time that Stoner’s work appeared, in which the classification of electrons by subgroups was not only improved, but the essential observation was also made that the number of energy levels of a single radiating electron of the alkali metals in an external magnetic field, for a given value of the principal quantum number, is equal to the number of electrons in the closed shells of the noble gases corresponding to the same principal quantum number. Pauli points out that this observation, in connection with his, i.e. Pauli’s, preceding results concerning the classification of spectral terms in strong magnetic fields, at once made it possible for him to give the general formulation of the exclusion principle. He formulates the idea of this principle as follows: the complex numbers of electrons in closed subgroups reduce to the simple number one if the groups are split by specifying the values of the four quantum numbers, provided that the degeneracy is completely removed. One electron occupies a nondegenerate energy level only once. The exposition of this formulation of the exclusion principle was given by Pauli in the spring of 1925 (Zschr. f. Physik 31, 765, 1925).

Pauli notes that, with the exception of specialists in the classification of spectra, the formulation of the exclusion principle at this stage seemed incomprehensible to physicists, since it was not clear what model representations could be connected with the fourth degree of freedom of the electron. This gap was filled thanks to Uhlenbeck and Goudsmit’s idea of the spin of the electron, which made it possible to understand the anomalous Zeeman effect. Since then the exclusion princip...

… are always associated precisely with the idea of spin. Pauli notes that, although he initially had strong doubts about the correctness of this idea because of its classical-mechanical character, Thomas’s calculation of the magnitude of the doublet splitting compelled Pauli to accept the idea of spin. On the other hand, his early statements concerning a “two-valuedness inaccessible to classical description” were confirmed by the subsequent development of the theory, which showed that the property of electron spin is essentially quantum-mechanical.

The subsequent development of the exclusion principle (Pauli principle) and its significance, extending far beyond the limits of spectroscopy, are well known.

E. Shpolsky