## Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente.

Berlin: Julius Springer, 1928. First edition.

A fine copy, from the library of Niels Bohr, of Fermi’s statistical approach to the determination of atomic structure. The association is particularly appropriate since Bohr had inaugurated the quantum-theoretical approach to atomic structure in 1913. Fermi’s approach was developed independently and simultaneously by Llewellyn Thomas, and is now known as the ‘Thomas-Fermi model.’ The Thomas-Fermi model has found modern applications in many fields through its ability to extract qualitative trends analytically and the ease with which the model can be solved.

“During the years 1926-1932 Fermi and his associates did first-class but conventional theoretical physics, within the pattern laid down by the physicists of northern Europe. These were the concluding years of the theory of atomic structure; with the invention of wave mechanics and the relativistic explanation of the electrons' intrinsic angular momentum, the theory as we know it today was completed, and Fermi helped complete the picture. He applied his degenerate gas theory to the electrons in atomic structure, producing [in the present paper] a statistical atomic model, and in 1928 we see him calculating the Rydberg correction to S-terms using this idea” (*Enrico Fermi 1901-1954: A Biographical Memoir*, National Academy of Sciences, p. 127).

From the earliest days of quantum mechanics, it has been clear that one could not hope to solve exactly most of the physically interesting systems, especially those with three or more particles. The Thomas-Fermi model aims to describe the statistical distribution of the electrons in a large atom, rather than the positions and momenta of each individual electron. Although only an approximation, it has proved extremely useful in the study of atoms and molecules, especially for those with large numbers of electrons. In fact, a rigorous analysis by Elliot Lieb and Barry Simon in 1977 showed that the approximation becomes exact in the limit as the atomic number tends to infinity. The model is equally applicable to gravitational problems and electrostatic ones, and so has applications to astrophysical problems such as neutron stars.

The best known ‘failure’ of the Thomas-Fermi model, first proved by Edward Teller in 1962, is that that it predicts that molecules do not bind (the energy of a cluster of several molecules is greater than the sum of the energies of the individual molecules). This ‘no binding’ property of clusters of atoms was used by Lieb and Walter Thirring in 1975 to prove the ‘stability of matter,’ in the sense that as the number of particles increases, the total energy decreases only linearly rather than as a higher power of the number of particles, as it would if electrons were bosons rather than fermions.

Pp. 73-79 in Zeitschrift für Physik, 48. Band, 1. & 2. Heft. 8vo (228 x 158 mm), pp. 148. Original printed wrappers. From the library of Niels Bohr with his name (‘N. Bohr’) stamped on upper cover and ‘Bohr’ signed in pencil in a different hand (Fermi’s?).

Item #3540

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Price:
$2,850.00
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