FROM CURRENT LITERATURE

MASSES OF ATOMIC NUCLEI AND THE QUESTION OF NUCLEAR SHELLS

In recent years, in order to explain a number of properties of atomic nuclei, the model of the so-called nuclear shells has become widely accepted; according to this model, at the numbers 2, 8, 20 (28), 50, 82, and 126 “protons” or neutrons, proton or neutron shells are filled.

The first indications of the special stability and prevalence of nuclei containing 20, 50, and 82 protons or neutrons were given as early as 1933 in a paper by the Soviet scientist I. P. Selinov ^1. In 1948 a theoretical explanation of the successive filling of nuclear shells was proposed, based on the assumption of the influence of spin-orbit interaction in the filling of nucleon levels in nuclei ^2.

A large number of papers by a number of Soviet physicists have been devoted to the question of nuclear shells.

The role of nuclear shells is manifested very clearly when comparing the precise values of the masses of various nuclei in connection with the fact that the binding energy of a nucleon whose addition marks the filling of a shell is noticeably higher than the average binding energy. Conversely, the binding energy of a nucleon added to a nucleus with the corresponding shell already filled is lower than the average binding energy. For comparing the binding energies of nucleons in different nuclei, much work was carried out in 1950–1952 on the mass-spectrographic determination of precise mass values for a number of nuclei from silicon to uranium. The table gives the corresponding data obtained by the groups of Duckworth ^3–10, Nier ^11,12, and Goudsmit ^13,14. In this connection, the nuclear masses given in the table on the basis of ^11,12 have been recalculated from packing fractions, while the data of the other works are given without any recalculations.

The material presented in the table is of independent interest for calculations of the heat effects of various nuclear reactions or the thresholds of such reactions. In this sense the table is a supplement to the reference tables of masses of light nuclei (usually up to iron) given in a number of courses on nuclear physics.

However, in addition to this, a comparison of the masses of various nuclei can be used to investigate the question of nuclear shells. It is precisely such a comparison that was carried out in ^15.

In the figure (p. 480), borrowed from ^15, the dependence is given of the average binding energy (per nucleon) on the mass number of nuclei for 115 stable nuclei of elements with \(Z > 21\). In addition to mass-spectroscopic data from works ^3–10, data on the heat effects of a number of nuclear transformations and on microwave absorption were used.

Masses of Atomic Nuclei

Continuation

Continuation

From the figure it is evident that there are a number of breaks in the smooth dependence of the mean binding energy on the mass numbers, associated with the filling of nuclear shells. In the region of the heaviest nuclei, the break toward an increase in the mean binding energy corresponds to the nucleus \({}_{82}\mathrm{Pb}^{208}_{126}\). This nucleus is characterized by the filling of both proton (82 protons) and neutron (126 neutrons) shells.

The filling of neutron shells (82 neutrons) corresponds to a break in the curve at the point corresponding to the nucleus \({}_{58}\mathrm{Ce}^{140}_{82}\). Shells containing 50

protons or neutrons, are filled in the nuclei \({}_{50}\mathrm{Sn}^{120}\) and \({}_{38}\mathrm{Sr}^{88}_{50}\), which likewise corresponds to kinks in the curve of the nucleon binding energy. Finally, the peak of the curve for the nucleus \({}_{28}\mathrm{Ni}^{62}_{34}\) corresponds to the filling of a shell at 20 protons. Thus, a systematic investigation of the masses of a series of nuclei over a broad interval of mass numbers has confirmed the basic propositions of the ideas concerning nuclear shells. It is of interest to investigate the masses of nuclei in intervals of mass numbers that have so far been little studied, and also to examine more closely the sums of already obtained data with the aim of clarifying the sequence of filling of nucleon levels in nuclei.

G. I.

References Cited

1. I. P. Selinov, JETP, 4, 666 (1934) (reported April 16, 1933).
2. M. G. Mayer, Phys. Rev., 74, 235 (1948).
3. H. Duckworth and H. Johnson, Phys. Rev., 78, 179 (1950).
4. H. Duckworth et al., Phys. Rev., 78, 479 (1950).
5. H. Duckworth et al., Phys. Rev., 79, 188 (1950).
6. H. Duckworth and R. Preston, Phys. Rev., 79, 402 (1950).
7. H. Duckworth and R. Preston, Phys. Rev., 82, 468 (1951).
8. H. Duckworth et al., Phys. Rev., 83, 1114 (1951).
9. C. Stanford, H. Duckworth et al., Phys. Rev., 85, 1039 (1952).
10. C. Kegley and H. Duckworth, Nature, 167, 1025 (1951).
11. A. Nier et al., Phys. Rev., 85, 726, L 12 (1952).
12. R. Halsted, Phys. Rev., 85, 726, L 13 (1952).
13. S. Goudsmit et al., Phys. Rev., 84, 824 (1951).
14. S. Goudsmit et al., Phys. Rev., 85, 630 (1952).
15. H. Duckworth, Nature, 170, 158 (1952).