Nuclear Shells: Angular and Magnetic Momenta of Nuclei

Abstract

Part I. Angular momenta. The experimental data on the number of isotopes per atom show marked regularities, which suggest closed shells in the nucleus. These regularities have been rigorously followed in arranging the first thirty elements into an isotopic system, with proton and neutron shells. In order to correlate both the angular and magnetic momenta of nuclei, it is necessary to choose certain $j$ values of the terms arising from the proton and neutron configurations, as the deepest terms. After this choice has been made, the assumption, that the $j$ values of the lowest terms are added vectorially with the $j$'s oppositely directed, makes it possible to account for all of the observed $i$ values. Apparently the $S$ states are exceptions to the general rule and have their $j$'s in the same direction.Part II. Magnetic momenta. Nuclear magnetic moments are discussed from the viewpoint of proton and neutron shells in the nucleus. The generalized $g$-formula is used to calculate the proton and neutron contributions to the $g$-factor. These two contributions are then combined by $\mathrm{jj}$ coupling to give the nuclear $g$ values. A magnetic moment of +2.7 nuclear magnetons for the proton, and +1.75 nuclear magnetons for the neutron are used in the calculations. The deepest proton and neutron terms fix the values of $l$, $j$ and $s$, so that, once having chosen these deepest terms, no arbitrariness exists in the calculations. A discussion of the correlated data is given.