Nuclear Energy Level Argument for a Spheroidal Nuclear Model

Recently there has been notable success, particularly by Maria Mayer, in explaining many nuclear phenomena including spins, magnetic moments, isomeric states, etc. on the basis of a single particle model for the separate nucleons in a spherical nucleus. The spherical model, however, seems incapable of explaining the observed large quadrupole moments of nuclei. In this paper it is shown that an extension of the logic of this model leads to the prediction that greater stability is obtained for a spheroidal than for a spherical nucleus of the same volume, when reasonable assumptions are made concerning the variation of the energy terms on distortion. The predicted quadrupole moment variation with odd $A$ is in general agreement with the experimental values as concerns variation with $A$, but are even larger than the experimental values. Since the true situation probably involves considerable "dilution" of the extreme single particle model, it is encouraging that the present predictions are larger rather than smaller than the experimental results. A solution is given for the energy levels of a particle in a spheroidal box.