Single-Particle States in Deformed Nonlocal Diffuse Boundary Potentials

Using the spherical wave functions generated in a previous investigation by Wyatt, Wills, and Green, the influence of spheroidal deformation is examined with the aid of perturbation theory. The combined calculations yield the energies of single-particle states for a diffuse boundary, nonlocal deformed potential. Specific calculations are performed for light nuclei around $A=25\mathrm{}$ and in the rare-earth region between $A=150\mathrm{}$ and $A=180\mathrm{}$. An analysis of nuclear ground-state spins and magnetic moments is presented in terms of the computed level schemes and wave functions. The results confirm the general aspects of the Nilsson, Mottelson results as obtained with adjusted harmonic oscillator potentials although some differences arise in detail. In particular, the calculated coefficients usually show less mixing of different angular momentum states in our case. The fact that the unperturbed potentials used in this calculation were obtained in the study of Wyatt, Wills, and Green from completely independent theoretical and experimental considerations is satisfying and further tends to confirm that the phenomenological model has a strong basis in reality. A discussion of the relationship of the phenomenological model to the self-consistent nuclear model of Brueckner is given.