Single Particle Motion in a Deformed, Nonlocal Potential Well

The effects of the nonlocal character of the average nucleon-nucleus interaction on single particle motion in a strongly deformed field are examined by using a simple phenomenological description of the nonlocal interaction and introducing an effective mass approximation for a finite nuclear system.The eigenvalues and eigenfunctions of the anisotropic harmonic oscillator potential are used as a starting point for a perturbative treatment of the nonlocal interaction, and the resulting energy level scheme is given as a function of the nuclear deformation. A conventional spin-orbit interaction has also been included in these calculations.The main effects of the nonlocal interaction appear as an increase in the level spacing of the unperturbed oscillator states combined with an additional interaction energy which can be interpreted as an effective angular momentum dependence of the average potential field.Calculations of nuclear equilibrium deformations based on the computed level schemes are presented. It is found that the preponderance of prolate nuclear shapes found empirically can be accounted for quite well by the nonlocal model and results essentially from the favoring of high angular momentum substates that are introduced by the nonlocal interaction.