Nuclear prolate-shape dominance with the Woods-Saxon potential

TL;DR

This study investigates the dominance of prolate shapes in nuclear ground states by calculating masses of over two thousand nuclei using an improved Woods-Saxon potential, analyzing effects of potential parameters and pairing correlations.

Contribution

It introduces an enhanced computational approach with the Woods-Saxon potential to analyze nuclear shape preferences, highlighting the influence of surface thickness and spin-orbit interactions.

Findings

Prolate-shape dominance varies across mass regions.

Surface thickness and spin-orbit effects strongly interfere.

Spherical nuclei ratios increase in weakly bound nuclei.

Abstract

We study the prolate-shape predominance of the nuclear ground-state deformation by calculating the masses of more than two thousand even-even nuclei using the Strutinsky method, modified by Kruppa, and improved by us. The influences of the surface thickness of the single-particle potentials, the strength of the spin-orbit potential, and the pairing correlations are investigated by varying the parameters of the Woods-Saxon potential and the pairing interaction. The strong interference between the effects of the surface thickness and the spin-orbit potential is confirmed to persist for six sets of the Woods-Saxon potential parameters. The observed behavior of the ratios of prolate, oblate, and spherical nuclei versus potential parameters are rather different in different mass regions. It is also found that the ratio of spherical nuclei increases for weakly bound unstable nuclei. Differences of the results from the calculations with the Nilsson potential are described in detail.