Nuclear prolate-shape dominance with the Woods-Saxon potential

We study the prolate-shape predominance of the nuclear ground-state deformation by calculating the masses of more than 2000 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 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. The ratio of spherical nuclei is found to increase for weakly bound unstable nuclei. Differences from the results of calculations performed using the Nilsson potential are described in detail.