  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.
