Prolate dominance of nuclear shape caused by a strong interference between the effects of spin-orbit and l 2 terms of the Nilsson potential

The origin of the dominance of prolate shapes over oblate ones of the ground states of atomic nuclei is investigated with the Nilsson-Strutinsky method. The number of prolate nuclei among all the deformed even-even nuclei is calculated as a function of the strengths of the spin-orbit and the ${l}^{2}$ terms of the Nilsson potential. The latter simulates a square-well-like radial profile of the mean potential. The proportion of prolate nuclei is 86% with the standard strengths corresponding to the actual atomic nuclei. By weakening the spin-orbit potential, the proportion oscillates strongly, having a local minimum value of 42% with about half of the standard strength and a local maximum value of 79% without the spin-orbit potential.