The role of spin-orbit potential in nuclear prolate-shape dominance

It is confirmed, in terms of the Woods-Saxon-Strutinsky method, that the spin-orbit potential plays a decisive role in the predominance of prolate deformation, which has been a long standing problem in nuclear physics. It is originated from the combined effects of the spin-orbit coupling and the diffused surface of the potential, in agreement with the previous work based on a more schematic Nilsson-Strutinsky method. The degree of prolate-shape dominance exhibits an oscillatory behavior with respect to the strength of spin-orbit potential and, the prolate-shape dominance is realized at the proper strength of the spin-orbit potential together with the standard surface diffuseness; this oscillatory behavior disappears in case of small diffuseness corresponding to ellipsoidal cavity. The calculated energy differences between oblate and prolate minima in this Letter are consistent with those of our extensive self-consistent calculations of the Hartree-Fock + BCS method with the Skyrme interaction.