Prolate dominance of nuclear shape caused by a strong interference between the effects of spin-orbit andl2terms of the Nilsson potential

Abstract

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 ratio of prolate nuclei is 86% with the standard strengths corresponding to the actual atomic nuclei. By weakening the spin-orbit potential, the ratio oscillates strongly, having a local minimum value of 45% with a half of the standard strength and a local maximum value of 78% without the spin-orbit potential.

Multi-quasiparticle excitation: Extending shape coexistence inA~190neutron-deficient nuclei

“…Compared to prolate shape, it is rare for nuclei to have oblate deformation. The importance of oblate shapes is not only due to their rare occurrence, but also because the small number of oblate shapes may have a direct link to the detailed form of the mean-field potential [22,23]. The observation of a region of nuclei with stable oblate shapes would thus form an interesting testing ground for various mean-field models.…”

Many-body approximations in thesd-shell “sandbox”

“…One observes the well known region of strongly prolate nuclei near 24 Mg. 28 Si is the most strongly oblately deformed, and there is an island of weak oblate deformation around 31 Si. It would be interesting to use our sd-shell sandbox to clarify the general question of why most nuclei are prolate deformed [8], by exploring the HFP results with different (but realistic) Hamiltonians.…”

“…• Solve the HF variational equation (8) and get the single-particle spectrum (φ ν , ǫ ν ), in general corresponding to a deformed field…”

Quantal rotation and its coupling to intrinsic motion in nuclei

“…However, it is more difficult to explain the fact that most nuclei have the prolate shape, not the oblate shape. There have been a number of works on this issue [26,27,28,29]. According to the classical periodic orbits, a recent analysis sheds new light on the prolate dominance in nuclei [30].…”

“…Note that the R-conjugate terms should be added in the right hand side of equation (27) when the R invariance is present [40].…”