Prolate-Oblate Difference and its Effect on Energy Levels and Quadrupole Moments

Abstract

From the microscopic calculation for the W, Os, and Pt nuclei, we obtain semiquantitative relations among the prolate-oblate difference of the potential energy of deformation, the ${2_{\gamma }}^{+}$ and $4^{+}$ level splitting, and the static quadrupole moment ${Q_2}^{+}$. These relations are applied to ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{110}{}_{}{}^{}\mathrm{Cd}$, and ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$. The important role of the $\beta -\gamma$ dependence of the mass parameters is demonstrated.