Effective valence proton numbers for nuclei withZ∼64

Abstract

The subshell effect for nuclei with proton number $Z\ensuremath{\sim}$ 64 has been known for many years. The most economic way to consider this effect is to use the effective valence proton number. In this Brief Report we extract effective valence proton numbers for nuclei in this region by using the systematics of the first ${2}^{+}$ energies (${E}_{{2}_{1}^{+}}$) of even-even nuclei, the ratios of the first ${4}^{+}$ and ${6}^{+}$ state energies with respect to ${E}_{{2}_{1}^{+}}$ (${R}_{4}$ and ${R}_{6}$), the $B(E2)$ values, the quadrupole deformation parameters ${e}_{2}$, and anomalous $g$ factors of the ${2}_{1}^{+}$ state for even-even nuclei. It is noticed that these physical quantities saturate when ${N}_{\mathrm{p}}{N}_{\mathrm{n}}$, the product of the valence proton number and the valence neutron number, is large enough; on the other hand, they go to saturation at different ``speeds.'' We show that the subshell effect is more evident for ${E}_{{2}_{1}^{+}}$ and yrast state energy ratios (${R}_{4}$ and ${R}_{6}$), and relatively less for other quantities.