Independent nucleon-pair motion and homologous structure in nuclei withA∼150

Abstract

Shell model calculations are carried out for nuclei with $148<~A<~152$ assuming ${}_{64}^{146}{\mathrm{Gd}}_{82}$ as an inert core. A weak coupling scheme is used to analyze the experimental data and the calculated results. The essential role of the proton intruder state $\ensuremath{\pi}{h}_{11/2},$ the large energy gaps between the neutron single-particle states $\ensuremath{\nu}{f}_{7/2}$ and the others, and the weak proton-neutron interaction provide a simple and interesting picture for the spectra and wave functions, i.e., the independent nucleon-pair motion and the corresponding homologous structure. The proton pairs in $\ensuremath{\pi}{h}_{11/2},$ $\ensuremath{\pi}{d}_{3/2},$ and $\ensuremath{\pi}{s}_{1/2}$ orbitals and the neutron pair in $\ensuremath{\nu}{f}_{7/2}$ or $\ensuremath{\nu}{f}_{7/2}{h}_{9/2}$ orbitals in nuclei ${}_{68}^{150,152}{\mathrm{Er}}_{82,84}$ and ${}_{66}^{150}{\mathrm{Dy}}_{84}$ are moving almost independently in the mean field provided by the core. Therefore, the yrast states below 5.3 MeV of these nuclei can be finely explained as the compositions of the excitations of these independent nucleon pairs. The negative parity levels of nuclei ${}_{66}^{149}{\mathrm{Dy}}_{83},$ ${}_{65}^{149}{\mathrm{Tb}}_{84},$ ${}_{67}^{151}{\mathrm{Ho}}_{84},$ and ${}_{69}^{153}{\mathrm{Tm}}_{84}$ can be well interpreted in terms of the concept of homologous states, i.e., the level structures in nuclei ${}_{66}^{149}{\mathrm{Dy}}_{83},$ ${}_{65}^{149}{\mathrm{Tb}}_{84},$ ${}_{67}^{151}{\mathrm{Ho}}_{84},$ and ${}_{69}^{153}{\mathrm{Tm}}_{84}$ are homologous to those of the parent structure in nuclei ${}_{66}^{148}{\mathrm{Dy}}_{82},$ ${}_{64}^{148}{\mathrm{Gd}}_{84},$ ${}_{66}^{150}{\mathrm{Dy}}_{84},$ and ${}_{68}^{152}{\mathrm{Er}}_{84},$ respectively. The level structure of the nucleus ${}_{68}^{151}{\mathrm{Er}}_{83},$ homologous to that of parent states in the nucleus ${}_{68}^{150}{\mathrm{Er}}_{82},$ is predicted and quite impressive in our full shell model calculation. This desires experiments to verify. The conditions for the onset of the independent nucleon-pair motion and the homologous structure are discussed in detail.