Nucleon-pair states of even-evenN=82isotones

Abstract

In this paper we study low-lying states of five $N=82$ isotones, $^{134}\mathrm{Te}, ^{136}\mathrm{Xe}, ^{138}\mathrm{Ba}, ^{140}\mathrm{Ce}$ and $^{142}\mathrm{Nd}$, within the framework of the nucleon-pair approximation (NPA). For the low-lying yrast states of $^{136}\mathrm{Xe}$ and $^{138}\mathrm{Ba}$, we calculate the overlaps between the wave functions obtained in the full shell-model (SM) space and those obtained in the truncated NPA space, and find that most of these overlaps are very close to 1. Very interestingly and surprisingly, for most of these yrast states, the SM wave functions are found to be well approximated by one-dimensional, optimized pair basis states, which indicates a simple picture of ``nucleon-pair states''. The positive-parity yrast states with spin $Jg6$ in these nuclei, as well as the ${8}_{2}^{+}$ state, are found to be well described by breaking one or two $S$ pair(s) of the ${6}_{1}^{+}$ or ${6}_{2}^{+}$ state (low-lying, seniority-two, spin-maximum, and positive-parity); similarly, negative-parity yrast states with spin $Jg9$ are well represented by breaking one or two $S$ pair(s) of the ${9}_{1}^{\ensuremath{-}}$ state (low-lying, seniority-two, spin-maximum, and negative-parity). It is shown that the low-lying negative-parity yrast states of $^{136}\mathrm{Xe}$ and $^{138}\mathrm{Ba}$ are reasonably described to be one-octupole-phonon excited states. The evolution of the ${6}_{1}^{+}$ and ${6}_{2}^{+}$ states for the five isotones are also systematically investigated.