Low-lying states of even-even N=80 isotones within the nucleon-pair approximation

Abstract

In this paper we study low-lying states of even-even $N=80$ isotones including $^{130}\mathrm{Sn}, ^{132}\mathrm{Te}, ^{134}\mathrm{Xe}, ^{136}\mathrm{Ba}$, and $^{138}\mathrm{Ce}$, within the nucleon-pair approximation of the shell model. We calculate low-lying energy levels of these nuclei with both positive and negative parities. The wave functions of yrast ${2}_{1}^{+}\ensuremath{-}{10}_{1}^{+}$ states and ${1}_{1}^{\ensuremath{-}}\ensuremath{-}{11}_{1}^{\ensuremath{-}}$ states of these nuclei are analyzed in detail. Our calculations show that most of these states have a very simple structure in nucleon-pair basis: the ${2}_{1}^{+}$ states of $^{132}\mathrm{Te}, ^{134}\mathrm{Xe}, ^{136}\mathrm{Ba}$, and $^{138}\mathrm{Ce}$ are dominated by one ${D}^{+}$ neutron pair and spin $J=2$ proton excitation; the ${4}_{1}^{+}$ and ${6}_{1}^{+}$ states of $^{132}\mathrm{Te}$ and $^{134}\mathrm{Xe}$ are dominated by the proton excitation, while the ${8}_{1}^{+}$ and ${10}_{1}^{+}$ states are dominated by ${S}^{+}$ pairs of protons and one spin-eight and spin-ten pair of valence neutron holes (i.e., seniority-two excitations); for negative-parity states, the lowest states with spin four to seven of $^{132}\mathrm{Te}, ^{134}\mathrm{Xe}, ^{136}\mathrm{Ba}$, and $^{138}\mathrm{Ce}$ are essentially given by ${S}^{+}$ pairs of protons and one broken pair with spin four to seven consists of ${h}_{11/2}{d}_{3/2}$ valence neutron holes. The necessity of $J=10$ pairing interaction in the phenomenological monopole plus quadrupole shell-model Hamiltonian for $N=80$ isotones is demonstrated with analytical formulas for simple nucleon-pair configurations, and the pattern of $g$ factors is discussed based on simple arguments. Our calculated $B(E2)$ transition rates and $g$ factors of the low-lying states are well consistent with the experimental data.