Nucleon-pair states of even-even Sn isotopes based on realistic effective interactions

Abstract

In this paper we study yrast states of $^{128,126,124}\mathrm{Sn}$ and $^{104,106,108}\mathrm{Sn}$ by using the monopole-optimized realistic interactions in terms of both the shell model (SM) and the nucleon-pair approximation (NPA). For yrast states of $^{128,126}\mathrm{Sn}$ and $^{104,106}\mathrm{Sn}$, we calculate the overlaps between the wave functions obtained in the full SM space and those obtained in the truncated NPA space, and find that most of these overlaps are very close to 1. Very interestingly, for most of these states with positive parity and even spin or with negative parity and odd spin, the SM wave function is found to be well represented by one nucleon-pair basis state, viz., a simple picture of ``nucleon-pair states'' (nucleon-pair configuration without mixings) emerges. In $^{128,126}\mathrm{Sn}$, the positive-parity (or negative-parity) yrast states with spin $J>10$ (or $J>7$) are found to be well described by breaking one or two $S$ pairs in the ${10}_{1}^{+}$ (or ${7}_{1}^{\ensuremath{-}}$) state, i.e., the yrast state of seniority-two, spin-maximum, and positive-parity (or negative-parity), into non-$S$ pair(s). Similar regularity is also pointed out for $^{104,106}\mathrm{Sn}$. The evolution of $E2$ transition rates between low-lying states in $^{128,126,124}\mathrm{Sn}$ is discussed in terms of the seniority scheme.