Pair correlations in low-lying T=0 states of odd-odd nuclei with six nucleons

Abstract

In this paper, we study pair correlations in low-lying $T=0$ states for two typical cases of odd-odd $N=Z$ nuclei. The first case is six nucleons in a single $j=9/2$ shell, for which we study the $S$-broken-pair approximation, the isoscalar spin-1 pair condensation, and the isoscalar spin-aligned pair condensation, with schematic interactions. In the second case, we study pair approximations and correlation energies for $^{22}\mathrm{Na}$, $^{34}\mathrm{Cl}$, $^{46}\mathrm{V}$, $^{62}\mathrm{Ga}$, and $^{94}\mathrm{Ag}$ in multi-$j$ shells with effective interactions. A few $T=0$ states are found to be well represented by isoscalar nucleon pairs. The isoscalar spin-aligned pairs play an important role for the yrast $T=0$ states with $I\ensuremath{\sim}2j$ and $I\ensuremath{\sim}{I}_{\mathrm{max}}$ in $^{22}\mathrm{Na}$, $^{46}\mathrm{V}$, and $^{94}\mathrm{Ag}$. The overlap between the isoscalar $\mathcal{J}=1$ pair wave function and the shell-model wave function is around 0.5 for the $I=1,3$ states of $^{34}\mathrm{Cl}$ and the $I=1$ state of $^{94}\mathrm{Ag}$. The $I=9$ state of $^{62}\mathrm{Ga}$ is very well described by the isoscalar $\mathcal{J}=3$ pair condensation. The broken-pair approximation (which is similar to the 2-quasiparticle excitation of the isovector pair condensation) is appropriate for quite few states, such as the $I=1\ensuremath{-}3$ states of $^{34}\mathrm{Cl}$ and the $I=5$ state of $^{62}\mathrm{Ga}$. The correlation energies are presented in this paper. It is noted that the picture based on nucleon-pair wave functions is not always in agreement with the picture based on correlation energies.