# Gamow-Teller transitions and proton-neutron pair correlation in $N=Z=$ odd $p$-shell nuclei

## TL;DR

This study investigates Gamow-Teller transitions in odd $p$-shell nuclei with $N=Z$ using advanced nuclear models, revealing dominant neutron-neutron and proton-neutron pair correlations and their role in transition strengths.

## Contribution

It introduces a detailed microscopic analysis of GT transitions in $p$-shell nuclei, highlighting the role of $nn$ and $pn$ pairs and providing insights into spin-isospin partner states.

## Key findings

- GT strengths exceed 50% of the sum rule for key transitions.
- Transitions involve $nn$ and $pn$ pairs with specific spin-isospin configurations.
- GT transitions serve as probes for identifying spin-isospin partner states.

## Abstract

We have studied the Gamow-Teller (GT) transitions from $N=Z+2$ neighbors to $N=Z=$ odd nuclei in $p$-shell region by using isospin-projected and $\beta\gamma$-constraint antisymmetrized molecular dynamics combined with generator coordinate method. The calculated GT transition strengths from $0^+1$ states to $1^+0$ states such as ${}^{6} \textrm{He}(0_1^+1)\rightarrow{}^{6} \textrm{Li}(1_1^+0)$, ${}^{10} \textrm{Be}(0_1^+1)\rightarrow{}^{10} \textrm{B}(1_1^+0)$, and ${}^{14} \textrm{C}(0_1^+1)\rightarrow{}^{14} \textrm{N}(1_2^+0)$ exhaust more than 50\% of the sum rule. These $N=Z+2$ initial states and $N=Z=$ odd final states are found to dominantly have $S=0,T=1$ $nn$ pairs and $S=1,T=0$ $pn$ pairs, respectively. Based on two-nucleon ($NN$) pair picture, we can understand the concentration of the GT strengths as the spin-isospin-flip transition $nn(S=0,T=1)\rightarrow pn(S=1,T=0)$ in $LS$-coupling scheme. The GT transition can be a good probe to identify the spin-isospin partner states with $nn$ pairs and $pn$ pairs of $N=Z+2$ and $N=Z=$ odd nuclei, respectively.