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

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

Figure 1

Spectra of ${}^6\mathrm{Li}$, ${}^{10}\mathrm{B}$, and ${}^{14}\mathrm{N}$ calculated by $T\beta \gamma$-AMD+GCM and those of the experimental data [22, 23, 24].

Figure 2

The colored contours show two-nucleon-pair density ${\rho }_{NN}\left(\mathit{r}\right)$ of (a)${}^6\mathrm{He}\left(0_1{}^{+}1\right)$, (b)${}^{10}\mathrm{Be}\left(0_1{}^{+}1\right)$, (c)${}^{14}\mathrm{C}\left(0_1{}^{+}1\right)$, (d)${}^6\mathrm{Li}\left(1_1{}^{+}0\right)$, (e)${}^{10}\mathrm{B}\left(1_1{}^{+}0\right)$, and (f)${}^{14}\mathrm{N}\left(1_2{}^{+}0\right)$. The blue contours show the one-body density distribution $\rho \left(\mathit{r}\right)$.

Figure 3

GT transitions ${}^6\mathrm{He}\to {}^6\mathrm{Li}$, ${}^{10}\mathrm{Be}\to {}^{10}\mathrm{B}$, and ${}^{14}\mathrm{C}\to {}^{14}\mathrm{N}$ calculated by $T\beta \gamma$-AMD+GCM.