Low-energy Gamow-Teller transitions in deformed $N=Z$ odd-odd nuclei

We investigated the Gamow-Teller (GT) transitions from ${}^{22}\mathrm{Ne}$ to ${}^{22}\mathrm{Na}$ by applying the isospin projected antisymmetrized molecular dynamics combined with the generator coordinate method. We found that the GT strength from ${}^{A}Z\left(J^{\pi }T\right)={}^{22}\mathrm{Ne}\left(0_1^{+}1\right)$ is fragmented into two final states ${}^{22}\mathrm{Na}\left(1_{1,2}^{+}0\right)$, which belong to $K=0$ and $K=1$ bands constructed by a prolately deformed ${}^{20}\mathrm{Ne}$ core with an $S=1$ proton-neutron ($pn$) pair. Coupling of the intrinsic spin of the $pn$ pair with the core deformation plays an important role in the GT fragmentation. The symmetry breaking in the intrinsic-spin rotation leads to the $\text{SU}\left(4\right)$ symmetry breaking of the $NN$ pair and causes the GT fragmentation. We compare the features of the GT transitions with those for ${}^{10}\mathrm{Be}\to {}^{10}\mathrm{B}$ and discuss the link between the $\text{SU}\left(4\right)$ symmetry and the GT fragmentation in deformed systems.

Figure 1

The low-lying spectra of ${}^{22}\mathrm{Na}$ in the $T=0$, $K=0,1,3$ bands. Calculated and experimental spectra are shown on the left and right, respectively. The experimental data are taken from [5].

Figure 2

The low-lying spectra of ${}^{22}\mathrm{Na}$ in the $T=1$, $K=0,2$ bands. For each band, calculated and experimental spectra are shown on the left and right, respectively. The experimental data are taken from [5].

Figure 3

The low-lying spectra of ${}^{22}\mathrm{Ne}$ in the $K=0,2$ bands. For each band, calculated and experimental spectra are shown on the left and right, respectively. The experimental data are taken from [5].

Figure 4

The GT transitions $K=2\to K=3$ with large $B\left(\mathrm{GT}\right)$ values are shown with solid arrows. The energy is measured from each ground state.

Figure 5

The spectra of initial and final states in ${}^{10}\mathrm{Be}\to {}^{10}\mathrm{B}(T=0)$. The energy is measured from each ground state. The states having large $B\left(\mathrm{GT}\right)$ are connected by arrows.

Figure 6

The two-nucleon-pair density ${\rho }_{NN}\left(\mathit{r}\right)$ of (a) ${}^{10}\mathrm{Be}\left(0_1^{+}1\right)$, (b) ${}^{22}\mathrm{Ne}\left(0_1^{+}1\right)$, (c) ${}^{10}\mathrm{B}\left(1_1^{+}0\right)$, (d) ${}^{22}\mathrm{Na}\left(1_1^{+}0\right)$, and (e) ${}^{22}\mathrm{Na}\left(1_2^{+}0\right)$. The one-body density distribution $\rho \left(r\right)$ is also shown by (blue) solid contour lines.

Figure 7

The spectra of initial and final states in ${}^{22}\mathrm{Ne}\to {}^{22}\mathrm{Na}(T=0)$. The energy is measured from each ground state. The states having large $B\left(\mathrm{GT}\right)$ are connected by arrows. The solid arrows are $K=0\to K=0$ transitions and the dashed arrows are $K=0\to K=1$ ones.

Figure 8

The $B\left(\mathrm{GT}\right)$ spectra obtained by calculations with the modified spin-orbit strengths with $\lambda =0.0,0.5,1.0,1.5,2.0$. $\lambda =1.0$ corresponds to the default strength. Each spectrum is smeared by a Gaussian with $\sigma =0.4$ so as to normalize the peak hight to the $B\left(\mathrm{GT}\right)$ value for the case of an isolated peak. For each $\lambda$, the energies are measured from ${}^{22}\mathrm{Na}\left(3_1^{+}0\right)$ and ${}^{10}\mathrm{B}\left(3_1^{+}0\right)$, respectively. The left and right panels show $B(\mathrm{GT};{}^{22}\mathrm{Ne}\to {}^{22}\mathrm{Na})$ and $B(\mathrm{GT};{}^{10}\mathrm{Be}\to {}^{10}\mathrm{B})$, respectively.