Ab initio calculations of Gamow-Teller strengths in the $sd$ shell

In the present work we perform a systematic shell-model study of Gamow-Teller transition-strength distributions in $sd$ shell nuclei using ab initio effective interactions. The ab initio effective interactions are based on in-medium similarity renormalization-group and coupled-cluster effective interaction approaches. The aim of the present work is to test the predictive power of ab initio effective interactions by using the available experimental data of Gamow-Teller strength distributions in $sd$ shell nuclei. We perform calculations for ${}^{20}\mathrm{Ne}\to {}^{20}\mathrm{F}$, ${}^{23}\mathrm{Na}\to {}^{23}\mathrm{Mg}$, ${}^{23}\mathrm{Na}\to {}^{23}\mathrm{Ne}$, ${}^{24}\mathrm{Mg}\to {}^{24}\mathrm{Na}$, ${}^{24}\mathrm{Mg}\to {}^{24}\mathrm{Al}$, ${}^{25}\mathrm{Mg}\to {}^{25}\mathrm{Al}$, ${}^{26}\mathrm{Mg}\to {}^{26}\mathrm{Na}$, ${}^{26}\mathrm{Mg}\to {}^{26}\mathrm{Al}$, ${}^{26}\mathrm{Si}\to {}^{26}\mathrm{Al}$, ${}^{27}\mathrm{Al}\to {}^{27}\mathrm{Si}$, ${}^{28}\mathrm{Si}\to {}^{28}\mathrm{P}$, ${}^{31}\mathrm{P}\to {}^{31}\mathrm{Si}$, and ${}^{32}\mathrm{S}\to {}^{32}\mathrm{P}$ transitions. For comparison we also show the results obtained by using the phenomenological USDB Hamiltonian. The phenomenological USDB results of the Gamow-Teller (${\mathrm{GT}}_{+}$ and ${\mathrm{GT}}_{-}$) strength distributions show reasonable agreements with the experimental data in comparison with the ab initio interactions. We also calculate the electron-capture reaction rates for ${}^{23}\mathrm{Na}(e^{-},\nu ){}^{23}\mathrm{Ne}$ and ${}^{25}\mathrm{Mg}(e^{-},\nu ){}^{25}\mathrm{Na}$ using ab initio and USDB interactions.

Figure 1

The calculated value of quenching factor for GT transitions in $T=1/2sd$ shell mirror nuclei with $A=17\text{–}39$ ($A=17\text{–}33$) using CCEI and USDB (IM-SRG) effective interactions.

Figure 2

Comparison of the experimental and theoretical $B\left(GT\right)$ distributions for ${}^{20}\mathrm{Ne}\to {}^{20}\mathrm{F}$.

Figure 3

Comparison of the experimental and theoretical $B\left(GT\right)$ distributions for ${}^{23}\mathrm{Na}\to {}^{23}\mathrm{Mg}$.

Figure 4

Comparison of experimental and theoretical $B\left(GT\right)$ distributions for ${}^{23}\mathrm{Na}\to {}^{23}\mathrm{Ne}$.

Figure 5

Comparison of experimental and theoretical $B\left(GT\right)$ distributions for ${}^{24}\mathrm{Mg}\to {}^{24}\mathrm{Na}$.

Figure 6

Comparison of the experimental and theoretical $B\left(GT\right)$ distributions for ${}^{24}\mathrm{Mg}\to {}^{24}\mathrm{Al}$.

Figure 7

Comparison of experimental and theoretical $B\left(GT\right)$ distributions for ${}^{25}\mathrm{Mg}\to {}^{25}\mathrm{Al}$.

Figure 8

Comparison of experimental and theoretical $B\left(GT\right)$ distributions for ${}^{26}\mathrm{Mg}\to {}^{26}\mathrm{Na}$.

Figure 9

Comparison of experimental and theoretical $B\left(GT\right)$ distributions for ${}^{26}\mathrm{Mg}\to {}^{26}\mathrm{Al}$.

Figure 10

Comparison of experimental and theoretical $B\left(GT\right)$ distributions for ${}^{26}\mathrm{Si}\to {}^{26}\mathrm{Al}$.

Figure 11

Comparison of experimental and theoretical $B\left(GT\right)$ distributions for ${}^{27}\mathrm{Al}\to {}^{27}\mathrm{Si}$.

Figure 12

Comparison of experimental and theoretical $B\left(GT\right)$ distributions for ${}^{28}\mathrm{Si}\to {}^{28}\mathrm{P}$.

Figure 13

Comparison of experimental and theoretical $B\left(GT\right)$ distributions for ${}^{31}\mathrm{P}\to {}^{31}\mathrm{Si}$.

Figure 14

Comparison of experimental and theoretical $B\left(GT\right)$ distributions for ${}^{32}\mathrm{S}\to {}^{32}\mathrm{P}$.

Figure 15

Calculated electron-capture rates on ${}^{23}\mathrm{Na}$ obtained by shell-model calculations with different effective interactions.

Figure 16

Calculated electron-capture rates on ${}^{25}\mathrm{Mg}$ obtained by shell-model calculations with different effective interactions.