$Ab~initio$ calculations for Gamow-Teller strengths in $sd$ 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 (IM-SRG) and coupled-cluster effective interaction (CCEI) 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 $^{20}$Ne $\rightarrow$ $^{20}$F, $^{23}$Na $\rightarrow$ $^{23}$Mg, $^{23}$Na $\rightarrow$ $^{23}$Ne, $^{24}$Mg $\rightarrow$ $^{24}$Na, $^{24}$Mg $\rightarrow$ $^{24}$Al, $^{25}$Mg $\rightarrow$ $^{25}$Al, $^{26}$Mg $\rightarrow$ $^{26}$Na, $^{26}$Mg $\rightarrow$ $^{26}$Al, $^{26}$Si $\rightarrow$ $^{26}$Al, $^{27}$Al $\rightarrow$ $^{27}$Si, $^{28}$Si $\rightarrow$ $^{28}$P, $^{31}$P $\rightarrow$ $^{31}$Si, and $^{32}$S $\rightarrow$ $^{32}$P transitions. For comparison we also show the results obtained by using the phenomenological USDB Hamiltonian. The phenomenological USDB results of the Gamow-Teller (GT$_+$/GT$_-$) strength distributions show reasonable agreements with the experimental data in comparison to the $ab~initio$ interactions. We also calculate the electron capture reaction rates for $^{23}$Na(e$^-$, $\nu$)$^{23}$Ne and $^{25}$Mg(e$^-$, $\nu$)$^{25}$Na using $ab~initio$ and USDB interactions.