Study of β+/EC-decay properties of sd shell nuclei using nuclear shell model

Our study employs the nuclear shell model to systematically compute the half-lives of $\beta$-decay for nuclei in the mass range of $A=18-39$, encompassing the majority of $sd$ shell nuclei. This analysis utilizes the USDB and SDNN Hamiltonians. The theoretical outcomes contain calculations of various parameters such as $Q$-values, half-lives, excitation energy, log$ft$ values, and branching ratios. We explore these results with axial–vector coupling constant for weak interactions, denoted as $g_A$ $(=1.27)$, and $\kappa$ value $(=6289)$. We perform calculations of Gamow Teller matrix elements for 116 decay processes to calculate the quenching factor; we found a quenching factor of $q=0.794\pm 0.05$ for the USDB interaction and $q=0.815\pm 0.04$ for the SDNN interaction. We have also calculated superallowed transitions $0^{+}\to 0^{+}$ for seven nuclei. Further, we have also included the electron capture phase space factor for the required nuclei to calculate the half-lives. This inclusion leads to small contribution in results, particularly for nuclei where electron capture (EC) plays a significant role. The overall results are in agreement with the experimental data.