Study of $\beta^- $ decays for sd model space with Shell model

This paper investigates the beta decay of nuclei within the sd model space, encompassing the $0d_{3/2}$, $0d_{5/2}$, and $1s_{1/2}$ shells. We comprehensively analyze their decay characteristics, including the half-life, $logft$ value, Q value, branching ratio, B(GT) value, M(GT), and R(GT) value. These results are compared with experimental data from Z = 8-19 nuclei, employing the nuclear shell model framework. The calculations are performed using the USDB\cite{usdb} interaction, which is well-suited for nuclei with active valence nucleons in the $0d_{3/2}$, $0d_{5/2}$, and $1s_{1/2}$ shells. The study offers valuable insights into the beta decay properties of these nuclei and contributes to our understanding of the nuclear shell structure.}