Nuclear structure properties of Si and P isotopes with the microscopic effective interactions

In the present work, we have reported comprehensive study of the $sd$-shell nuclei Si and P with neutron number varying from $N = 9$ to $N = 20$ using the microscopic effective valence shell interactions, namely, N3LO, JISP16 and DJ16A. These effective $sd$-shell interactions are developed using the \textit{ab initio} no-core shell model wave functions and the Okubo-Lee-Suzuki transformation method. For comparison, we have also performed shell model calculations with the empirical USDB interaction. Energy spectra and electromagnetic properties of these isotopic chains have been studied. Theoretically calculated shell model results are compared with the available experimental data, to check the predictive strength of these microscopic interactions. It is found that the binding energies of the ground states are better reproduced with the DJ16A interaction as compared to other microscopic interactions and a proton subshell closure at $Z=14$ is obtained in Si. Spin-tensor decomposition of two-body interaction is presented to understand the contributions from central, vector and tensor components into these interactions. Spectroscopic strengths of $^{23}$Al($d$,$n$)$^{24}$Si are examined for the newly performed experiment at NSCL.