Shell model study of isobaric analog states for $T_z= \pm 2$ nuclei using isospin non-conserving interactions

In order to comprehend the process underlying mirror energy differences in mirror pairs, we have performed shell-model calculations for $T_z= \pm 2$ $sd$-shell nuclei in the mass range $A$= 20 to 36 and neutron number varying from $N$= 8 to 20. Isospin-symmetry breaking (ISB) is responsible for the mirror energy difference of excited states. We have investigated the {\color{black}isospin non-conserving} interactions: USDC and USDCm to explore the low-lying energy spectra, mirror energy differences, isoscalar ($M_0$), isovector ($M_1$) matrix elements, \textit{E2} transition probability, magnetic ($\mu$), and quadrupole moments ($Q$) of mirror-pair and compared them with their available experimental data. The impact of single-particle states on weakly bound and unbound nuclear states are investigated, especially those of the $s$-wave. We have also analyzed single proton/neutron separation energies and proton/neutron occupancy for ($T_z$=-2)/($T_z$=+2) $sd$-shell nuclei.