Shell model study of isobaric analog states for |Tz| = 3/2 nuclei using isospin-breaking interactions

Abstract

In mirror nuclei, the mirror energy difference in the excited states is caused by isospin-symmetry breaking. In the present work, the mechanism underlying mirror energy differences in mirror-pair is explored within the shell model formalism. For that, we performed shell-model calculations by focusing on the $T_z=\pm 3/2$ mirror pairs across sd-shell nuclei in the mass range A= 19-37. We used two recently developed USD-family isospin symmetry-breaking interactions, USDC and USDCm, for this purpose to explore low-lying energy spectra and mirror energy differences. The influence of single-particle states, particularly those of the s-wave, on weakly bound and unbound nuclear states was examined. Additionally, we also explored electromagnetic properties such as E2 transition probability, magnetic (μ), and quadrupole moments (Q) of those mirror pairs and compared them with the experimental data. Furthermore, we evaluated the isoscalar ($M_0$) and isovector ($M_1$) matrix elements of the E2 transition probabilities along with calculating the single proton/neutron separation energies. While the calculated results using both these interactions are in good agreement with the experimental data, the USDCm performs better for mirror energy differences.