In this study, we calculated the binding energy of nuclei, which holds atomic nuclei together, by utilizing electron scattering transformations in the shell model to explore the nuclear structure for proton-rich pairs of mirror nuclei: 34Ca-34Si, 0Ca-35P, 36Ca-36S, and 37Ca-37Cl. The proton envelope that surrounds the proton-rich nucleus explains why the nucleus charge and its mirror image have different radii. The wave functions for single particles were adopted from the Skyrme-Hartree-Fock approximation and Wood-Saxon potential to compute the mirror radii, mirror charge radii, and skin thickness for protons and neutrons. It was noted that the results depend on the mass numbers of the mirror nuclei and the types of wave functions. Additionally, the displacement energy of the mirror nuclei was calculated, and a mathematical relationship was found linking it with the variance in mirror charge radii. The calculated results were compared with the available practical values, where they were found to agree with the experimental data.
Hassan et al. (Mon,) studied this question.