Investigation of the relationship between mirror proton radii and neutron-skin thickness

Through systematic investigations using the axially deformed solutions of the Skyrme-Hartree-Fock-Bogoliubov equations with 132 sets of Skyrme interaction parameters, it is confirmed that the neutron-skin thickness (S-n) of a neutron-rich nucleus is proportional to the difference between the proton radii of mirror nuclei (R-p(mir)). This indicates that S-n may be deduced from R-p(mir). Compared with the results of the Skyrme-Hartree-Fock model, pairing effects are found to enhance the correlation for most mirror pairs, whereas deformation effects may weaken the correlation. Furthermore, the correlation between and is studied for isotones with and , Sn R-p(mir) is studies for isotones with N = 20 and N = 28 which reveals a stronger linear correlation with increasing |N - Z|. This result demonstrates that it is possible to extract the neutron-skin thickness of an unstable nucleus from the proton radii difference of the mirror nuclei of its isotones.