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(Sn)of a neutron-rich nucleus is proportional to the difference between the proton radii of mirror nuclei(R_(p)^(mir)).This indicates that Sn 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 Sn and R_(p)^(mir) is studied 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.