Correlation between the charge radii difference in mirror partner nuclei and the symmetry energy slope

Abstract

A correlation between the charge radii difference of mirror partner nuclei $\Delta{R_{\mathrm{ch}}}$ and the slope parameter $L$ of symmetry energy has been built to ascertain the equation of state of isospin asymmetric nuclear matter. In this work, the influences of pairing correlations and isoscalar compression modulus on the $\Delta{R_{\mathrm{ch}}}$ are systematically investigated based on the Skyrme energy density functional theory. The calculated results suggest that the linear correlation between $\Delta{R_{\mathrm{ch}}}$ and $L$ is decreased by the surface pairing correlations. The slope parameter deduced from the difference of charge radii of mirror-pair nuclei $^{32}$Ar-$^{32}$Si, $^{36}$Ca-$^{36}$S, $^{38}$Ca-$^{38}$Ar, and $^{54}$Ni-$^{54}$Fe falls into the range of $L$=42.57-50.64 MeV, that is, the rather soft equation of state of asymmetric nuclear matter. Besides, the range of the slope parameter can also be influenced by the effective forces classified by various isoscalar incompressibility coefficients.