Constraining nuclear symmetry energy with the charge radii of mirror-pair nuclei

The nuclear charge radius plays a vital role in determining the equation of state of isospin asymmetric nuclear matter. Based on the correlation between the differences in charge radii of mirror-partner nuclei and the slope parameter ($L$) of symmetry energy at the nuclear saturation density, an analysis of the calibrated slope parameter $L$ was performed in finite nuclei. In this study, relativistic and non-relativistic energy density functionals were employed to constrain the nuclear symmetry energy through the available databases of the mirror-pair nuclei ${}^{36}$Ca-${}^{36}$S, ${}^{38}$Ca-${}^{38}$Ar, and ${}^{54}$Ni-${}^{54}$Fe. The deduced nuclear symmetry energy was located in the range 29.89-31.85 MeV, and $L$ of the symmetry energy essentially covered the range 22.50-51.55 MeV at the saturation density. Moreover, the extracted $L_s$ at the sensitivity density ${\rho }_s=0.10{\mathrm{f}\mathrm{m}}^{-3}$ was located in the interval range 30.52-39.76 MeV.