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

Abstract

Difference in the charge radii of mirror nuclei $\mathrm{\ensuremath{\Delta}}{R}_{\text{ch}}$ was proposed as a probe to the slope parameter of symmetry energy $L$. However, it has not been studied systematically by different models with pairing effects. In this work, we study the linear correlations between $\mathrm{\ensuremath{\Delta}}{R}_{\text{ch}}$ and $L$ using 36 functionals including Skyrme and covariant models for 16 pairs of spherical or nearly spherical mirror nuclei, while the pairing effects are considered by Bogoliubov transformation. With the consideration of more models, the linear correlations between $\mathrm{\ensuremath{\Delta}}{R}_{\text{ch}}$ and $L$ are weakened. The pairing effects further decrease the correlation. Besides the slope parameter, the curvature of symmetry energy ${K}_{\text{sym}}$ and symmetry energy at nucleon density $0.1\phantom{\rule{0.28em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}\phantom{\rule{4pt}{0ex}}{E}_{\text{sym}}(0.1)$ also play a role in determining $\mathrm{\ensuremath{\Delta}}{R}_{\text{ch}}$. We find $\mathrm{\ensuremath{\Delta}}{R}_{\text{ch}}$ in $^{14}\mathrm{O}\text{\ensuremath{-}}^{14}\mathrm{C},$ $^{22}\mathrm{Si}\text{\ensuremath{-}}^{22}\mathrm{O},$ $^{36}\mathrm{Ca}\text{\ensuremath{-}}^{36}\mathrm{S},$ $^{38}\mathrm{Ca}\text{\ensuremath{-}}^{38}\mathrm{Ar},$ $^{54}\mathrm{Ni}\text{\ensuremath{-}}^{54}\mathrm{Fe},$ $^{58}\mathrm{Zn}\text{\ensuremath{-}}^{58}\mathrm{Ni},$ $^{60}\mathrm{Ge}\text{\ensuremath{-}}^{60}\mathrm{Ni},$ $^{22}\mathrm{Mg}\text{\ensuremath{-}}^{22}\mathrm{Ne},$ and $^{34}\mathrm{Ar}\text{\ensuremath{-}}^{34}\mathrm{S}$ are not suitable to be taken as a probe to study $L$. Taking $^{54}\mathrm{Ni}\text{\ensuremath{-}}^{54}\mathrm{Fe}$ as an example, we find it seems hard to constrain $L$ even with a high experimental accuracy of $\mathrm{\ensuremath{\Delta}}{R}_{\text{ch}}$. However, there is a possibility to provide an upper or lower limit of $L$ from $\mathrm{\ensuremath{\Delta}}{R}_{\text{ch}}$ of mirror pairs $^{44}\mathrm{Cr}\text{\ensuremath{-}}^{44}\mathrm{Ca}$ and $^{46}\mathrm{Fe}\text{\ensuremath{-}}^{46}\mathrm{Ca}$.