How do mirror charge radii constrain density dependence of the symmetry energy?

Abstract

It has recently been suggested that differences in the charge radii of mirror nuclei ($\Delta R_{\mathrm{ch}}^{\mathrm{mirr}}$) are strongly correlated with the neutron-skin thickness ($R_{\mathrm{skin}}$) of neutron-rich nuclei and with the slope of the symmetry energy ($L$). To test this assumption, we present ab initio calculations of $R_{\mathrm{skin}}$ in ${}^{48}$Ca and ${}^{208}$Pb, $\Delta R_{\mathrm{ch}}^{\mathrm{mirr}}$ in ${}^{36}$Ca${-}^{36}$S, ${}^{38}$Ca${-}^{38}$Ar, ${}^{41}$Sc${-}^{41}$Ca, ${}^{48}$Ni${-}^{48}$Ca, ${}^{52}$Ni${-}^{52}$Cr, and ${}^{54}$Ni${-}^{54}$Fe mirror pairs, and $L$. Employing the recently developed 34 chiral interaction samples, identified by the history matching approach, we conduct rigorous statistical analysis of correlations among $\Delta R_{\mathrm{ch}}^{\mathrm{mirr}}$, $R_{\mathrm{skin}}$ and $L$, accounting for quantified uncertainties from low-energy constants of chiral interaction, chiral effective field theory truncation and many-body method approximation. The ab initio results reveal an appreciable $\Delta R_{\mathrm{ch}}^{\mathrm{mirr}}-L$ correlation in $fp$-shell mirror pairs. However, contrary to previous studies, the present calculation finds that the studied $sd$-shell mirror pairs do not exhibit any $\Delta R_{\mathrm{ch}}^{\mathrm{mirr}}-L$ correlation.