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

TL;DR

This study uses ab initio calculations to investigate how mirror charge radii relate to neutron-skin thickness and symmetry energy slope, revealing correlations in some nuclei but not others, challenging previous assumptions.

Contribution

It provides the first comprehensive ab initio analysis of mirror charge radii correlations with symmetry energy parameters across multiple nuclei, with rigorous uncertainty quantification.

Findings

Correlation between mirror charge radii difference and symmetry energy slope in fp-shell nuclei.

No correlation found in sd-shell mirror pairs, contrary to previous expectations.

Quantitative assessment of uncertainties from chiral interactions and many-body methods.

Abstract

It has recently been suggested that differences in the charge radii of mirror nuclei ($\Delta R^{\rm mirr}_{\rm ch}$) are strongly correlated with the neutron-skin thickness ($R_{\rm skin}$) of neutron-rich nuclei and with the slope of the symmetry energy ($L$). To test this assumption, we present ab initio calculations of $R_{\rm skin}$ in $^{48}$Ca and $^{208}$Pb, $\Delta R^{\rm mirr}_{\rm ch}$ 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 $\Delta R^{\rm mirr}_{\rm ch}$, $R_{\rm skin}$ 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 $\Delta R^{\rm mirr}_{\rm ch}-L$ 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 $\Delta R^{\rm mirr}_{\rm ch}-L$ correlation.