Implications of the Ca − 36 S 36 and Ca − 38 Ar 38 difference in mirror charge radii on the neutron matter equation of state

Charge radii of the unstable $^{36}$Ca and $^{38}$Ca nuclei were recently determined and used to compute differences in charge radii between mirror nuclei $ \Delta R_{{}\rm ch} $ for the $^{36}$Ca-$^{36}$S and $^{38}$Ca-$^{38}$Ar mirror pairs. Given the correlation between $ \Delta R_{\rm ch} $ and the slope of the symmetry energy $ L $ at the nuclear saturation density, we deduce $ L = 5-70 $ MeV, which rules out a large fraction of models that predict a ``stiff" equation of state. This is the most precise determination of $L$ in this model based on electromagnetic probes of nuclear ground states. The determined range is consistent with earlier analyses from both laboratory experiments and astrophysical observations, including the recent detection of gravitational waves from the merger of two neutron stars.