Ab initio computations of the fourth-order charge density moments of ${}^{48}$Ca and ${}^{208}$Pb

Neutron skins of neutron-rich nuclei connect nuclei with the matter in neutron stars. High-precision measurements of nuclear charge densities to extract higher-order moments are proposed to be sensitive to neutron radii and skin thicknesses. We investigate the charge density of ${}^{48}$Ca and ${}^{208}$Pb, leading candidates for such studies, with ab initio nuclear structure calculations. We find strong correlations between the fourth-order charge density moment $R_{\mathrm{c}\mathrm{h}}^4$ and the charge and neutron radii, allowing us to predict $R_{\mathrm{c}\mathrm{h}}^4$ for ${}^{48}$Ca and ${}^{208}$Pb. We find a substantially weaker correlation between the fourth-order charge density moment and the neutron skin, limiting the ability of high-precision electron scattering to determine the neutron skin in a model-independent manner.