Characterizing the nuclear models informed by PREX and CREX: a view from Bayesian inference

New measurements of the weak charge density distributions of ^48Ca and ^208Pb challenge existing nuclear models. In the post-PREX-CREX era, it is unclear if current models can simultaneously describe weak charge distributions along with accurate measurements of binding energy and charge radii. In this letter, we explore the parameter space of relativistic and non-relativistic models to study the differences between the form factors of the electric and weak charge distributions, Δ F=F_ch-F_w, in ^48Ca and ^208Pb. We show, for the first time, the parts of the mean-field models that are the most important in determining the relative magnitude of the neutron skin in lead and calcium nuclei. We carefully disentangle the tension between the PREX/CREX constraints and the ability of the RMF and Skyrme models to accurately describe binding energies and charge radii. We find that the nuclear symmetry energy coefficient S_V and the isovector spin-orbit coefficient b'_4 play different roles in determining Δ F of ^48Ca and ^208Pb. Consequently, adjusting S_V or b'_4 shifts predicted Δ F values toward or away from PREX/CREX measurements. Additionally, S_V and the slope L are marginally correlated given the constraints of our Bayesian inference, allowing us to infer them separately from PREX and CREX data.