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

TL;DR

This study uses Bayesian inference to analyze how nuclear models can simultaneously fit weak charge distributions, binding energies, and charge radii of calcium and lead isotopes, revealing key parameters influencing neutron skin predictions.

Contribution

It identifies the roles of symmetry energy and isovector spin-orbit coefficients in determining weak form factor differences, providing new insights into model parameter sensitivities post-PREX and CREX measurements.

Findings

S_V and b'_4 influence ΔF predictions.

Bayesian inference separates S_V and L effects.

Models show tension between weak charge data and other nuclear properties.

Abstract

New measurements of the weak charge density distributions of $^{48}$Ca and $^{208}$Pb 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 electric and weak form factors, $\Delta F=F_{ch}-F_{W}$, in $^{48}$Ca and $^{208}$Pb. We show, for the first time, which aspects of mean-field models 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-2/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 $\Delta F$ of $^{48}$Ca and $^{208}$Pb. Consequently, adjusting $S_V$ or $b'_4$ shifts predicted $\Delta F$ values toward or away from PREX-2/CREX measurements. Additionally, $S_V$ and the slope L are marginally correlated given the prior constraints of our Bayesian inference, allowing us to infer them separately from PREX-2/CREX data.