PREPRINT
F935F81A-07FF-4144-88CA-3BB3D46F90F3

# Bayesian Inference of the Symmetry Energy and the Neutron Skin in ${}^{48}$Ca and ${}^{208}$Pb from CREX and PREX-2

Zhen Zhang, Lie-Wen Chen
arXiv:2207.03328

Submitted on 7 July 2022

## Abstract

Using the recent model-independent determination of the charge-weak form factor difference $\mathrm{\Delta }{F}_{\mathrm{C}\mathrm{W}}$ in ${}^{48}$Ca and ${}^{208}$Pb by the CREX and PREX-2 collaborations, we perform Bayesian inference of the symmetry energy ${E}_{\mathrm{s}\mathrm{y}\mathrm{m}}\left(\rho \right)$ and the neutron skin thickness $\mathrm{\Delta }{r}_{\mathrm{n}\mathrm{p}}$ of ${}^{48}$Ca and ${}^{208}$Pb within the Skyrme energy density functional (EDF). We find the inferred ${E}_{\mathrm{s}\mathrm{y}\mathrm{m}}\left(\rho \right)$ and $\mathrm{\Delta }{r}_{\mathrm{n}\mathrm{p}}$ separately from CREX and PREX-2 are compatible with each other at $90\mathrm{%}$ C.L., although they exhibit strong tension at $68.3\mathrm{%}$ C.L. with CREX (PREX-2) favoring a very soft (stiff) ${E}_{\mathrm{s}\mathrm{y}\mathrm{m}}\left(\rho \right)$ and rather small (large) $\mathrm{\Delta }{r}_{\mathrm{n}\mathrm{p}}$. By combining the CREX and PREX-2 data, we obtain ${E}_{\mathrm{s}\mathrm{y}\mathrm{m}}\left({\rho }_{0}\right)={30.2}_{-3.0}^{+4.1}$ MeV, the symmetry energy slope parameter $L={15.3}_{-41.5}^{+46.8}$ MeV at saturation density ${\rho }_{0}$, $\mathrm{\Delta }{r}_{\mathrm{n}\mathrm{p}}{\left(}^{48}\mathrm{C}\mathrm{a}\right)={0.149}_{-0.032}^{+0.035}$ fm and $\mathrm{\Delta }{r}_{\mathrm{n}\mathrm{p}}{\left(}^{208}\mathrm{P}\mathrm{b}\right)={0.139}_{-0.063}^{+0.070}$ fm at $90\mathrm{%}$ C.L.. The ${E}_{\mathrm{s}\mathrm{y}\mathrm{m}}\left(\rho \right)$ and $\mathrm{\Delta }{r}_{\mathrm{n}\mathrm{p}}$ from combining CREX and PREX-2 are closer to the corresponding results from CREX alone, implying the PREX-2 is less effective to constrain the ${E}_{\mathrm{s}\mathrm{y}\mathrm{m}}\left(\rho \right)$ and $\mathrm{\Delta }{r}_{\mathrm{n}\mathrm{p}}$ due to its lower precision of $\mathrm{\Delta }{F}_{\mathrm{C}\mathrm{W}}$. Furthermore, we find the Skyrme EDF results inferred by combining the CREX and PREX-2 data at $90\mathrm{%}$ C.L. nicely agree with the measured dipole polarizabilities ${\alpha }_{D}$ in ${}^{48}$Ca and ${}^{208}$Pb as well as the neutron matter equation of state from microscopic calculations.

## Preprint

Comment: 6 pages, 4 figures, 2 tables

Subjects: Nuclear Theory; Astrophysics - High Energy Astrophysical Phenomena; High Energy Physics - Phenomenology; Nuclear Experiment