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

Abstract

Using the recent model-independent determination of the charge-weak form factor difference $\Delta F_{\mathrm{CW}}$ in ${}^{48}$Ca and ${}^{208}$Pb by the CREX and PREX-2 collaborations together with some well-determined properties of doubly magic nuclei, we perform Bayesian inference of the symmetry energy $E_{\mathrm{sym}}(\rho )$ and the neutron skin thickness $\Delta r_{\mathrm{np}}$ of ${}^{48}$Ca and ${}^{208}$Pb within the Skyrme energy density functional (EDF). We find the inferred $E_{\mathrm{sym}}(\rho )$ and $\Delta r_{\mathrm{np}}$ separately from CREX and PREX-2 are compatible with each other at $90\%$ C.L., although they are inconsistent at $68.3\%$ C.L. with CREX (PREX-2) favoring a very soft (stiff) $E_{\mathrm{sym}}(\rho )$ and rather small (large) $\Delta r_{\mathrm{np}}$. By combining the CREX and PREX-2 data, we obtain a soft symmetry energy around saturation density ${\rho }_0$ and thinner $\Delta r_{\mathrm{np}}$ of ${}^{48}$Ca and ${}^{208}$Pb, which are found to be closer to the corresponding results from CREX alone, implying the PREX-2 is less effective to constrain the $E_{\mathrm{sym}}(\rho )$ and $\Delta r_{\mathrm{np}}$ due to its lower precision of $\Delta F_{\mathrm{CW}}$. Furthermore, we find the Skyrme EDF results inferred by combining the CREX and PREX-2 data 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. The implications of the inferred soft $E_{\mathrm{sym}}(\rho )$ around ${\rho }_0$ are discussed.

Comments: 8 pages, 7 figures, 3 tables. Significantly expanded to include many details and discussions. Accepted version to appear in PRC