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

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 $E_{\mathrm{s}\mathrm{y}\mathrm{m}}(\rho )$ 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 $E_{\mathrm{s}\mathrm{y}\mathrm{m}}(\rho )$ 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) $E_{\mathrm{s}\mathrm{y}\mathrm{m}}(\rho )$ and rather small (large) $\mathrm{\Delta }{r}_{\mathrm{n}\mathrm{p}}$. By combining the CREX and PREX-2 data, we obtain $E_{\mathrm{s}\mathrm{y}\mathrm{m}}({\rho }_0)={30.2}_{-3.0}^{+4.1}$ MeV, the symmetry energy slope parameter $L={15.3}_{-41.5}^{+46.8}$ MeV at saturation density ${\rho }_0$, $\mathrm{\Delta }{r}_{\mathrm{n}\mathrm{p}}{(}^{48}\mathrm{C}\mathrm{a})={0.149}_{-0.032}^{+0.035}$ fm and $\mathrm{\Delta }{r}_{\mathrm{n}\mathrm{p}}{(}^{208}\mathrm{P}\mathrm{b})={0.139}_{-0.063}^{+0.070}$ fm at $90\mathrm{\%}$ C.L.. The $E_{\mathrm{s}\mathrm{y}\mathrm{m}}(\rho )$ 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 $E_{\mathrm{s}\mathrm{y}\mathrm{m}}(\rho )$ 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.