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 $ΔF_{\rm CW}$ 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 $E_{\rm sym}(ρ)$ and the neutron skin thickness $Δr_{\rm np}$ of $^{48}$Ca and $^{208}$Pb within the Skyrme energy density functional (EDF). We find the inferred $E_{\rm sym}(ρ)$ and $Δr_{\rm np}$ 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) $E_{\rm sym}(ρ)$ and rather small (large) $Δr_{\rm np}$. By combining the CREX and PREX-2 data, we obtain a soft symmetry energy around saturation density $ρ_0$ and thinner $Δr_{\rm np}$ 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 $E_{\rm sym}(ρ)$ and $Δr_{\rm np}$ due to its lower precision of $ΔF_{\rm CW}$. Furthermore, we find the Skyrme EDF results inferred by combining the CREX and PREX-2 data nicely agree with the measured dipole polarizabilities $α_D$ in $^{48}$Ca and $^{208}$Pb as well as the neutron matter equation of state from microscopic calculations. The implications of the inferred soft $E_{\rm sym}(ρ)$ around $ρ_0$ are discussed.