Determination of symmetry energy from experimental and observational constraints; prediction on CREX

Abstract

Taking $r_{\mathrm{skin}}^{208}(\mathrm{PREX})=0.33_{-0.18}^{+0.16}\mathrm{fm}$ as an experimental constraint and $M_{\max }^{\mathrm{NS}}\ge 2{\mathrm{M}}_{\mathrm{sun}}$ as an observational (astrophysical) constraint, we determine an indisputable range for $J$, $L$, $K_{\mathrm{sym}}$ defined in Eq.~\eqref{eq-S-sym}. For this purpose, we take a statistical approach. We first accumulate the 206 EoS data from theoretical works and take correlation between $r_{\mathrm{skin}}^{208}$ and $L$ for the 206 EoSs, where 7 Gogny EoSs are obtained by our calculations. Since the correlation coefficient is $R=0.99$, we can regard $L$ as a function of $r_{\mathrm{skin}}^{208}$, so that we succeed in deducing an empirical constraint $L=31-161$~MeV from $r_{\mathrm{skin}}^{208}(\mathrm{PREX})=0.15-0.49$~fm. For the 47 EoSs satisfying the observational constraint, 46 EoSs satisfy the empirical constraint. The 46 EoSs yield $J=29-44$~MeV, $L=37-135$~MeV, $K_{\mathrm{sym}}=(-137)-(160)$~MeV. The is a primary result. When we take correlation between $r_{\mathrm{skin}}^{48}$ and $r_{\mathrm{skin}}^{208}$ for the 206 EoSs, $R$ is 0.99. The $r_{\mathrm{skin}}^{48}$--$r_{\mathrm{skin}}^{208}$ relation allows us to transform $r_{\mathrm{skin}}^{208}(\mathrm{PREX})$ into the corresponding data on $r_{\mathrm{skin}}^{48}$ In order to estimate a value of $r_{\mathrm{skin}}^{48}$ for ongoing CREX, we take the weighted mean and its error of two present data on $r_{\mathrm{skin}}^{48}$ and transformed PREX value on $r_{\mathrm{skin}}^{48}$. The weighted mean is $r_{\mathrm{skin}}^{48}=0.17$~fm. This is a prediction for the central value of CREX.