We establish a correlation for the symmetry energy at saturation density $S_0$, slope parameter $L$, and curvature parameter $K_{\text{sym}}$ based on widely different mean-field interactions. With the help of this correlation and available empirical and theoretical information, the density-dependent behavior around the saturation density is determined. We compare the results obtained with the present approach with those by other analyses. With this obtained density-dependent behavior of the symmetry energy, the neutron skin thickness of ${}^{208}$Pb and some properties of neutron stars are investigated. In addition, it is found that the expression $S\left(\rho \right)=S_0(\rho /{\rho }_0){}^{\gamma }$ or $S\left(\rho \right)=12.5\left(\rho /{\rho }_0\right){}^{2/3}+C_p\left(\rho /{\rho }_0\right){}^{\gamma }$ does not reproduce the density dependence of the symmetry energy as predicted by the mean-field approach around nuclear saturation density.

• Received 17 October 2011

DOI:https://doi.org/10.1103/PhysRevC.85.034308