LAUSR

We use a finite range simple effective interaction to construct nuclear equations of state for the study of the density dependence of the nuclear symmetry energy. The EoSs provide good descriptions of the nuclear symmetry energy at a subsaturation density $\rho_c=0.11$ fm$^{-3}$ and at a density around two times the saturation density $\rho_0$. We obtain a correlation between the neutron skin thickness in $^{208}$Pb and the density slope parameter at the subsaturation density. A linear relation is obtained between the neutron skin thickness and the parameter $\beta^{\prime}=\frac{L(\rho_c)}{3E_s(\rho_0)}$, where $E_s(\rho_0)$ and $L(\rho_c)$ are respectively the nuclear symmetry energy at saturation density and the density slope parameter at the subsaturation density.