Nuclear Symmetry Energy and Neutron Skin Thickness of $^{208}Pb $ using a finite range effective interaction
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 $ρ_c=0.11$ fm$^{-3}$ and at a density around two times the saturation density $ρ_0$. 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 $β^{\prime}=\frac{L(ρ_c)}{3E_s(ρ_0)}$, where $E_s(ρ_0)$ and $L(ρ_c)$ are respectively the nuclear symmetry energy at saturation density and the density slope parameter at the subsaturation density.