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We use a finite range simple effective interaction to construct nuclearequations of state for the study of the density dependence of the nuclearsymmetry energy. The EoSs provide good descriptions of the nuclear symmetryenergy at a subsaturation density $\rho_c=0.11$ fm$^{-3}$ and at a densityaround two times the saturation density $\rho_0$. We obtain a correlationbetween the neutron skin thickness in $^{208}$Pb and the density slopeparameter at the subsaturation density. A linear relation is obtained betweenthe 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 densityand the density slope parameter at the subsaturation density.

Nuclear Symmetry Energy and Neutron Skin Thickness of $^{208}Pb $ using a finite range effective interaction