A new analytical approximation for the second term in the thermodynamic perturbation theory of simple hard-core fluids

An analytical expression for the second term in the thermodynamic perturbation theory of liquids is proposed. The expression is derived by invoking the mean spherical approximation for the direct correlation function of the whole system. We have made then another simplifying approximation to reach an entirely analytical expression for the second term in the thermodynamic perturbation theory. The new resulted second order term in the perturbation theory, although simple and analytical, is shown to be as nearly accurate as the Barker-Henderson second order term for the case of moderate- to long-ranged hard-core Yukawa potentials and the Sutherland potential.