Perturbation Theory and Equation of State for Fluids

In the perturbation theory studied by Barker and Henderson, an expansion is made of the free energy in terms of a strength parameter $\lambda$ that multiplies the attractive part of the potential. This expansion is shown here to converge very rapidly for the Lennard-Jones liquid. Taking as zeroth-order approximation the system with only repulsive forces, Barker and Henderson have shown that it can be approximated by hard spheres with a temperature-dependent diameter. We show by a direct computation that this approximation is excellent. In the spirit of the $\lambda$ expansion, we can write down a semiempirical equation of state which is applied with success to the Lennard-Jones fluid, argon, and xenon. It is seen that the large scale density variation characteristic of the critical point lowers the critical temperature by 6%.