Simple variational method for the closures of the Ornstein-Zernike equation: A study of liquid instability

In this paper a simple variational method is proposed for the solution of the integral equations for hard-core fluids. The variational method is applied to the equations of the mean-spherical approximation for systems consisting of square-well particles at very high densities. Using the static structure-factor singularity as a condition of absolute instability, no high density limit of metastable states is found, up to the density corresponding to the random dense packing.