Cluster expansion for fluids with long-range interactions

We apply Kac's method of functional integration to a spatially non-uniform fluid with short and long-range interactions. The system with short-range interactions is treated as a reference system to which the long-range pair interaction is added as a perturbation. All equilibrium distribution functions of the reference system are assumed known. We show by diagram analysis that by a suitable choice of the density profile of the reference system the thermodynamic potential can be expressed in terms of a cluster expansion containing only irreducible diagrams. For a spatially uniform fluid in the thermodynamic limit our results reduce to those obtained by Siegert et al.