On Fluids of Particles with Short-Range Repulsion and Weak Long-Range Attractive Interaction

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Abstract
We have obtained an appreciably simplified derivation of the expansion in inverse range of the thermodynamic functions of a system of particles with short‐range repulsion and weak long‐range attractive interaction. We assume all properties of the system with only the short‐range repulsive interaction to be known and consider this system as a reference system for the purpose of a perturbation expansion. We derive corrections to the van der Waals equation and to the Maxwell construction. The terms in our expansion are integrals over products of the modified Ursell functions of the reference system only and factors which are the transformed long‐range potential. A simple rule is given to determine the order, in the inverse range of the attractive potential, of each term in the expansion. The simplification of the derivation is achieved by avoiding the expansion and subsequent resummation of any functions pertaining to the reference system.