New, thermodynamically consistent, integral equation for simple fluids

TLDR

The paper introduces an integral equation that blends hypernetted‑chain and Percus‑Yevick approximations based on interparticle separation. Thermodynamic consistency is enforced by an adjustable parameter α in the mixing function. For simple 1/rⁿ fluids the parameter α is density‑independent and the integral equation solutions agree closely with Monte Carlo data; for the one‑component plasma α varies slowly with density yet still yields good agreement, demonstrating clear advantages over earlier thermodynamically consistent equations.

Abstract

A new integral equation in which the hypernetted-chain and Percus-Yevick approximations are "mixed" as a function of interparticle separation is described. An adjustable parameter $\ensuremath{\alpha}$ in the mixing function is used to enforce thermodynamic consistency. For simple $\frac{1}{{r}^{n}}$ potential fluids, $\ensuremath{\alpha}$ is constant for all densities, and the solutions of the integral equations are in very good agreement with Monte Carlo calculations. For the one-component plasma, $\ensuremath{\alpha}$ is a slowly varying function of density, but the agreement between calculated solutions and Monte Carlo is also good. This approach has definite advantages over previous thermodynamically consistent equations.