New, thermodynamically consistent, integral equation for simple fluids

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.