AN ACCURATE INTEGRAL-EQUATION THEORY FOR HARD-SPHERES - ROLE OF THE ZERO-SEPARATION THEOREMS IN THE CLOSURE RELATION

We evaluate a number of current closure relations used in the integral equations for hard sphere fluids, such as the Percus-Yevick, Martynov-Sarkisov, Ballone-Pastore-Galli-Gazillo, and Verlet modified (VM) closures with respect to their abilities of satisfying the zero-separation theorems for hard spheres. Only the VM closure is acceptable at high densities (p similar to 0.7), while all fail at lower densities (lim 0<p<0.5). These shall have deleterious effects when used in perturbation theories, especially at low densities. To improve upon this, we propose a closure, ZSEP, that is flexible and suited to satisfying the known zero separation theorems [e.g., the ones for the cavity function y(0) and the indirect correlation gamma(0), and others for their derivatives dy(0)/dr, etc.], plus the pressure consistency condition. This particular closure, after numerical solution with the Ornstein-Zernike equation, is shown to perform well at high densities (p similar to 0.9) as well as low densities (0.1<p<0.5) for the cavity function y(r), the pair correlation function g(r), and the bridge function B(r). Derived thermodynamic properties: pressure, isothermal compressibility, and chemical potential are also highly accurate. Comparison with available Monte Carlo data bears this out. We have formulated a ''consistent'' and accurate integral equation theory for hard spheres over a wide range of density states. (C) 1995 American Institute of Physics.