Integral Euqations for Fluids with Long-Range and Short-Range Potentials

Four new integral equations for the radial distribution function g(r) suitable for a fluid (including a charged-particle system, such as plasmas, electrolyte solutions and molten salts) interacting via a potential consisting of a strong repulsive short-range part and a slow-varying long-range part are derived by Percus’ functional-expansion method. The first equation of them is composed of two equations: one is the Percus-Yevick (PY) equation involving the short-range part of the potential and the other an equation involving the long-range part. The second is an extended PY equation in which the long-range potential is taken into account in the form of the Hartree field. The third equation is derived on the basis of an improvement on the thermodynamical equation determining the density n(r|U) in a nonuniform system under an external field U(r). The fourth equation is a combination of the second and third equations. As an illustration, the first integral equation is solved for a system with potential v(r)= erf(ζr)(Ze)2/r+hard-sphere for θ from 10.0 to 0.01, where θ=kBTa/(Ze)2, a=[3/4πn0]1/3, n0 the average density and Z the valency. The result for θ=10.0 agrees quite well with the non-linear Debye-Huckel result. At θ=1.0 there is a close agreement between the present result and the Monte Carlo result. As θ increases, g(r) begins to oscillate around unity and resembles g(r) of a neutral fluid.