Ornstein-Zernike equation for the direct correlation function with a Yukawa tail

Abstract

The Ornstein-Zernike (OZ) equation with a core condition h(x)=-1 for x<1 and a direct correlation function of Yukawa form c(x)=K exp[-z(x-1)]/x for x>1 was solved analytically by one of us recently [E. W., Mol. Phys. 25, 45 (1973)]. The equation is of interest (i) as the mean-spherical approximation for a potential that is the sum of hard-sphere and Yukawa terms; (ii) as a generalized mean-spherical approximation for a hard-sphere system; and (iii) as the key ingredient in the generalized mean-spherical approximations for ionic and polar fluids of J.S. Høye, J.L. Lebowitz, and G. Stell, J. Chem. Phys. 61, 3253 (1974). Here we analyze the solution of the above equation to give a quantitatively useful picture of its character. A rapidly convergent expansion in K is obtained. In addition, a general cluster expansion for the solution of the OZ equation with arbitrary c(x) previously derived by one of us (G.S.) is applied to the equation to yield a complementary representation of its solution. Detailed numerical results are given. Copyright © 1975 American Institute of Physics.