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 xc (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‐sphrerical approximations for ionic and polar fluids of Ho/ye, Lebowitz, and 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.