Analytic formulation of the WCA type perturbation theory for a hard-core with one-Yukawa tail fluid

Abstract

The optimized renormalized potential C(r), the key ingredient of the Anderson-Chandler-Weeks type perturbation theory, is analytically calculated for a hard-core one-Yukawa fluid. Our method makes use of the mean spherical approximation analytic solution of the Ornstein-Zernike equation for the direct correlation function of two-Yukawa functions form. One of the functions is related to the interaction potential of the system whereas the other serves to obtain the GMSA solution for the hard-sphere distribution functions c HS(r) and g HS(r), which are utilized in the method. C(r) is then used in various perturbation schemes (EXP, LIN, LIN + SQ, QUAD) to calculate thermodynamic properties and g(r) for one-Yukawa fluid and the results are compared with Henderson et al. Monte Carlo data. These results are good, notably in LIN + SQ and QUAD approximations, but the results with the use of the best available g HS(r) are slightly worse than those using the Percus-Yevick approximation to g HS(r). This emphasizes already known conclusions about limitations of EXP and related schemes.