Transformation of the Ornstein-Zernike Relation for Fluid Mixtures

where r= lrl, r' = lr'l, and Pr is the number density of particles of species r. Equation (1) is called the Ornstein-Zernike (OZ) relation for the fluid mixture. Baxter presented two transformations of the OZ relation for a single-component fluid_n·' 1 Both of these are suitable for use with approximate theories where the direct correlation functions can be assumed to be of finite range. The first transformation vvas generali~ed to the case of fluid mixtures by Hiroike and Fukui. 31 The generalized transformation was applied to a mixture of hard spheres by Hiroike,'1 and recently to a binary mixture of hard spheres with non-additive diameters by Perry and Silbert. 51 The second transformation was generalized to the case of fluid mixtures by Baxter himsel£. 61 The purpose of the present paper is to derive Baxter's generalized trsnsformation without the assumption that the direct correlation functions are of finite range. The derivation itself is much simpler than Baxter's, in which usc was made of the Wiener-Hopf technique.