Solution of Ornstein-Zernike Equation for a Mixture of Hard Spheres with Yukawa Closure: the Case of Factorizable Coefficients

The solution of Blum and Høye, which is the solution of Ornstein-Zernike equation for a mixture of hard spheres with Yukawa closure: c i j ( r )=Σ n K i j ( n ) exp (- z n r )/ r for r >σ i j , c i j ( r ) and σ i j being respectively the direct correlation function and the closest distance between i - and j -type spheres, has been studied in the case of factorizable coefficients, namely, K i j ( n ) = K ( n ) d i ( n ) d i ( n ) . In this case it is shown that (i) the set of algebraic equations defining the solution is remarkably simplified and, in particular, that (ii) in the single Yukawa-term case the set is solved and the solution is given by rational functions of a parameter. The latter is the generalization of the Blum's solution for a primitive model of electrolytic solutions in the sense of producing the Blum's solution as the limiting case.