Yukawa fluids in the mean scaling approximation: I. The general solution

A new general form of the multi-Yukawa, multicomponent closure of the Ornstein-Zernike equation for factored interactions is derived. The general solution is given in terms of an M x M scaling matrix Gamma obtained by solving M (equal to the number of Yukawa terms in the closure) equations together with M(M - 1) symmetry conditions 2piK((n)) Sigma(j)rho(j)X(j)((n))(B) over cap (j)(z(n)) + z(n) Sigma(k)rho(k)a(k)((n))Pi(k)((n)) + Sigma(m)z(n)/z(n)+z(m) {Sigma(k)rho(k)a(k)((n))a(k)((m))} Sigma(j)rho(j)X(j)((m))Pi(j)((n)) = Delta(approximate to(n)) where Delta(approximate to(n)) is of higher order in the density, and all quantities are algebraic functions of Gamma. Explicit formulae for the thermodynamic properties are also provided.