  In this paper we develop a theory to calculate the solvent mediated
interaction potential between solute particles dispersed in a solvent. The
potential is a functional of the instantaneous distribution of solute particles
and is expressed in terms of the solute-solvent direct pair correlation
function and the density-density correlation function of the bulk solvent. The
dependence of the direct pair correlation function on multi-point correlations
of the solute distribution is simplified with a mean field approximation. A
self consistent approach is developed to calculate the effective potential
between solute particles, the solute-solvent and the solute-solute correlation
functions. The significance of the solvent fluctuations on the range of the
effective potential is elucidated. The theory is applied to calculate
equilibrium properties of the Asakura-Oosawa (AO) model for several values of
solute and solvent densities and for several values of the particles size
ratio. The results give a quantitative description of many-body effect on the
effective potential and on the pair correlation functions.
