Ornstein-Zernike Relation for a Fluid Mixture with Direct Correlation Functions of Finite Range

The Ornstein-Zernike relation for an n -component fluid mixture is investigated under the assumption that the direct correlation function between two particles of species i and j , c i j ( r ), is zero when r is greater than R i j ≡( R i + R j )/2 ( i , j =1, 2, …, n ). The relation is transformed so as to involve the radial distribution function g i j ( r ) only for r which is smaller than R i j ( i , j =1, 2, …, n ). The result is applied to a mixture of hard spheres in which R i , giving the range of the direct correlation functions, is assumed to be the diameter of the hard spheres of species i ( i =1, 2, …, n ). The direct correlation functions are found in the explicit forms, which are in complete agreement with those obtained by Lebowitz in case of a binary mixture.