Integral Equations for Distribution Functions in Fluids

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Abstract
Starting from a chain of exact equations due to Mayer, integral equations are derived for the two‐, three‐, and four‐particle distributions for a fluid mixture. An equation similar in form, but having some advantages over the hyper‐netted chain equation, is obtained for the pair distribution function. This equation reduces in first approximation to the Percus‐Yevick equation, but exhibits corrections to the latter depending on the three‐ and four‐particle distribution functions. The solution of the equations for the three‐ and four‐particle distribution functions is discussed, and it is found that a potential difficulty arises through the divergence of Neumann's expansion at sufficiently high densities.