An approximation for the two particle distribution of a hard-sphere fluid near a hard wall at low densities

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Abstract
A suitable mean density average for the two particle distribution function g(2)(r1,r2) of a nonuniform simple fluid is proposed. The mean takes into account all the intermediate densities of the system between the r1 and r2 points. The approximation is tested in a hard-sphere fluid near a hard wall at low densities where exact results are available. The approximation gives better results for the structure of the density profile, adsorption and surface tension than any other approach (scale particle theory, Percus–Yevick, and hypernetted chain closures and superposition approximation).