Parametric integral equation for radial distribution functions

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Abstract
An integral equation is proposed whose solutions approximate the radial distribution functions of classical fluids whose single-type particles interact with pairwise radial forces. The equation contains a parameter which is adjustable to improve moderate- and high-density solutions. The equation is applied to the hard-sphere model of a fluid, solutions are obtained for four densities, and the pressure equation of state is expressed in terms of a 2 × 2 Padé approximant. A single value of the parameter yields pressures which are in excellent agreement with "exact" values.