Pair Distribution in the Rigid-Sphere System by the Method of Particle Scaling

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Abstract
By use of the scale of interaction distance as a coupling constant, integral equations for the molecular distribution functions are derived and discussed with particular reference to the calculation of the pair distribution for rigid-sphere systems. It is shown that considerable improvement over the usual superposition approach results upon retention of the superficial form of the superposition approximation, but with a suitably defined effective local density. Specifically, the equation becomes exact over half the range of the coupling parameter. The fourth virial coefficient in the equation of state is correct in this theory, in comparison with an ordinary superposition value 61% low. Generalization of the effective density analysis to the case of arbitrary potentials is briefly discussed.

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