Perturbation theory for the radial distribution function

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Abstract
Perturbation theory is used to consider expansions for the radial distribution function, g 2(r), of a fluid with a soft core. We consider the Lennard-Jones (12, 6) potential and divide it into repulsive and attractive regions. In the repulsive region we expand the function exp (β u(r))g 2(r) about a hard sphere value. For the first-order contribution of the attractive region we consider a simple approximation to the exact analytical expression. The resulting g 2(r) is accurate at densities below about ρσ 3=0·5.