The radial distribution function at low densities: Exact results for small and large separations for smooth potentials

Explicit expressions are obtained for the r→0 and r→∞ limits of the first density coefficient of the radial distribution function. This double integral has also been evaluated numerically by the Clenshaw–Curtis quadrature for Lennard-Jones and inverse power potentials. Our numerical results agree closely with previous work where overlap exists and confirm our analytic results in the r→0 and r→∞ regions.