Exact and approximate values for the radial distribution function at low densities for the 6:12 potential

Abstract

If the radial distribution function, g(r), is expanded in powers of the density, the second term in this expansion involves a double integral. This integral has been evaluated numerically and values are reported for a wide range of temperatures and intermolecular separations. In addition, three approximations to this integral which have been proposed by Rowlinson are examined. These approximations have been proposed for the regions of high and low temperatures and for the region r∼r _m, where r _m is the separation corresponding to the minimum in the intermolecular potential. The first two approximations are found to be very reliable while the third is good at high temperatures and moderately good at low temperatures but rather poor at intermediate temperatures.