Direct correlation function: Hard sphere fluid

The direct correlation function c (r) and in particular the ’’tail’’ of the direct correlation function d (r) are calculated for hard spheres from reliable expressions for the radial distribution function of the hard sphere fluid. This permits a direct examination of the Percus–Yevick (PY) approximation d (r) =0. It is found that the PY approximation is very poor over-all but fairly reasonable in the most important region r ? σ. Finally a simple but relable parametrization of d (r) for hard spheres is proposed.