Application of the cluster variation method to the hole theory of fluids

The pair approximation of the cluster variation method is applied to the hole theory of classical fluids and the melting transition of the hard-sphere system is discussed. The exact free volume of the hard-sphere molecule is used to make up an effective ‘interaction’ assigned to a cluster which consists of an occupied site by a molecule and its nearest neighbour sites occupied by molecules and holes. This method supplies much improved results compared with those of the molecular-field approximation which corresponds to the site approximation in the cluster variation method.