A self-consistent cell model for the melting transition in hard sphere systems

The Bethe approximation is applied to the zero- and single-occupancy cell model for hard spheres. The resulting self-consistency equations are solved numerically, for both two- and three-dimensional systems. In both cases there are solutions of two kinds, one representing the solid phase and the other the fluid phase. Cluster corrections to the Bethe approximation are also evaluated. When a reasonable choice of cell size is made and cluster corrections are included, the predicted melting parameters agree well with the results of computer simulations. Thus the self-consistent cell model provides a unified theory of solids, fluids and melting.