Statistical mechanical theory for nonuniform fluids. II. Hard-sphere fluid in the presence of an external field

In Part I of this study, we extended a formal theory for the statistical mechanics of a nonuniform classical fluid to the hard-sphere fluid system and developed a perturbation theory of nonuniform simple fluids. In this paper, we apply our theory to the problem of the soft-wall/hard-sphere fluid interface by solving for the external potential required to yield the known hard-sphere fluid density in contact with a structureless 9-3 soft repulsive wall potential. We find excellent agreement between the solution for the external potential and the 9-3 wall potential. Using the "local density approximation," the comparison shows poor agreement