Structure and thermodynamics of hard<i>D</i>-dimensional spheres: overlap volume function approach

Abstract

A very simple ansatz for the direct correlation functions of hard D-dimensional spheres is presented. For D = 1 and 3, it reduces exactly to the Percus-Yevick (PY) theory, yielding results which are very close to the PY theory for the other dimensions. A generalized Carnahan-Starling equation of state is proposed, which is in excellent agreement with the available computer simulation results. Finally, a generalized Verlet-Weis procedure for the pair distribution function g(r, η), is proposed. The important case of hard discs (D = 2) is studied in detail, leading to excellent results for g(r, η).