Possible Generalization of the Ashcroft-Lekner Hard-Sphere Model for the Structure Factor

Abstract

A generalization of the Ashcroft-Lekner (AL) hard-sphere mode for calculation of structure factor is proposed. The AL model is derived from the Wertheim-Thiele solution of the Percus-Yevick integral equation for the case of hard spheres. This generalization introduces a correct hard-sphere equation of state for dense fluids into the AL model. This allows us to determine one coefficient of the AL model exactly and gives a condition on the other two coefficients in terms of the packing fraction. However, in order to determine all the three coefficients uniquely, we need a third condition which is proposed to be obtained from a fit to the experimental data at one point. Our generalization of the AL model is expected to yield a structure factor for dense systems in better agreement with the experimental data, at least for machine calculations on hard-sphere systems.