Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function

Abstract

<p>Explicit analytical expressions are presented for the density derivative, ∂<i>g</i>_HS(<i>R</i>; ρ)/∂ρ, of the Percus–Yevick approximation to the hard-sphere radial distribution function for <i>R</i> ≤ 6σ, where σ is the hard-sphere diameter and ρ = (<i>N</i>/<i>V</i>)σ³ is the reduced density, where <i>N</i> is the number of particles and <i>V</i> is the volume. A FORTRAN program is provided for the implementation of these for <i>R</i> ≤ 6σ, which includes code for the calculation of <i>g</i>_HS(<i>R</i>; ρ) itself over this range. We also present and incorporate within the program code convenient analytical expressions for the numerical extrapolation of both quantities past <i>R</i> = 6σ. Our expressions are numerically tested against exact results.</p