Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function. (1st September 2016) - Kelly, Braden D.
ABSTRACT: Explicit analytical expressions are presented for the density derivative, ∂ g HS ( R ; ρ)/∂ρ, of the Percus–Yevick approximation to the hard-sphere radial distribution function for R ≤ 6σ, where σ is the hard-sphere diameter and ρ = ( N / V )σ 3 is the reduced density, where N is the number of particles and V is the volume. A FORTRAN program is provided for the implementation of these for R ≤ 6σ, which includes code for the calculation of g HS ( R ; 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 R = 6σ. Our expressions are numerically tested against exact results. Abstract :