A rapidly convergent method of solving the OZ equation

Abstract

A new method is proposed for solving numerically the Ornstein-Zernike equation for systems with a spherically symmetrical pair-potential. The method is based on expansion of the function Γ(r)=r[h(r) - c(r)] in suitable basis functions and on a combination of Newton-Raphson and direct iterations. Tests on the PY and HNC approximations for hard spheres and Lennard-Jones fluid have shown that the proposed method is three to nine times as rapid as the related and so far the most efficient method of Gillan. Other advantages besides the speed are low sensitivity to the choice of initial estimate and a relatively simple computational scheme.