Exact solution of the Percus-Yevick integral equation for fluid mixtures of hard hyperspheres

TL;DR

This paper proves that the rational function approximation (RFA) method provides the exact solution to the Percus-Yevick integral equation for binary mixtures of hard hyperspheres in odd dimensions, confirming its accuracy for structural and thermodynamic properties.

Contribution

It demonstrates that the RFA technique yields the exact solution of the PY closure for binary mixtures of hard hyperspheres in arbitrary odd dimensions.

Findings

RFA method gives the exact PY solution for binary mixtures in odd dimensions.

Direct correlation functions vanish outside the hard core as required by PY.

Analysis of Fourier transforms confirms the validity of the RFA approach.

Abstract

Structural and thermodynamic properties of multicomponent hard-sphere fluids at odd dimensions have recently been derived in the framework of the rational function approximation (RFA) [Rohrmann and Santos, Phys. Rev. E \textbf{83}, 011201 (2011)]. It is demonstrated here that the RFA technique yields the exact solution of the Percus-Yevick (PY) closure to the Ornstein-Zernike (OZ) equation for binary mixtures at arbitrary odd dimensions. The proof relies mainly on the Fourier transforms $\hat{c}_{ij}(k)$ of the direct correlation functions defined by the OZ relation. From the analysis of the poles of $\hat{c}_{ij}(k)$ we show that the direct correlation functions evaluated by the RFA method vanish outside the hard core, as required by the PY theory.