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

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 $\mathbf{\text{83}}$, 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 ${\widehat{c}}_{ij}(k)$ of the direct correlation functions defined by the OZ relation. From the analysis of the poles of ${\widehat{c}}_{ij}(k)$ we show that the direct correlation functions evaluated by the RFA method vanish outside the hard core, as required by the PY theory.