Calculation of correlation functions of hard spheres in the generalized mean spherical approximation

Wiener-Hopf factorization technique as suggested by Baxter has been used to solve the Ornstein-Zernike equation for a system of hard spheres in the framework of a generalized mean spherical model. The method reported here yields unambiguous and accurate values of the radial distribution function $g\left(r\right)\mathrm{}$, direct correlation function $C\left(r\right)\mathrm{}$, and the structure function $S\left(k\right)\mathrm{}$. These thermodynamic quantities have been calculated from low to fairly high densities and, with a normalized $g\left(R\right)\mathrm{}$, they have been compared with the molecular-dynamics values of Alder and Hecht.