A REAL FUNCTION REPRESENTATION FOR THE STRUCTURE OF THE HARD-SPHERE FLUID

We present an analytic expression containing no imaginary terms for the radial distribution function of hard spheres in the Percus-Yevick approximation up to the distance of 4sigma (though extendable beyond that), where sigma is the hard-sphere diameter. It is shown that a third-order recursive ordinary differential equation for the total correlation function of the hard-sphere fluid can be derived from the Percus Yevick integral equation using Baxter's factorization method. We have solved this differential equation with its boundary conditions and obtained a result which is equivalent to that obtained by Smith and Henderson, but which contains only real functions. This result is useful in perturbation theories where the evaluation of integrals involving the radial distribution function is required since the expressions presented here are now integrable.