ON SOME PROPERTIES OF THE HARD-SPHERE RADIAL-DISTRIBUTION FUNCTION

We present closed-form expressions for derivatives at contact of the hard-sphere radial distribution function (RDF) in the Percus-Yevick theory. The derivatives of lower order coincide with well-known results. Corresponding expressions are also derived using the Verlet-Weis algorithm. These results are compared with values extracted from recent Monte Carlo data on the HS RDF and an accurate expression for the first-order derivative is given. Expressions for moments of the HS correlation function are also obtained in the Percus-Yevick theory. All of these quantities are useful in the perturbation theory of liquids.