PERCUS-YEVICK PAIR-DISTRIBUTION FUNCTIONS OF A BINARY HARD-SPHERE SYSTEM COVERING THE WHOLE R-RANGE

We present explicit formulae which allow an economical but very accurate evaluation of the pair-distribution functions g(ij)(r) for the whole range of distances of an additive binary hard-sphere system within the Percus-Yevick approximation. The method is based on the fact that for such a system the Laplace-transforms g triple overdot ij(t) of the g(ij)(r) are known analytically. The inversion of the Laplace-transform is performed in two different ways: the first one-preferably applied from the contact up to distances of a few diameters-calculates the inverse by means of an exact analytical procedure, whereas the other one-very useful for intermediate and large distances-uses an asymptotic method, truncating a rapidly converging series expansion. In the overlap region of the two methods we can obtain perfect agreement (i.e. up to machine precision), including the first few terms of this expansion. Both formulae are presented as general as possible to allow an easy extension to other binary hard-core systems.