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The use of stereology to determine the partial two-body correlation functions for hard sphere ensembles

The authors present here a method of finding the bulk two-body correlation functions for an isotropic ensemble of hard spheres by examining a single section through the ensemble. The authors derive an integral equation which gives the probability of seeing a disc of radius sigma 1 a distance rho from a disc of radius sigma 2, in the cross-section. The authors solve this explicitly for the case where the distribution of sphere radii in the bulk is a discrete distribution and hence obtain a discrete set of partial two-body correlation functions for the bulk ensemble.