Series expansions for clustering in continuum--percolation models with interactions

The low-density expansions of the concentration of monomers, dimers, trimers, and the mean cluster size are computed exactly, up through three-body cluster integrals, for a continuum--percolation model of spheres characterized by both exclusion-volume repulsions and short-range attractions. The compactness of trimers for our model is studied in the dilute limit. Interestingly, the [1,1] Pade approximant of the mean cluster size yields percolation thresholds which exhibit the proper qualitative dependence on the strengths of the repulsive and attractive interactions. The predicted thresholds agree qualitatively well with the trends reported in a Monte Carlo study by Bug et al