Analytic representation for the pair-correlation function of a hard-sphere Yukawa system

Abstract

We present the analytic expressions for the pair-correlation function g(r) of a one-component hard-sphere system with k Yukawa-tails for r-values up to 7 hard-sphere diameters d. Explicit calculations for the one-Yukawa case show that—in contrast to the pure hard-sphere case— contributions from the sixth and the seventh shell (i.e. 5d ⩽ r ⩽ 7d) to integrals involving the pair-correlation function are not negligible. Only for small densities is inclusion of a smaller number of shells sufficient. For very weakly screened potentials where the long distance oscillations of the pair-correlation function are still pronounced, we would have to take into account a larger number of shells: for these cases our procedure is no longer applicable since the necessary expressions become too complicated to be tractable.