Decay of pair correlation functions

Abstract

The decay equation, which determines the correlation length and the period of the pair correlation function of a fluid at large distances, is discussed using the Ornstein–Zernike equation when the direct correlation function vanishes rapidly at large distances. The decay equation is solved numerically using the exact hard sphere and sticky hard sphere fluid results from the Percus–Yevick approximation. In the case of the hard sphere fluid, oscillatory decay is always obtained. For the sticky hard sphere fluid, we obtain a locus both in the pressure–temperature plane and the density–temperature plane such that the decay is monotonic inside and oscillatory outside the locus.