THE DECAY OF THE PAIR CORRELATION-FUNCTION IN SIMPLE FLUIDS - LONG-RANGED VERSUS SHORT-RANGED POTENTIALS

This paper is concerned with two aspects of the theory of the decay of g(r), the radial distribution function of a liquid. For models in whi ch the attractive interatomic potential is short ranged, asymptotic de cay falls generically into two classes: (a) monotonic decay for which r(g(r) - 1) approximately exp(-alpha0r) and (b) damped oscillatory dec ay for which this function approximately exp(-alphaBAR0r) cos(alpha1r - theta). Crossover between the two classes (alpha0 = alphaBAR0) defin es the Fisher-Widom line of the particular model. This line is calcula ted for a truncated Lennard-Jones fluid using an accurate (HMSA) integ ral-equation theory. We find that it intersects the liquid branch of t he liquid-vapour coexistence curve at T/T(c) almost-equal-to 0.9 and r ho/rho(c) almost-equal-to 1.9, where T(c) and rho(c) are the critical temperature and density, respectively. The location of the line relati ve to coexistence is very similar to that calculated earlier using the random phase approximation (RPA) for a square-well fluid, suggesting that in this region it is not particularly sensitive to choice of pote ntial or of theory. In the second part of the paper we develop a theor y for the intermediate-range and asymptotic decay of g(r) for a fluid whose potential includes power-law (dispersion) contributions. Althoug h power-law decay dominates at longest range, we show that intermediat e-range oscillatory structure is determined by a single complex pole. Explicit calculations, within the RPA, for a model potential with a 1/ r6 tail show that at high densities this pole is located close to that of a reference model with a short-ranged truncated potential and the intermediate- and short-range structure of the two models is almost id entical. However, since there is no pure imaginary pole for the long-r anged potential, there is no pure exponential decay of correlations an d, therefore, no sharply defined Fisher-Widom line. Intermediate-range oscillations in g(r) are eroded at lower densities but the mechanism is different from that in the short-ranged models. In addition, we fin d that the pole structure of models with large truncation lengths is v ery different from that of the full potential making asymptotic analys is for such models of little practical use.