Pair correlation function decay in models of simple fluids that contain dispersion interactions

We investigate the intermediate-and longest-range decay of the total pair correlation function h(r) in model fluids where the inter-particle potential decays as -r(-6), as is appropriate to real fluids in which dispersion forces govern the attraction between particles. It is well-known that such interactions give rise to a term in q3 in the expansion of (c) over cap (q), the Fourier transform of the direct correlation function. Here we show that the presence of the r(-6) tail changes significantly the analytic structure of (h) over cap (q) from that found in models where the inter-particle potential is short ranged. In particular the pure imaginary pole at q = i alpha(0), which generates monotonic-exponential decay of rh(r) in the short-ranged case, is replaced by a complex (pseudo-exponential) pole at q = i alpha(0) + alpha(1) whose real part a1 is negative and generally very small in magnitude. Near the critical point alpha(1) similar to -alpha(2)(0) and we show how classical Ornstein-Zernike behaviour of the pair correlation function is recovered on approaching the mean-field critical point. Explicit calculations, based on the random phase approximation, enable us to demonstrate the accuracy of asymptotic formulae for h(r) in all regions of the phase diagram and to determine a pseudo-Fisher-Widom (pFW) line. On the high density side of this line, intermediate-range decay of rh(r) is exponentially damped-oscillatory and the ultimate long-range decay is power-law, proportional to r(-6), whereas on the low density side this damped-oscillatory decay is sub-dominant to both monotonic-exponential and power-law decay. Earlier analyses did not identify the pseudo-exponential pole and therefore the existence of the pFW line. Our results enable us to write down the generic wetting potential for a 'real' fluid exhibiting both short-ranged and dispersion interactions. The monotonic-exponential decay of correlations associated with the pseudo-exponential pole introduces additional terms into the wetting potential that are important in determining the existence and order of wetting transitions.