Equilibrium properties of fluids in the semiclassical limit

Abstract

The problem of calculating the equilibrium properties of dense fluids in the semiclassical limit when the quantum effects are small is studied. Expressions are given for the pressure, free energy, and the radial distribution function in terms of the properties and correlation functions of the classical system and s-body "modified" Mayer functions f^s1,2,...,s. It is shown that the correct radial distribution function of a fluid in the semiclassical limit is generated from the classical radial distribution function if we replace in turn each f⁰ bond (f⁰₁₂=e^−βφ(1,2)−1) by an effective feff bond, where f^eff=f⁰+(1+f⁰) f^II+(1+f⁰)(1+f^II) L and where L is subset of the line-irreducible graphs each of which contain one f^III bond. The effective pair bond correct to the second order in thermal wavelength λ (={2πh²β/m}^½) for a fluid of hard spheres is calculated for λ/d=0.1, and 0.2 at reduced densities ρ=0.3 and 0.6. The most striking effect of the quantum mechanics on the structure of a hard-sphere fluid is found at and near the point of contact of the hard spheres.