Computation of the static structure factor of the path-integral quantum hard-sphere fluid

Abstract

A calculation of the quantum static structure factor of the path-integral hard-sphere fluid is presented. The starting point is an approximate path-integral partition function factorized into two parts: one depending upon the necklace center-of-mass coordinates and the other consisting of independent bead packets associated with each particle in the sample. This produces two Ornstein–Zernike equations, namely linear response (true particle) and center of mass, formally identical to the well-known classical version and that can be solved with the aid of Baxter’s equations and Dixon–Hutchinson’s variational procedure. Linear response and center-of-mass direct correlation functions and their corresponding structure factors are computed from r-space radial distribution functions obtained with several propagators: crude, Barker’s, Jacucci–Omerti’s, and Cao–Berne’s. The results show: features of Baxter’s equations; the proximity between the quantities arising from the efficient propagators; the convergence of the crude propagator quantities to the latter; and the usefulness of the Feynman–Hibbs Gaussian picture (even in this context) to get one-particle quantum functions. The validity of the approximate partition function under the present working conditions is also stated, and an assessment of the quantum effects on the structure factor is made by comparing the classical Percus–Yevick and the path-integral results. Isothermal compressibilities are compared with Yoon–Scheraga’s data and the agreement is excellent.