The radial and background distribution functions of Quantum Hard Spheres

Abstract

The radial and background distribution functions of Quantum Hard Spheres (QHS) are studied and analytical expressions are obtained that can be used to evaluate perturbation terms of the Helmholtz free energy for quantum fluids like hydrogen and helium. The provided analytical expressions were obtained from Path-Integral Monte Carlo (PIMC) simulations for quantum hard spheres (QHS) and results are given for the first perturbation terms of model systems like quantum square-well and Lennard-Jones fluids. As part of this study, we use the Clausius virial theorem and the mean-value theorem from integral calculus to provide a generalization of the standard contact-value/pressure relation for classical hard-spheres, in order to obtain the QHS pressure. Within this information, it is also possible to provide extensions to the quantum regime of the zero-separation theorems.