The Structure of Quantum Fluids: Helium and Neon

Abstract

A procedure for the evaluation of the path integrals for the two-particle statistical density matrix at low temperatures is described. It is applied to both helium and neon, the first being the paradigm of a quantum mechanical gas and the second exhibiting weaker, but still significant, quantum effects at temperatures above the triple point. The density independent part of the pair-correlation functions and the second virial coefficients are obtained from these quantities. Three- and many-particle quantum properties are examined by approximating the Slater sum by a product of Boltzmann factors, each factor containing an effective pair-potential defined from the results of the two-particle case. The radial distribution function, obtained from a Percus-Yevick equation using this effective potential, demonstrates the validity of using the effective potential approximation as a tool for studying quantum properties by giving satisfactory results for helium and good agreement with experiment for neon.