Quantum-Mechanical Pair-Correlation Function of Hard Spheres

Abstract

The density‐independent part of the quantum‐mechanical direct and exchange pair‐correlation functions for hard spheres has been calculated for λ T / σ = 1.4, 2, 2.93761, 4, 6, 8, and 10 . In addition, points were obtained very near the surface of the sphere for λ T / σ = 0.025 and 0.05 . The results delineate the approach of the direct (Boltzmann)correlation function to the classical limit and emphasize the rapid disappearance of the effects of statistics with increasing temperature. These features are explained using Wiener (path) integrals. Analytical expressions valid near the surface of the sphere are derived and compare well with numerical results. Virial coefficients obtained from the correlation functions are in satisfactory agreement with very precise value calculated by Boyd, Larsen, and Kilpatrick.