On the pair correlation function for hard spheres at low density and temperature

Abstract

A quantum-mechanical calculation of the pair correlation function for hard spheres in the low-density limit has been made. This calculation is, therefore, valid at low temperatures, where quantum-mechanical diffraction and symmetry effects are important. Results are given for various temperatures and hard-sphere diameters. The pair correlation function is presented in the form g = gB + gS, where gB is the correlation function for Boltzmann particles and gS describes the symmetry effects. It is found that gS(R) for any value of the separation R is always smaller than the corresponding value for free particles.