Eur. Phys. J. B 48, 385-391 (2005)
https://doi.org/10.1140/epjb/e2005-00414-x

Particle densities for dilute hard-sphere Bose or Fermi gases in an external potential

Institute for Theoretical Physics, Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, P.R. China

Corresponding author: ^a xzwang@sjtu.edu.cn

Received: 22 July 2005
Revised: 16 October 2005
Published online: 23 December 2005

Abstract

We prove that if the diameter of a hard-sphere is much smaller than the size of an external potential, the s-wave pseudopotential reduces to the Huang-Yang s-wave pseudopotential. We obtain the first-order virial expansions of particle densities for dilute hard-sphere Bose or Fermi gases in an arbitrary external potential. In the absence of an external potential, the results reduce to the Huang-Yang-Luttinger and Lee-Yang virial expansions. In the quasi-classical limit, the results reduce to the results of the local density approximation.