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
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.
PACS: 05.30.-d – Quantum statistical mechanics / 05.30.Jp – Boson systems / 05.30.Fk – Fermion systems and electron gas / 31.15.Bs – Statistical model calculations (including Thomas-Fermi and Thomas-Fermi-Dirac models)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005