Imperfect Bose Gas with Hard-Sphere Interaction

Phys. Rev. 105, 776 – Published 1 February 1957
Kerson Huang, C. N. Yang, and J. M. Luttinger


The method developed in the previous paper for the treatment of the quantum-mechanical N-body hard-sphere problem is applied to a calculation of the grand partition function of an imperfect Bose gas with hard-sphere interactions. The grand partition function is calculated to second order in an expansion in powers of aλ, where a is the hard-sphere diameter and λ the thermal wavelength. The approximate equation of state for the gas phase is thereby obtained by calculating all the virial coefficients to order (aλ)2.

The first-order energy levels obtained in the previous paper embody some interesting physical properties. A fictitious system with exactly such energy levels is considered. The partition function for such a system can be calculated exactly and the exact equation of state obtained. It is shown that there is a phase transition, which more closely resembles an ordinary gas-liquid transition than the Bose-Einstein condensation.


  • Received 22 October 1956
  • Published in the issue dated February 1957

© 1957 The American Physical Society

Authors & Affiliations

Kerson Huang and C. N. Yang

  • The Institute for Advanced Study, Princeton, New Jersey

J. M. Luttinger

  • University of Michigan, Ann Arbor, Michigan

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