J. Phys. I France
Volume 5, Numéro 2, February 1995
Page(s) 181 - 203
DOI: 10.1051/jp1:1995120
J. Phys. I France 5 (1995) 181-203

Ursell operators in statistical physics I: Generalizing the Beth Uhlenbeck formula

P. Grüter and F. Laloë

Laboratoire Kastler Brossel, 24 rue Lhomond, 75005 Paris, France

(Received 4 February 1994, revised 8 September 1994, accepted 26 October 1994)

The Beth Uhlenbeck formula gives an exact (quantum) expression of the second virial correction to the equation of state of a (slightly degenerate) dilute gas. We show how this result can be extended to arbitrary degeneracy provided that the interaction potential has a sufficiently short range. For this purpose we develop a formalism based on the use of Ursell operators, which contain no symmetrization in themselves (they correspond to an auxiliary system of distinguishable particles) and we show how they can be used for a system of identical particles. A concise expression generalizing the Beth Uhlenbeck formula is obtained, which is equally valid for bosons and fermions Higher order corrections are also introduced. The formalism is rather general and will be applied to other cases in forthcoming articles.

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