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Journal Articles Journal de Physique I Year : 1995

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

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Abstract

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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Dates and versions

jpa-00247049 , version 1 (01-01-1995)

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P. Grüter, F. Laloë. Ursell operators in statistical physics I: Generalizing the Beth Uhlenbeck formula. Journal de Physique I, 1995, 5 (2), pp.181-203. ⟨10.1051/jp1:1995120⟩. ⟨jpa-00247049⟩
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