URSELL OPERATORS IN STATISTICAL PHYSICS .1. GENERALIZING THE BETH-UHLENBECK FORMULA

The Beth Uhlenbeck formula gives an exact (quantum) expression of the second virial correction to the equation of state of a (slightly degen erate) dilute gas. We show how this result can be extended to arbitrar y degeneracy provided that the interaction potential has a sufficientl y short range. For this purpose we develop a formalism based on the us e of Ursell operators, which contain no symmetrization in themselves ( they correspond to an auxiliary system of distinguishable particles) a nd we show how they can also be used for a system of identical particl es. A concise expression generalizing the Beth Uhlenbeck formula is ob tained, which is equally valid for bosons and fermions. Higher order c orrections are also introduced. The formalism is rather general and wi ll be applied to other cases in forthcoming articles.