URSELL OPERATORS IN STATISTICAL PHYSICS .2. MICROSCOPIC PROPERTIES OFA DILUTE QUANTUM GAS

We apply the formalism of Ursell operators, introduced in a previous a rticle, to the calculation of reduced density operators (one and two-b ody density operators) in a dilute quantum gas; the calculation is not a fugacity expansion and is therefore not limited to low degrees of d egeneracy. We obtain quantum corrections for the one-particle density operator as a function of the second Ursell operator. For the two-body density operator, we examine how statistics and interactions combine their effects on the correlations between particles; in particular we discuss in detail how hard cores potentials affect the short range cor relations, a non-perturbative effect.