The quantum second virial coefficient Bq for 3He is calculated from first principles at low density in the temperature range 0.005–10 K. By “first principles”, it is meant that the many-body phase shifts are first determined within the Galitskii–Migdal–Feynman formalism; they are then plugged into the Beth–Uhlenbeck formula for Bq. A positive Bq corresponds to an overall repulsive interaction; a negative Bq represents an overall attractive interaction. The s-wave scattering length a0 is calculated quite accurately as a function of the temperature T. The effect of the (low-density) medium on Bq is studied. Bq is then used to determine the volume of 3He at the saturation curve. The compressibility is evaluated as a measure of the non-ideality of the system.

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The second virial coefficient B for 132xenon (132Xe) vapor is evaluated over the broad temperature-range 0.1 mK–30 000 K. The classical expression for B, Bcl, is used, as well as the first quantum correction Bqc, and the quantum second virial coefficient, Bq. The borderline interfacing the classical and quantum regimes is explored. It turns out that B is a powerful indicator of the demarcation boundary between the classical and quantum regimes. Equally important is that a very large negative Bq is symptomatic of conditions favoring clustering. Small 132Xe clusters are predicted at low temperatures ~10−2 K. Our results are compared to previous results whenever possible. The agreement is very good.