Unitary boson-boson and boson-fermion mixtures: third virial coefficient and three-body parameter on a narrow Feshbach resonance

Abstract: We give exact integral expressions of the third cluster or virial coefficients of binarymixtures of ideal Bose or Fermi gases, with interspecies interactions of zero range andinfinite s-wave scattering length. In general the result dependson three-body parameters R_t appearing inthree-body contact conditions, because an Efimov effect is present or because the mixtureis in a preefimovian regime with a mass ratio close to an Efimov-effect threshold. We givea new, exact integral expression of R_t for the microscopicnarrow Feshbach resonance model. A divergence of R_t in the preefimovianregime at a scaling exponent s= 1 / 2 is predicted and physically discussed. Theanalytical results are applied to typical species used in cold atom experiments. Graphical abstract: [Figure not available: see fulltext.]