Bose-Fermi mixtures in the molecular limit

We consider a Bose-Fermi mixture in the molecular limit of the attractive interaction between fermions and bosons. For a boson density smaller than or equal to the fermion density, we show analytically how a T-matrix approach for the constituent bosons and fermions recovers the expected physical limit of a Fermi-Fermi mixture of molecules and atoms. In this limit, we derive simple expressions for the self-energies, the momentum distribution function, and the chemical potentials. By extending these equations to a trapped system, we determine how to tailor the experimental parameters of a Bose-Fermi mixture in order to enhance the indirect Pauli exclusion effect on the boson momentum distribution function. For the homogeneous system, we present finally a diffusion Monte Carlo simulation which confirms the occurrence of such a peculiar effect.