Boson induced s-wave pairing in dilute boson-fermion mixtures

We show that in dilute boson-fermion mixtures with fermions in two internal states, even when the bare fermion-fermion interaction is repulsive, the exchange of density fluctuations of the Bose condensate may lead to an effective fermion-fermion attraction, and thus to a Cooper instability in the s-wave channel. We give an analytical method to derive the associated Tc in the limit where the phonon branch of the Bogoliubov excitation spectrum of the bosons is important. We find a Tc of the same order as for a pure Fermi gas with bare attraction.