  We consider a mixture of a single-component Bose gas and a two-component
Fermi gas at temperatures where the Bose gas is almost fully condensed. In such
a mixture, two fermionic atoms can interact with each other by exchanging a
phonon that propagates through the Bose condensate. We calculate the
interaction potential due to this mechanism and determine the effective s-wave
scattering length for two fermions that interact, both directly by the
interatomic potentials, as well as by the above mentioned exchange mechanism.
We find that the effective scattering length is quite sensitive to changes in
the condensate density and becomes strongly energy dependent. In addition, we
consider the mechanical stability of these mixtures and also calculate the
dispersion and the damping of the various collisionless collective modes of the
gas.
