  An effective interaction between fermions in a Bose-Fermi mixture is derived.
It is induced by density fluctuations of the bosonic background. The
contributions from states containing both one and two virtual phonons are taken
into account self-consistently. The time dependence of the effective
interaction has been removed by assuming that the velocity of the fermions at
the Fermi surface is much larger than the sound velocity in the Bose gas. The
fermions are considered in only one magnetic state, so that pairing can be
effective only in odd-l channels. It has been found that the onset of the
superconducting phase can occur at temperatures (> 100nK) of the same order of
magnitude as the Fermi temperature (300nK), and the energy gap in the
excitation spectrum is a small fraction (1%) of the Fermi energy.
