  The pairing of fermionic atoms in a mixture of atomic fermion and boson gases
at zero temperature is investigated. The attractive interaction between
fermions, that can be induced by density fluctuations of the bosonic
background, can give rise to a superfluid phase in the Fermi component of the
mixture. The atoms of both species are assumed to be in only one internal
state, so that the pairing of fermions is effective only in odd-l channels. No
assumption about the value of the ratio between the Fermi velocity and the
sound velocity in the Bose gas is made in the derivation of the energy gap
equation. The gap equation is solved without any particular "ansatz" for the
pairing field or the effective interaction. The p-wave superfluidity is studied
in detail. By increasing the strength and/or decreasing the range of the
effective interaction a transition of the fermion pairing regime, from the
Bardeen-Cooper-Schrieffer state to a system of tightly bound couples can be
realized. These composite bosons behave as a weakly-interacting Bose-Einstein
condensate.
