  We develop a diagrammatic approach for solving few-body problems in
heteronuclear fermionic mixtures near a narrow interspecies Feshbach resonance.
We calculate s-, p-, and d-wave phaseshifts for the scattering of an atom by a
weakly-bound dimer. The fermionic statistics of atoms and the composite nature
of the dimer lead to a strong angular momentum dependence of the atom-dimer
interaction, which manifests itself in a peculiar interference of the scattered
s- and p-waves. This effect strengthens with the mass ratio and is remarkably
pronounced in 40K-(40K-6Li) atom-dimer collisions. We calculate the scattering
length for two dimers formed near a narrow interspecies resonance. Finally, we
discuss the collisional relaxation of the dimers to deeply bound states and
evaluate the corresponding rate constant as a function of the detuning and
collision energy.
