  We investigate the fermionic quasiparticle branch of superfluid Fermi gases
in the BCS-BEC crossover and calculate the quasiparticle lifetime and energy
shift due to its coupling with the collective mode. The only close-to-resonance
process that low-energy quasiparticles can undergo at zero temperature is the
emission of a bosonic excitation from the phononic branch. Close to the minimum
of the branch we find that the quasiparticles remain undamped, allowing us to
compute corrections to experimentally relevant quantities such as the energy
gap, location of the minimum, effective mass, and Landau critical velocity.
