  We study the process of absorption or emission of a bosonic collective
excitation by a fermionic quasiparticle in a superfluid of paired fermions.
From the RPA equation of motion of the bosonic excitation annihilation
operator, we obtain an expression of the coupling amplitude of this process
which is limited neither to resonant processes nor to the long wavelength
limit. We confirm our result by independently deriving it in the functional
integral approach using the gaussian fluctuation approximation, and by
comparing it in the long wavelength limit to the quantum hydrodynamic result.
Last, we give a straightforward application of the coupling amplitude we obtain
by calculating the lifetime of the bosonic excitations of arbitrary wave
number. We find a mode quality factor that decreases from its maximum at low
wave numbers and vanishes when the bosonic branch hits the pair-breaking
continuum.
