  We argue that the well known Dynes formula [Dynes R C {\it et al.} 1978 {\it
Phys. Rev. Lett.} {\bf 41} 1509] for the superconducting quasiparticle density
of states, which tries to incorporate the lifetime broadening in an approximate
way, cannot be justified microscopically for conventional superconductors.
Instead, we propose a new simple formula in which the energy gap has a finite
imaginary part $-\Delta_2$ and the quasiparticle energy is real. We prove that
in the quasiparticle approximation 2$\Delta_2$ gives the quasiparticle decay
rate at the gap edge for conventional superconductors. This conclusion does not
depend on the nature of interactions that cause the quasiparticle decay. The
new formula is tested on the case of a strong coupling superconductor
Pb$_{0.9}$Bi$_{0.1}$ and an excellent agreement with theoretical predictions is
obtained. While both the Dynes formula and the one proposed in this work give
good fits and fit parameters for Pb$_{0.9}$Bi$_{0.1}$, only the latter formula
can be justified microscopically.
