Electronic inelastic lifetime near a mobility edge

We calculate the inelastic quasiparticle lifetime ${\ensuremath{\tau}}_{\mathrm{in}}$ due to a Coulomb interaction in disordered bulk metals. The calculation is perturbative with respect to the interaction, but for an arbitrary disorder. We find that ${\ensuremath{\tau}}_{\mathrm{in}}$ is very sensitive to the critical current dynamics in the vicinity of a metal-insulator transition. Wegner scaling at the mobility edge yields a linear temperature dependence of ${\ensuremath{\tau}}_{\mathrm{in}}^{\ensuremath{-}1}$, in agreement with a recent experiment.