Inelastic scattering time in two-dimensional disordered metals
The particle-particle diffusion propagator is evaluated diagrammatically in two dimensions in the presence of inelastic scattering due to screened Coulomb interactions. As expected, an inelastic scattering rate $\frac{1}{{\ensuremath{\tau}}_{\ensuremath{\epsilon}}}\ensuremath{\propto}T\mathrm{ln}T$ cuts off the backscattering divergence responsible for localization. The ${\ensuremath{\tau}}_{\ensuremath{\epsilon}}$ thus determined is the same as the quasiparticle lifetime determined from the self-energy of the one-particle Green's function.