A calculation of the electron quasiparticle lifetime in a disordered metal due to electron-electron scattering is given. The calculation takes account of the diffusive nature of electron motion which leads to enhancement of the diagonal exchange term of the electron self-energy. The lifetime, as a function of temperature, behaves as $T^{-\frac{d}{2}}$ where $d$ is the dimensionality, in contrast to the $T^{-2\mathrm{}}$ behavior of ordinary Fermi-liquid theory. At $d=2\mathrm{}$, a logarithmic singularity occurs which leads to ${\left(T\ln T\right)}^{-1\mathrm{}}$ behavior of the lifetime and a failure of the quasiparticle picture near the Fermi surface. The calculated lifetime agrees in temperature, Fermi energy, and elastic mean-free-path dependence with recent experiments on silicon inversion layers.

• Received 27 July 1981

DOI:https://doi.org/10.1103/PhysRevB.24.6783