Energy dependence of quasiparticle relaxation in a disordered fermi liquid

A spectroscopic method is applied to measure the inelastic quasiparticle relaxation rate in a disordered Fermi liquid. The quasiparticle relaxation rate gamma is deduced from the magnitude of fluctuations in the local density of states, which are probed using resonant tunneling through a localized impurity state. We study its dependence on the excitation energy E measured from the Fermi level. In a disordered metal (heavily doped GaAs) we find that gamma~E3/2 within the experimentally accessible energy interval, in agreement with the Altshuler-Aronov theory for electron-electron interactions in diffusive conductors.