Electron-electron scattering rate in disordered mesoscopic systems

The inelastic quasiparticle lifetime due to the electron-electron interaction (out-scattering time in the kinetic equation formalism) is calculated for finite metallic diffusive systems (quantum dots) in the whole range of parameters. Both cases of ''continuous'' (the inelastic level broadening much exceeds the mean level spacing) and ''discrete'' spectrum are analyzed. In particular, the crossover between one- and zero-dimensional regimes is studied in detail. In the case of a continuous spectrum the out-scattering time is shown to be the same as the inelastic time entering expressions for universal conductance fluctuations and persistent currents. It is also found to be shorter than the phase-breaking time in two- and one-dimensional systems, while in zero-dimensional systems these two times coincide. In the case of a discrete spectrum for small enough systems a universal behavior of the scattering time is obtained. For temperatures below the mean level spacing the out-scattering rate is shown to be vanishingly small.