The relaxation rate in hot-electron dynamics: beyond the first-order Born approximation in kinetic theory

The validity of a perturbative approach to studying the lifetime of excited electrons in an electron gas is analysed in a range of metallic densities. The relaxation rate is calculated using a kinetic theory framework with second-order Born and partial-wave approximations for the scattering amplitude. The comparison of the terms obtained by physically motivated Thomas-Fermi-type potentials shows that the next-to-leading correction to the first-order result is small only for high densities of the electron gas. At low densities, a nonperturbative estimation of the relaxation rate is needed. An analytic expression of practical use which incorporates both the role of screening and scattering is derived. A comparison with experimental data obtained for an Ag(111) surface is made. The agreement found supports an inherent consistency, under the experimental conditions and down to (E-EF) 0.4 eV, of the theoretical description based on a three-dimensional Fermi-liquid model