The linewidth of surface states of simple metals

The linewidths (inverse lifetimes) Γ_e-e of Be(0001) and Mg(0001) surface electronic states are calculated as the projection of the imaginary part of the self-energy operator of a quasiparticle onto the state. The screened Coulomb interaction is calculated using a model potential, which takes into account the energy gap in the band structure and a surface state located in this gap. The wave functions and energies of electron states are calculated by a self-consistent film pseudopotential method. It is shown that Γ_e-e essentially depends on the position of the surface state in the Brillouin zone. The difference between the calculated values of Γ_e-e and those obtained in a homogeneous electron gas model is shown to be basically due to transitions from surface bands.