Role of the intrinsic surface state in the decay of image states at a metal surface

The role of the intrinsic surface state $(n=0)$ in the decay of the first image state $(n=1)$ at the (111) surface of copper is investigated. Inelastic linewidths are evaluated from the knowledge of the imaginary part of the electron self energy, which we compute, within the GW approximation of the many-body theory, by going beyond a free-electron description of the metal surface. Single-particle wave functions are obtained by solving the Schr\"odinger equation with a realistic one-dimensional model potential, and departure of the motion along the surface from free-electron behavior is considered through the introduction of the effective mass. The decay of the first image state of Cu(111) into the intrinsic surface state is found to result in a linewidth that represents 40% of the total linewidth. The dependence of linewidths on the momentum of the image state parallel to the surface is also investigated.