Lifetimes of Image-Potential States on Copper Surfaces

The lifetime of image states, related to the coupling of surface electronic states with the solid substrate, has been recently determined for quantum numbers $n\ensuremath{\le}6$ on Cu(100) by using time-resolved two-photon photoemission in combination with the coherent excitation of several states [U. H\"ofer et al., Science 277, 1480 (1997)]. We evaluate the lifetimes of image states on copper surfaces from the self-energy of the excited quasiparticle, which we compute within the $\mathrm{GW}$ approximation. Single-particle wave functions are obtained by solving the Schr\"odinger equation with a realistic one-dimensional model potential, and the screened interaction is evaluated in the random-phase approximation. Our results are in agreement with experimentally determined decay times.