Many-body effects on the lifetime of Shockley states on metal surfaces

The lifetime of Shockley states on metal surfaces is calculated on the assumption that the Coulomb interaction between electrons in Shockley states is mainly responsible for the finite lifetime of these states, and that the Coulomb interaction would be screened by the bulk electrons. With single-particle wave functions of Shockley states, the Fourier expansion component of the screened Coulomb potential, Vs, is calculated, and the dependence of Vs on the lattice constant and the width of the projected band gap at the edge of the first Brillouin zone are investigated. A second-order perturbation calculation with respect to Vs is made for the self-energy of a single electron in Shockley states, and lifetimes of these states are calculated. Then, effects of the penetration into the bulk of Shockley states on the lifetime are investigated, and lifetimes of Shockley states on Cu(1 1 1), Ag(1 1 1) and Au(1 1 1) surfaces are evaluated.