Lifetime of Shockley states on metal surfaces

The lifetime of Shockley states on metal surfaces is calculated under the a ssumption that the Coulomb interaction between electrons in Shockley states is mainly responsible for the finite lifetime of these states, and that th e 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, V-s, is calculated, and the dependence of V-s on the lattice constant and the width of the projected band gap at t he edge of the first Brillouin zone (<(<Gamma>)over bar>) are investigated. A second-order perturbation calculation with respect to V-s is performed f or the self-energy of a single electron in Shockley states, and then the li fetimes of these states on Cu(111) and Ag(111) surfaces are evaluated. Our results qualitatively agree with experimental results.