Lifetime of Shockley States on Metal Surfaces

The lifetime of Shockley states on metal surfaces is calculated under 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, V s , is calculated, and the dependence of V s on the lattice constant and the width of the projected band gap at the edge of the first Brillouin zone (\(Γ̄\)) are investigated. A second-order perturbation calculation with respect to V s is performed for the self-energy of a single electron in Shockley states, and then the lifetimes of these states on Cu(111) and Ag(111) surfaces are evaluated. Our results qualitatively agree with experimental results.