Electronic pseudocharge model for the Cu(111) longitudinal-surface-phonon anomaly observed by helium-atom scattering

The phonon-dispersion curves of the Cu(111) surface have been calculated in the framework of an electronic multipole model. The electronic pseudocharges are located at the midpoints between nearest-neighbor ions of the lattice and are expanded in terms of their dipole and quadrupole deformabilities. The anomalous longitudinal resonance observed by helium-atom scattering (HAS) is accounted for by increasing the dipolar and quadrupolar bulk deformabilites at the surface. Moreover the model explains in a straightforward way the apparent contradiction between force constants obtained from a fit of the HAS data and of similar dispersion curves measured by electron scattering. Thus the enhanced inelastic HAS intensity of the longitudinal resonance, which previously required extreme force-constant adjustments, is instead attributed to an additional contribution from the inelastic interaction of the He atoms with the dipolar and quadrupolar modulations of the surface electron density.