ONE-PHONON CALCULATION OF ATOM-SURFACE INELASTIC-SCATTERING OF THE HE-CU(111) SYSTEM

With use of the distorted-wave Born approximation derived from an ab initio time-independent scattering theory, an expression for the differential reflection coefficient for one-phonon transitions is presented. In addition, the relation between the truncation of the interaction potential and the Debye-Waller factor is discussed. Numerical calculations are carried out for the He-Cu(111) system. The copper surface is taken to be a slab of 80 layers with nearest-neighbor interactions for the computation of the phonon dispersion relations and polarization vectors. The plate modes corresponding to the lowest two nearly-degenerate dispersion curves are mapped onto the Rayleigh modes. With use of a pair potential proposed by others, the differential reflection coefficient for one-phonon transitions corresponding to the Rayleigh modes is calculated. The phonon wave vectors are chosen to lie along the [11BAR0] direction, with magnitudes ranging from 0.05 to 0.60 angstrom-1. The shape of the differential reflection coefficient is in good agreement with experiment. It is found that the projectile mainly interacts with the vibrational motion of the atoms in the first layer of the crystal and that the interactions involving the displacements of the second or deeper layers only reduce the differential reflection coefficient slightly. The change in the differential reflection coefficient due to the Debye-Waller factor is found to be small, as the temperature increases from 60 to 300 K. Further, it is found that the differential reflection coefficient increases with increasing temperature due to the Bose-Einstein distribution of the phonons and is larger for phonon annihilation than for phonon emission because of the density of the final states of the projectile and the kinematic conditions of the scattering.