7.1.3.3.2 Dynamical effects of the attractive potential

This chapter discusses dynamic repulsion, cutoff factor and dynamical effects of the attractive potential of surfaces. In most of the inelastic scattering calculations performed to date, static repulsive potential (V_rep) has been approximated by a pairwise sum of Born-Mayer or Yukawa potentials, or even more drastically by a vibrating wall, soft or hard. The dynamical effects of static attractive potential (V_att) can be fully included in the calculation if V_att is represented by a pairwise sum, but it is usually assumed with some justification that V_att does not contribute appreciably to the inelastic matrix elements, except at small lateral momentum transfer. Since the prime interest is in the study of surface phonon spectra throughout the surface Brillouin zone, the dynamical (V_att) can then be neglected altogether. The displacement of the turning point of He-surface collision is affected by the displacement of the underlying surface atoms. The cutoff factor in momentum space reduces the contribution to the scattering of short-wavelength phonons. Three types of resonant one-phonon scattering processes can occur on a corrugated surface. In a process of the first type the He atom is elastically scattered (diffracted) from the initial state into a surface-bound state, and then inelastically scattered out of it. In a process of the second type the He atom is inelastically scattered from the initial state into a surface-bound state, and then elastically scattered out of it. In a process of the third type, an inelastic one-phonon transition occurs between the surface-bound states of binding energies.