EXACT THEORY OF LONG-WAVELENGTH ONE-PHONON AMPLITUDES IN ATOM-SURFACE SCATTERING

We derive an expression for the probability of creating or annihilating one long-wavelength surface or bulk phonon during a scattering event, which depends on the bulk elastic constants but is independent of the details of the atom-target potential and force-constant changes near the surface. This expression is exact if the inelastic scattering is "weak" (in a precisely defined sence). This theory should be experimentally verifiable, e.g., for 20-meV He atoms scattered from a W surface.