An expression is derived 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 of force constant changes near the surface. This expression is exact if the inelastic scattering is weak (the meaning of which is explained in the text). This theory should be experimentally verifiable, e.g. for 20 meV He atoms scattered from a W-surface.
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