Multiphonon inelastic scattering of helium atoms from crystal surfaces

The transition from single phonon to multiphonon energy transfer in atom–surface collisions

“…This multiphonon theory has previously been able to explain the shape and temperature dependence of the background in a number of atom-surface scattering systems. [43][44][45] In the classical limit of high temperatures and large projectile energies Eq. ͑1͒ can be evaluated in closed form to give 25,26 dR…”

“…͑4͒ by noting that the nth order term in the multiphonon expansion involves an nth order convolution on the phonon spectral density, which tends to wash out all of the details. Ample experimental and theoretical evidence for this effect exists, 28,[43][44][45]52 and this relative in-sensitivity to the form of the phonon spectral density is the justification for our use of the Debye model. The only important defect of the Debye model results from the fact that it overestimates the correlation at large separation distances.…”

“…At very low energies and surface temperatures the single phonon events are predominant, but with increasing beam energies and surface temperatures the single quantum peaks decrease in intensity while the broad diffuse multiphonon background increases in intensity and width. 23 The quantum peaks decrease in intensity according to the well known Debye-Waller behavior and the point at which they disappear altogether marks the onset of the classical regime. At the highest surface temperatures studied here the limit of large phonon quantum numbers is reached and the system becomes fully classical as expected from the correspondence principle of quantum mechanics.…”