Quantum versus semiclassical treatment of multiphonon effects in He-atom scattering from surfaces

Debye-Waller factor in He→Cu(001) collisions revisited: the role of the interaction potentials

“…Inelastic processes are then treated as a perturbation of the distorted waves brought about by the vibrations of the surface. In the weak coupling limit the thus calculated inelastic scattering spectrum reduces, up to a kinematic Jacobian-like factor, to the standard inelastic reflection coefficient calculated in the DWBA [14,15]. On the other hand, for strong coupling the scattering spectrum is expressed in terms of uncorrelated and correlated multiphonon scattering processes in which only one phonon can be exchanged at a certain instant, and the normalization of the entire spectrum is given by the DWF [15].…”

“…In the surface scattering experiments it gives a measure of the intensity I 0 of the elastically scattered specular beam relative to the incoming beam intensity I in and in this respect it differs from the notion introduced in neutron scattering from crystals [11,12]. So defined DWF, commonly written in the form I 0 /I in = exp(−2W ) where 2W is the corresponding Debye-Waller exponent, becomes essential in the multiphonon scattering regime because it provides the normalization proper of the scattering spectrum [13,14,15] which should obey the unitarity principle (optical theorem). Also, in contrast to the measurements of the single phonon scattering spectra, the measurements of the DWF provide values which in a sense are "absolute", i.e.…”

“…E i in this expression is sometimes also corrected for the surface potential well depth D (Beeby's correction [17]) in which case (h∆k z ) 2 is replaced by (h∆k z ) 2 + 8M He D. However, the form of the DW exponent (1) can be justified only in the regime of impulsive scattering [11,12] and therefore its validity is of limited range. In particular, for incident energies typical of thermal energy He atom scattering from surface phonons and soft projectile-surface interactions the approximation of impulsive scattering has been shown to become unreliable [15] for making quantitative comparisons with the experimental data.…”

“…Recently developed fully quantum, three dimensional (as regards the particle dynamics) and unitary multiphonon He atom scattering formalism [15] embodies also a general expression for the DWF as an essential ingredient. The application of this formalism to multiphonon He→Cu(001) collisions produced a nice agreement of theoretical predictions [10] with the experimental multiphonon spectra [9] by using the same interaction parameters as in the one-phonon theory, i.e.…”

“…This task is carried out in the present work by making use of the quoted novel multiphonon scattering formalism [13,14,15,10]. In the following sections we focus our attention specifically on the problem of which effects the various model potentials employed in recent interpretations of the one- [2,3,4,5,6] and multiphonon HAS spectra from Cu(001) [9,10] may have on the magnitude of the DWF and its variation with T s .…”