Phonon sudden theory of Debye-Waller attenuation. Temperature dependence of rotational energy transfer in molecule/surface scattering

A model for the description of thermal attenuation in atom, molecule/surface scattering is presented. It is based on the energy sudden approximation for all degrees of freedom, i.e., phonons, diffraction, and rotation, and leads to a generalized Debye-Waller factor that depends on the rotational transition and is valid for arbitrary interaction potentials. The traditional Debye-Waller factor is recovered for a hard potential. Assuming a Debye frequency spectrum for the phonons we present two model calculations for molecule/surface scattering. In the first case we assume a pairwise interaction between the atoms of the molecule and the surface atoms and observe a temperature dependence of the rotational transition probabilities, which is due to both the rotational energy transfer and the rotational dependence of the Debye-Waller factor. In the second case we model NO/Ag(111) scattering and conclude that a variation of the surface temperature has only a slight influence on the final rotational state distribution which is in accordance with the experimental findings of Auerbach et al. The mean rotational energy transfer shows a slight linear increase with the temperature as recently observed by Kubiak et al.