An evaluation of the kinematic approximation in helium atom scattering using wavepacket calculations

We use 2-D wavepacket calculations to examine the scattering of helium atoms from dynamic assemblies of surface adsorbates, and in particular to explore the validity of the widely used kinematic scattering approximation. The wavepacket calculations give exact results for quasi-elastic scattering that are closely analogous to time-of-flight (TOF) experiments and they are analysed as such. A scattering potential is chosen to represent 8 meV helium atoms scattering from sodium atoms adsorbed on a Cu(001) surface and the adsorbates in the model move according to an independent Langevin equation. The energy broadening in the quasi-elastic scattering is obtained as a function of parallel momentum transfer and compared with the corresponding results using the kinematic scattering approximation. Under most circumstances the kinematic approximation and the more accurate wavepacket method are in good agreement; however, there are cases where the two methods give different results. We relate these differences to pathological features in the scattering form-factor.