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

Andrew R Alderwick,Andrew P Jardine,William Allison,John Ellis

doi:10.1016/j.susc.2018.04.019

Abstract

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.

Highlights

The technique of helium atom scattering has been recognised for many years as being sensitive to the presence of surface adsorbates [1,2]
The kinematic analysis follows the method used by Jardine et al [31], where the kinematic lineshape is first broadened by convolution with the energy resolution and analysed identically to the data from the wavepacket calculation
Quasi-elastic scattering of helium atoms, and the helium spin-echo method, has become an important approach for studying the dynamics of adsorbate motion on surfaces

Summary

Introduction

The technique of helium atom scattering has been recognised for many years as being sensitive to the presence of surface adsorbates [1,2]. It was possible to avoid many of the difficulties using a hard-wall potential and a single scattering approximation for the dynamics. Those approximations are only valid in the case of weakly corrugated systems. Such as surface-steps and isolated adsorbates, the scattering cannot be fully described without the inclusion of multiple scattering and the hard-wall model is difficult to justify at a quantitative level [7,8]. Exact modelling of helium scattering from surfaces requires a fully quantum approach, with a realistic, soft, helium-surface potential. Such calculations are computationally expensive, even for fixed geometries, and only recently have they been used widely [8,9,10,11,12,13,14,15]

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