Inelastic Gas-Surface Scattering.
Helium and molecular hydrogen scattering from copper is calculated to examine general features of scattering for these systems, especially the quantum mechanics of the scattering process, both for the motion of the particle and the excitations of the lattice. This thesis outlines the nature of the scattering problem, develops techniques for calculating scattering probabilities, develops an approximation for the potential, and calculates scattering probabilities. The quantum mechanics of the system is essential both for the particle because of diffraction, discrete rotational transitions, and selective adsorption and for the lattice because the occupation of only a few phonon modes changes during the scattering. In many ways it is similar to neutron scattering from solids except the scattering is much stronger so that its theoretical treatment, while similar to the Born approximation used for neutron scattering, uses distorted waves instead of plane waves. Using a formal method of thermally averaging the scattering probabilities of self-consistent one-phonon approximation is developed to study the effect of inelastic scattering on diffraction and selective adsorption resonances. The relationship of this scheme to the distorted wave Born approximation is shown in a diagrammatic expansion of the distorted wave Born series. These calculations use a form for the interaction potential chosen to simplify the numerical calculation while retaining the essential physics of the interaction. It is assumed that: the surface is flat, only the harmonic coupling to the phonons is important, the phonon density of states is given by an isotropic elastic continuum model, and the coupling to the phonons is separable with gaussian dependence on the phonon parallel wavevector and z dependence given by the derivative of the static surface potential. He scattering calculations test how well these approximations reproduce experimental results and how the scattering probabilities depend on the details of the potential. H(,2) and D(,2) trapping on surfaces is studied for the effects due to the rotational degrees on freedom. HD scattering is used to examine the effect of inelastic scattering on rotationally inelastic scattering both for non-resonant scattering and for selective adsorption resonances.
- Pub Date:
- Physics: Condensed Matter