Mean field approach to molecule–surface scattering at finite temperature: One phonon theory

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Abstract
A theory is presented for the phonon inelastic scattering of light atoms and molecules from surfaces. Both the gas species and the thermal fluctuations of the solid are treated in a fully quantum fashion. A self-consistent field method is used to reduce the evolution of the reduced density matrix to the propagation of a single wave function and a set of coefficients describing phonon excitation and annihilation. The method allows one to extend recent time dependent molecule–surface scattering theories to finite temperature, with only a small increase in computer time. Agreement is found with experimental data for the thermal attenuation of diffraction peaks for He scattered from Cu. Energy transfer is found to be sensitive to the steepness of the repulsive potential, the molecular kinetic energy, and the angle of incidence, and only weakly dependent on the well depth. The ‘‘Beeby correction’’ is examined and shown to be invalid, except at very low beam energies where there is a small correlation between well depth and inelastic scattering. For this model, energy transfer does not scale with the normal component of the beam energy.