Lie algebraic method for vibrational and rotational transitions in inelastic collisions of a molecule with a solid surface

Abstract

The vibrational and rotational transitions of a diatomic molecule in inelastic gas-surface scattering have been studied using the Lie algebraic approach of Alhassid and Levine [Phys. Rev. A 18 (1978) 89]. We have build a Hamiltonian describing the molecule-surface scattering and used it to construct a dynamical Lie algebra h 6. The expressions for the wavefunction of the system near the surface ( z 2~ 0) are explicitly obtained. All the internal rotational and vibrational modes of a diatomic molecule and their coupling have been taken into account in the theoretical model. This wavefunction is applied to compute analytically the transition probabilities from an initial-vibrational state to another final one, for a model problem of H 2 scattering from the LiF(001) surface. The computed probabilities are in good agreement with those obtained using an accurate coupled-channel method.