LIE ALGEBRAIC-METHOD FOR VIBRATIONAL AND ROTATIONAL TRANSITIONS IN INELASTIC-COLLISIONS OF A MOLECULE WITH A SOLID-SURFACE

The vibrational and rotational transitions of a diatomic molecule in i nelastic gas-surface scattering have been studied using the Lie algebr aic approach of Alhassid and Levine [Phys. Rev. A 18 (1978) 89]. We ha ve 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 similar to 0) are explicitly obtained, All the internal rotational and vibrational modes of a diatomic molecule and their coupling have been taken into accoun t in the theoretical model. This wavefunction is applied to compute an alytically the transition probabilities from an initial rotation-vibra tional state to another final one, for a model problem of H-2 scatteri ng from the LiF(001) surface. The computed probabilities are in good a greement with those obtained using an accurate coupled-channel method.