The electron impact vibrational excitation of H 2 molecules physisorbed on a free-electron metal surface is studied theoretically at collision energies of a few eV. The role of the short-lived low-lying 2Σ u resonance is investigated. The electron scattering by a free H 2 molecule is described by the R-matrix method and the corresponding results are used to model the electron scattering by the physisorbed molecule with the coupled angular mode (CAM) method. The strength of the vibrational excitation and, in particular, the overtone vibrational excitation ratio are found to be smaller for the physisorbed molecule than for the free molecule. However, the energy dependence of the vibrational excitation process is found to be weakly influenced by the physisorption, as observed experimentally by Demuth et al. [Phys. Rev. Lett. 47 (1981) 1166].
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