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Starting from a simple model Hamiltonian an explicit expression for the resonant vibrational excitation cross section is obtained. The formula is applied to calculate the excitation functions for the symmetric-stretch vibrational channels of the 3.8 eV shape resonance of CO 2 . The regular and non-trivial energy and channel-number dependence of the cross section is nicely reproduced. The results show a remarkable improvement over those obtained with existing theories which express the cross sections in terms of conventional vibrational overlap factors.
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Domcke et al. (1977) studied this question.
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