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Approximate expressions for inelastic elements of the S matrix are given in terms of integrals over vibrational functions and R-matrix electron states. The magnitude and symmetry of these integrals determine the vibrations that are excited by various resonances, and the present analysis successfully predicts the spectra measured for benzene, ethylene, and formaldehyde. The recently observed s-wave component in the rotational excitation of ${\mathrm{N}}_{2}$ is also explained by the treatment. The theory shows how vibrational excitation can give information about the symmetries of resonant electronic states. This can be particularly useful when angular distribution measurements are unavailable.

Selection rules for vibrational energy loss by resonant electron impact in polyatomic molecules