Differential Cross Sections for the Electron-Impact Excitation of Vibrational Levels in Molecules

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Abstract
The angular dependence of scattered electrons which have excited a particular vibrational level of the ground electronic state of a molecule is investigated. General expressions are developed for the differential electron‐scattering cross sections for the excitation of vibrational levels in terms of derivatives of the ground‐state electron density and derivatives of the total electric dipole and quadrupole moments. Results for the small‐angle limit are obtained, and the errors in the theory and their possible effect on the small‐angle scattering are discussed. It is shown that contributions to the scattering from overtone and combination frequencies increase in comparison to contributions from the infrared allowed fundamental transitions with increasing scattering angle. The relationship between the electronic contribution to the large‐angle scattering and certain vibrational corrections to the vibrationally averaged three‐dimensional molecular electron density is pointed out.