The theory of electron scattering by molecules is presented in terms of Feshbach's projection-operator formalism with special attention to the problem of molecular rotational excitation. The absolute orders of magnitude and the energy dependence of the cross section for resonance rotational excitation are calculated for the (${\mathrm{N}}_2$, $e$) system. The characteristic multipeak structure for resonance elastic scattering and vibrational excitation is again found for resonance rotational excitation. A comparison of the calculated results with experimental measurements is made for peak positions in the cross section for resonance elastic scattering, which may be considered as a special case of resonance rotational excitation (i.e., $\Delta l_0=0\mathrm{}$). Cross sections for simultaneous rotational and vibrational excitation of ${\mathrm{N}}_2$ are also calculated. The total partial cross sections for resonance vibrational excitation are then obtained as a sum of all the corresponding partial cross sections with different allowed rotational transitions. The energy dependence of the newly obtained vibrational excitation cross section compares favorably with experimental observations.

• Received 2 August 1965

DOI:https://doi.org/10.1103/PhysRev.146.61