Hybrid theory and calculation ofe-N2scattering

A theory of electron-molecule scattering is developed which is a synthesis of close-coupling and adiabatic-nuclei theories. Specifically, the theory is close coupling with respect to vibrational degrees of freedom but adiabatic-nuclei with respect to rotation. In addition, this theory can be applied to any number of partial waves required; the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations and not on experiment can be given as to which partial waves and energy domains require the various approximations. The theory allows all cross sections (i.e., pure rotational, vibrational, simultaneous vibration-rotation, differential, and total) to be calculated. Explicit formulas for all these cross sections are given. The theory is applied to low-energy $e$-${\mathrm{N}}_2$ scattering. The fixed-nuclei results are such that the criterion shows clearly that vibrational close coupling is necessary, but only for the ${\Pi }_g$ partial wave. The contribution of remaining partial waves can be obtained directly from the adiabatic-nuclei approximation. The close-coupling calculation for the ${\Pi }_g$ wave is carried out, and we find that it does give rise to the substructure as well as the gross structure of the 2.4-eV resonance. When this amplitude is combined with the adiabatic amplitudes, we can compute absolute values of all cross sections of interest. In particular we find that vibrational excitation cross sections are about twice as large as previously inferred. The momentum-transfer cross section can also be computed, and it too reveals substructure within the gross structure resonance.