Calculating vibrational-excitation cross sections off the energy shell: A first-order adiabatic theory

We report the implementation of a first-order nondegenerate adiabatic theory for vibrational excitation of H2 by electrons with energies from threshold to 10 eV. Solution of the scattering equations in this method is far simpler than in a full close-coupling calculation because the method is based on an adiabatic factorization of the electron-molecule scattering ket. The method, however, yields low-energy cross sections that are far more accurate than those of traditional adiabatic-nuclei approximations because its transition matrix is calculated off the energy-momentum shell