A Semi-Classical Model for Computing Vibrationally-Resolved Electron-Impact Ionization Cross Sections.*

A semi-classical model is presented for computing vibrationally-resolved electron-impact ionization cross sections for molecular nitrogen. The model extends the approach used by Wünderlich for molecular hydrogen. The multi-reference configuration interaction (MRCI) method is used with complete active space self-consistent field (CASSCF) reference wavefunctions in Molpro to compute the required electronic wavefunctions and potential energy curves (PECs). The target electron kinetic energy and the transition energy model parameters are calculated directly from the computed electronic wavefunctions. The partial cross sections for a given state-to-state, vibrationally-resolved ionization (p', v') to (p'', v'') are quantified using Franck-Condon Factors (FCFs), which are computed from the nuclear wavefunctions obtained from the Fourier Grid Hamiltonian method using the MRCI PECs. Total cross sections for a given (p', v') state are presented as a summation over the vibrational quantum number v'' of the partial cross sections (p', v') to (p'', v''), where a simplified closure relation for FCFs sets the maximum required v''. The total cross sections for several transitions are compared to literature values.