Simple systematization of vibrational excitation cross-section calculations for resonant electron-molecule scattering in the boomerang and impulse models

Abstract

Vibrational excitation (f i) cross-sections f i (E) in resonant e- N2 and e- H2 scattering are calculated from transition matrix elements T f, i (E) obtained using Fourier transform of the cross correlation function 〈 φ f (R) ∫ ψ i (R,t) 〉, where ψ i (R,t) ≃ e-i H A2 - (R) t φ i (R) with time evolution under the influence of the resonance anionic Hamiltonian H A2- (A2- = N2- H2-) implemented using Lanczos and fast Fourier transforms. The target (A2) vibrational eigenfunctions φ i (R) and φ f (R) are calculated using Fourier grid Hamiltonian method applied to potential energy (PE) curves of the neutral target. Application of this simple systematization to calculate vibrational structure in e- N2 and e- H2 scattering cross-sections provides mechanistic insights into features underlying presence/absence of structure in e- N2 and e- H2 scattering cross-sections. The results obtained with approximate PE curves are in reasonable agreement with experimental/calculated cross-section profiles, and cross correlation functions provide a simple demarcation between the boomerang and impulse models. © 2007 American Institute of Physics.