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

Abstract

Vibrational excitation (ν_f←ν_i) cross-sections σ_νf-νi(E) in resonant e-N₂ and e-H₂ scattering are calculated from transition matrix elements T_νf,νi(E) obtained using Fourier transform of the cross correlation function <φν_f(R)|ψν_i(R,t)>, where ψν_i(R,t) ≅ e^{-iHA₂-(R)t/h}φ_νi(R) with time evolution under the influence of the resonance anionic Hamiltonian HA₂^-(A₂^- = N₂^-/H₂^-) implemented using Lanczos and fast Fourier transforms. The target (A₂) vibrational eigenfunctions φν_i(R) and φν_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.