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 ‹ Φ_νf (R) |φ_νi (R,t)›⁠, where φ_νi(R,t) ≅e^{−iH_A2−(R)t∕ℏ}Φ_νi(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 _νi (R) and Φ _νf (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.