Vibrational excitation resulting from electron capture in LUMO of F2 and HCl – A treatment using the time-dependent wave packet approach#

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Vibrational excitation cross-sections \(\sigma_{\nu_f \leftarrow \nu_i } (E)\) in resonant e-F2 and HCl scattering are calculated from transition matrix elements \(T_{\nu_f \leftarrow \nu_i } (E)\) obtained using Fourier transform of the cross correlation function \(\left\langle {\phi_{\nu_f } \left( R \right)\vert \Psi_{\nu_i } \left( {R,t} \right)} \right\rangle \) where \(\Psi_{\nu_i } \left( {R,t} \right)\approx e^{-i\hbar H_{AB^-} \left( R \right)t}\phi_{\nu { }_i} \left( R \right)\). Time evolution under the influence of the resonance anionic Hamiltonian H AB - (AB=F2/HCl) is effected using Lanczos reduction technique followed by fast Fourier transform and the target (AB) vibrational eigenfunctions \(\phi _{\nu_i } \left( R \right)\) and \(\phi_{\nu_f } \left( R \right)\) are calculated using Fourier grid Hamiltonian method applied to potential energy (PE) curve of the neutral target. The resulting vibrational excitation cross-sections provide reasonable agreement with experimental and other theoretical results. The vibrational excitation cross-sections in e-F2 and e-HCl scattering have been calculated with local complex potential based time dependent wave packet approach and compared with those of other theoretical/experimental results.