Abstract
We treat vibrational excitation of hydrogen by low-energy electrons using an improved nonlocal resonance model. The model is based on accurate ab initio data for the $^{2}\ensuremath{\Sigma}_{u}^{+}$ shape resonance and takes full account of the nonlocality of the effective potential for nuclear motion. Integral vibrational excitation cross sections were calculated for numerous initial and final rovibrational states of the hydrogen molecule, and the dependence of the vibrational excitation cross section on the rovibrational initial target state has been investigated. The vibrational excitation cross sections are in very good agreement with measurements for the transitions $v=0\ensuremath{\rightarrow}1$ and $v=0\ensuremath{\rightarrow}2$, while for higher vibrational channels the agreement is less satisfactory. However, the oscillatory structures in $v=0\ensuremath{\rightarrow}4$ vibrational excitation and higher channels predicted by Domcke and collaborators and measured by Allan are described by the present calculation, in very good agreement with the experimental data. A detailed analysis of the origin of the oscillations has been performed. It is shown that the oscillations can be qualitatively understood within the so-called boomerang model of Herzenberg. The resonance contribution to the vibrationally elastic scattering $(v\ensuremath{\rightarrow}v)$ is also discussed. It is found that this cross section is dominated at low energies by the resonance contribution, as predicted by Schulz. The calculated integral vibrational excitation cross sections generally are in good agreement with other theoretical data obtained by different approaches. A comprehensive study of the effect of isotopic substitution has been performed, and an inverse isotope effect in vibrational excitation has been found for certain vibrational levels of the target.
Published Version
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