Elastic electron scattering by ethylene, C2H4

As a prototypical polyatomic molecule, ethylene, C2H4, has been of interest from the earliest days of electronmolecule collision studies 1 and has continued to attract interest up to the present 2 . Recent careful and detailed measurements 3 of the low-energy elastic differential cross section DCS pose a challenge to theory, exhibiting features that have not been reproduced in high-level calculations 4–6 , including our own. In particular, the calculated DCS fails to exhibit the local minimum that is observed in smallangle scattering above the energy of the * resonance. Buckman and Chadderton 7 and Kitajima and co-workers 8 have noted the ubiquity of similar minima in low-energy electron-molecule scattering and the desirability of improved calculations in this energy range. The principal limiting approximations in calculations of electron-molecule elastic collision cross sections arise in the treatment of polarization effects—that is, the dynamic response of the target molecule to the presence of the projectile—and in the treatment of nuclear motion. Most calculations have been carried out in the fixed-nuclei approximation, which breaks down when the interaction time is long. An exception is the study of Trevisan and co-workers 5 , who included the symmetric stretch vibration in the adiabatic approximation. Vibrational effects proved important in the immediate vicinity of the * resonance but were minor at higher or lower energies, and below 8 eV, the results of Trevisan and co-workers, though the best computed values reported to date, do not agree in detail with the measurements, particularly at small scattering angles. To improve our understanding of what is required to compute accurate electron-molecule cross sections in the lowenergy range, we conducted an extensive study of lowenergy elastic electron scattering by two small molecules that display low-energy shape resonances, N2O and C2H4. In the course of our study, we examined vibrational effects to some degree, and we also experimented with different one-electron basis sets, but we focused on the representation of polarization as likely the most critical limiting factor. Results for N2O will be reported separately. In this paper, we present results for C2H4 that demonstrate the effectiveness of a straightforward procedure for incorporating polarization effects. As will be seen, the procedure adopted is successful at capturing details of the low-energy DCS, including the small-angle minimum, that were not obtained in previous calculations.