Polarization effects on electronic excitation of theã B31ustate of ethylene by low-energy electron impact

Abstract

In this work, we investigated the influence of polarization effects on the electronic excitation of the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{a}\text{ }{^{3}B}_{1u}$ state of ethylene. We employed the Schwinger multichannel method implemented with pseudopotentials to compute the elastic and the inelastic scattering cross sections for energies between 0 and 8 eV. Elastic calculations were performed in the static-exchange and static-exchange plus polarization approximations, and inelastic calculations were performed in a two-channel approximation with and without the inclusion of polarization effects. The scattering amplitudes are generated in the scope of the minimal orbital basis for single configuration interactions strategy. Ethylene presents a shape resonance in the ${^{2}B}_{2g}$ symmetry located close to the threshold of the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{a}\text{ }{^{3}B}_{1u}$ state. We show that the inclusion of polarization effects has a great influence on the excitation cross section and also that, in this case, just the two-channel close coupling without polarization is not enough to provide reliable results. In particular, our computed inelastic differential cross sections obtained with the proper treatment of polarization are in better agreement with the experimental values. They are smaller in magnitude than those obtained in the two-channel calculation without the inclusion of polarization effects. These results confirm our expectations reported in a recent publication on electron collisions with furan [da Costa, Bettega, and Lima, Phys. Rev. A 77, 012717 (2008)].