Electron collisions with ethylene: The role of multichannel-coupling effects

Romarly F. da Costa, Márcio H. F. Bettega, Márcio T. do N. Varella, Eliane M. de Oliveira, and Marco A. P. Lima

Phys. Rev. A 90, 052707 – Published 10 November 2014

Abstract

We report integral and differential cross sections for elastic and electronically inelastic ( $X^{1} A_{g} \to \tilde{a}^{3} B_{1 u}$ ) electron scattering by ethylene. The Schwinger multichannel method with pseudopotentials in the $N_{open}$ -channel-coupling scheme at the static-exchange-plus-polarization approximation is employed to calculate the scattering amplitudes at impact energies ranging from 5.7 to 50 eV. We discuss the multichannel-coupling effects in the calculated cross sections, in particular, how the number of excited states included in the open-channel space impacts the convergence of the elastic and the ( $X^{1} A_{g} \to \tilde{a}^{3} B_{1 u}$ ) excitation cross sections at higher collision energies. We found good agreement between the present calculated total cross section (which includes elastic, inelastic, and ionization contributions, the latter estimated with the binary-encounter-Bethe model) and the experimental data.

Received 5 September 2014

DOI:https://doi.org/10.1103/PhysRevA.90.052707

Authors & Affiliations

Romarly F. da Costa^1,2,*, Márcio H. F. Bettega³, Márcio T. do N. Varella⁴, Eliane M. de Oliveira², and Marco A. P. Lima²

¹Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-580 Santo André, São Paulo, Brazil
²Instituto de Física “Gleb Wataghin,” Universidade Estadual de Campinas, 13083-859 Campinas, São Paulo, Brazil
³Departamento de Física, Universidade Federal do Paraná, CP 19044, 81531-990 Curitiba, Paraná, Brazil
⁴Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970 São Paulo, São Paulo, Brazil

^*romarly.costa@ufabc.edu.br

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Vol. 90, Iss. 5 — November 2014

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Images

Figure 1
Differential cross sections for elastic electron scattering by ethylene molecules at incident energies of (a) 10 eV, (b) 15 eV, (c) 20 eV, and (d) 30 eV. Dotted (blue) line, 1-channel coupling plus polarization; dashed (orange) line, 2-channel coupling plus polarization; solid (violet) line, 17-channel coupling plus polarization; thick solid black line, 45-channel coupling plus polarization; and thin solid (blue) line, 45-channel coupling plus polarization with ficticious thresholds (see text for details). Open (green) diamonds, open black circles, (turquoise) asterisks (at 15.5 eV), and filled (red) circles: experiments from Refs. [7, 8, 9, 27], respectively.
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Figure 2
Differential cross sections for the $X^{1} A_{g} \to \tilde{a}^{3} B_{1 u}$ electronic transition of the ethylene molecule for electron impact energies of (a) 5.7 eV, (b) 7 eV, (c) 9 eV, and (d) 11 eV. Dashed (orange) line, 2-channel coupling plus polarization; long-dashed black line, 3-channel coupling plus polarization; dashed-dotted (dark-green) line, 8-channel coupling plus polarization; solid (violet) line, 17-channel coupling plus polarization. Filled (magenta) circles and open black downward triangles: experiments Refs. [13, 18], respectively.
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Figure 3
Same as Fig. 2, but at electron impact energies of (a) 15 eV, (b) 18 eV, (c) 20 eV,(d) 30.0 eV, (e) 40.0 eV, and (f) 50.0 eV. Dashed (orange) line, 2-channel coupling plus polarization; solid (violet) line, 17-channel coupling plus polarization; thick solid black line, 45-channel coupling plus polarization; thin solid (blue) line, 45-channel coupling plus polarization with ficticious thresholds (see text for details). Filled (magenta) circles and open black triangles: experiments of Refs. [13, 18], respectively, both at 14.5 eV instead of 15 eV.
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Figure 4
Total and integral cross sections for the energy region 0–50 eV. Thin solid (blue) line, 1-channel coupling plus polarization (the optical theorem gives the same result as the elastic transition); dashed (orange) line, elastic transitions for 2-channel coupling plus polarization; solid (orange) line, total cross section for 2-channel coupling plus polarization; thick dashed black line, elastic transitions for 45-channel coupling plus polarization; thick solid black line, total cross section for 45-channel coupling plus polarization; dot-dashed (indigo) line, ionization cross sections using the BEB aproximation; dot-dot-dashed (indigo) line, total cross sections for 45-channel coupling plus polarization plus ionization using the BEB approximation. Filled black circles, filled (red) squares, filled (green) diamonds, filled (blue) upward triangles, and filled (yellow) downward triangles: experiments of Refs. [1, 2, 3, 4, 5], respectively.
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Figure 5
Outgoing angular momentum convergence in the differential cross sections for the $X^{1} A_{g} \to \tilde{a}^{3} B_{1 u}$ electronic transition of the ethylene molecule for electron impact energies of (a) 15.0 eV, (b) 18.0 eV, (c) 20.0 eV, (d) 30.0 eV, (e) 40.0 eV, and (f) 50.0 eV. Short-dashed (orange) line, $ℓ_{\max} = 10$ , 2-channel coupling plus polarization; dashed-dotted (orange) line, $ℓ_{\max} = 2$ , 2-channel coupling plus polarization; thin solid (orange) line, $ℓ_{\max} = 3$ , 2-channel coupling plus polarization; short-dashed (violet) line, $ℓ_{\max} = 10$ , 17-channel coupling plus polarization; dashed-dotted (violet) line, $ℓ_{\max} = 2$ , 17-channel coupling plus polarization; short-dashed black line, $ℓ_{\max} = 10$ , 17-channel coupling plus polarization; dashed-dotted black line, $ℓ_{\max} = 2$ , 17-channel coupling plus polarization; thin solid black line, $ℓ_{\max} = 3$ , 17-channel coupling plus polarization; thick (cyan) dot-dot-dashed line, in and out angular momemtum representation with $ℓ_{\max} = 3$ , 17(45)-channel coupling plus polarization; thin solid (violet) line, in and out angular momentum representation with $ℓ_{\max} = 4$ , 17(45)-channel coupling plus polarization. Filled (magenta) circles and open black downward triangles: experiments of Refs. [13, 18], respectively.
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