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Partial ionisation cross sections for the binary-encounter Bethe model

Anthony Jeseněk, Alejandro Luque, Nikolai Lehtinen

Abstract

The original binary-encounter Bethe model of Kim and Eugene Rudd (1994 Phys. Rev. A 50 3954-67) has proven to be an accurate analytical representation of total impact ionisation cross sections of electrons colliding with atoms and molecules. It is based on a decomposition into partial ionisation cross sections from electrons in bound orbitals. Despite the model's accuracy for total ionisation, its individual partial cross sections for ionisation rely on thresholds calculated theoretically which systematically overestimate the experimental orbital binding energies. Here, we examine the BEB model's performance when based on experimental ionisation thresholds. The resulting partial cross sections of the various final (excited) ionic states produced could help to prefigure subsequent optical radiations and non-radiative transitions in models of plasma physics.

Partial ionisation cross sections for the binary-encounter Bethe model

Abstract

The original binary-encounter Bethe model of Kim and Eugene Rudd (1994 Phys. Rev. A 50 3954-67) has proven to be an accurate analytical representation of total impact ionisation cross sections of electrons colliding with atoms and molecules. It is based on a decomposition into partial ionisation cross sections from electrons in bound orbitals. Despite the model's accuracy for total ionisation, its individual partial cross sections for ionisation rely on thresholds calculated theoretically which systematically overestimate the experimental orbital binding energies. Here, we examine the BEB model's performance when based on experimental ionisation thresholds. The resulting partial cross sections of the various final (excited) ionic states produced could help to prefigure subsequent optical radiations and non-radiative transitions in models of plasma physics.
Paper Structure (23 sections, 6 equations, 4 figures)

This paper contains 23 sections, 6 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The orbital binary-encounter Bethe model
  3. The scaling parameter $K_j$
  4. The dipole oscillator strength
  5. The Hartree-Fock orbitals
  6. Ionisation channels
  7. Application
  8. Atoms
  9. C.
  10. N.
  11. O.
  12. F.
  13. Diatomic molecules
  14. N$_2$.
  15. CO.
  16. ...and 8 more sections

Figures (4)

  • Figure 1: Partial ionisation cross sections obtained with the BEB model for atomic oxygen (top), nitric oxide (middle) and ozone (bottom) with parameters reported in table \ref{['tab:long']}. Lighter colours are associated to outer orbitals (lower binding energies). Different line styles distinguish ionisations corresponding to a removal of an electron from a same orbital but with different ionic outcomes. Coupling between momenta of unpaired electrons leads to different ionic states whose multiplicities reflect their intensity as in atomic oxygen and the triplets and singlets in nitric oxide. The orbital picture does not apply well to ozone. Although the first three ionic states may still be identified with electron ejection from an orbital with a leading configuration [in square brackets], ionisations from deeper valence orbitals (*) may only be identified with final ionic states whose many vibrational bands overlap over a certain region in the photoelectron spectrum, and which are bundled together to form the "partial" impact ionisation cross sections drawn on the bottom graph.
  • Figure 2: Partial ionisation cross sections from the 1s shell of C, N and O atoms in their free form and bound in various molecules. The 1s binding energies $I$ are reported in the first rows of table \ref{['tab:long']} for each gaseous element. The scaling energy $K$ is calculated with eq. (\ref{['eq:K-sc']}). Fluorescence factors used to convert experimental data are from Tawara1973: $\omega_{C_{1s}}=2.47e-3$Honicke2023, $\omega_{N_{1s}}=4.35e-3$, $\omega_{O_{1s}}=6.91e-3$Liu2000 (see main text for explanation).
  • Figure 3: "Orbital" ionisation cross sections obtained with the BEB model for atomic nitrogen (top), molecular oxygen (middle) and carbon dioxide (bottom). Solid lines (---) show the sum of partial cross sections from ionisation channels associated to removal from a molecular orbital with parameters reported in table \ref{['tab:long']}. Dashed lines (-----) of the same colour correspond to original BEB model with theoretical thresholds from Hartree-Fock calculations. The shattered lines ($\cdots$-----) show the BSR calculations for N from Wang2014N. Higher ionisation thresholds directly imply roughly proportionally lower cross sections as can be identified from eq. (\ref{['eq:beb']}). This difference permains on the total ionisation cross section in fig. \ref{['fig:BEB']}.
  • Figure 4: Sum of partial ionisation cross sections from the BEB model with experimental ionisation thresholds $I$ (table \ref{['tab:long']}) in red solid (---) and original Hartree-Fock theoretical binding energies in cyan (---) compared with experimentally measured total ionisation cross sections for four atoms, four diatomic and four triatomic molecules. For atomic targets (left column), BSR calculations are shown in light green (---) from Wang2013CWang2014NTayal2016OGedeon2014F. Experimental data are from Brook1978phe-Atom-2Thompson1995Hayes1987Gaudin1967Schram1965Schram1966Almeida1995Rejoub2002Rapp1965Orient1987Itikawa2006Itikawa2009Itikawa2016Shen2018Kim1981Djuric1988Straub1998Lindsay2000Newson1995phe-Molc-5.1. The alignment of the source labels echoes the 4$\times$3 grid, although some sources give data for many different targets.