Electron-impact-ionization cross sections for excited states of ${\mathrm{B}}^{q+}$ ($q=0--2$) and an investigation into $n$ scaling of ionization cross sections

Electron-impact-ionization cross sections for excited states of $B^{q +}$ ( $q = 0 - 2$ ) and an investigation into $n$ scaling of ionization cross sections

Teck-Ghee Lee, S. D. Loch, C. P. Ballance, J. A. Ludlow, and M. S. Pindzola

Phys. Rev. A 82, 042721 – Published 29 October 2010

Abstract

Nonperturbative $R$ -matrix-with-pseudostates (RMPS) and time-dependent close-coupling (TDCC) methods are used to determine electron-impact-ionization cross sections for the excited states of B, $B^{+}$ , and $B^{2 +}$ . RMPS calculated cross sections are presented for the $1 s^{2} 2 s^{2} 3 l$ and $1 s^{2} 2 s^{2} 4 l$ configurations of B, the $1 s^{2} 2 s 3 l$ and $1 s^{2} 2 s 4 l$ configurations of $B^{+}$ , and the $1 s^{2} 3 l$ , $1 s^{2} 4 l$ , and $1 s^{2} 5 l$ configurations of $B^{2 +}$ . It is shown that the TDCC-calculated cross sections for the $1 s^{2} 2 s^{2} 3 s$ configuration of B, the $1 s^{2} 2 s 3 s$ configuration of $B^{+}$ , and the $1 s^{2} 3 s$ configuration of $B^{2 +}$ are in reasonable agreement with the RMPS results. Furthermore, $n$ scaling of these nonperturbative cross sections is investigated and a scheme proposed to allow for the extrapolation of electron-impact-ionization cross sections to higher $n$ shells. Two semiempirical ionization cross-section expressions are fitted to the peak of the highest $n$ -bundled RMPS cross sections for B, $B^{+}$ , and $B^{2 +}$ . These are subsequently used for accurate evaluation of the higher $n$ -shell ionization cross sections needed to obtain temperature- and density-dependent generalized collisional-radiative ionization coefficients for the impurity and transport modeling of magnetic fusion plasmas.

Received 7 May 2010

DOI:https://doi.org/10.1103/PhysRevA.82.042721

Authors & Affiliations

Teck-Ghee Lee, S. D. Loch, C. P. Ballance, J. A. Ludlow, and M. S. Pindzola

Department of Physics, Auburn University, Auburn, Alabama 36849, USA

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Vol. 82, Iss. 4 — October 2010

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Figure 1
Total electron-impact-ionization cross sections for the $3 l$ excited states of B. Circles, raw RMPS for $1 s^{2} 2 s^{2} 3 s$ ; squares, raw RMPS for $1 s^{2} 2 s^{2} 3 p$ ; diamonds, raw RMPS for $1 s^{2} 2 s^{2} 3 d$ . Solid line, fit to low-energy raw RMPS data for $1 s^{2} 2 s^{2} 3 s$ ; dashed line, fit to low-energy raw RMPS data for $1 s^{2} 2 s^{2} 3 p$ ; dot-dashed line, fit to low-energy raw RMPS data for $1 s^{2} 2 s^{2} 3 d$ ( $1 Mb = 10^{- 18} {cm}^{2}$ ).Reuse & Permissions
Figure 2
Total electron-impact-ionization cross sections for the $nl$ excited states of B. (a) Solid line, RMPS for direct ionization of $1 s^{2} 2 s^{2} 3 s$ ; dashed line, RMPS for direct ionization of $1 s^{2} 2 s^{2} 3 p$ ; dot-dashed line, RMPS for direct ionization of $1 s^{2} 2 s^{2} 3 d$ . The solid squares are the TDCC results for $1 s^{2} 2 s^{2} 3 s$ . (b) Solid line, RMPS for $1 s^{2} 2 s^{2} 4 s$ ; dashed line, RMPS for $1 s^{2} 2 s^{2} 4 p$ ; dot-dashed line, RMPS for $1 s^{2} 2 s^{2} 4 d$ ; double-dot dashed line, RMPS for $1 s^{2} 2 s^{2} 4 f$ ( $1 Mb = 10^{- 18} {cm}^{2}$ ).Reuse & Permissions
Figure 3
Total electron-impact-ionization cross sections for the $nl$ excited states of $B^{+}$ . (a) Black line, RMPS for $1 s^{2} 2 s 3 s$ ; the solid black squares are the TDCC results for $1 s^{2} 2 s 3 s$ ; and red line, RMPS for $1 s^{2} 2 s 3 p$ ; blue line, RMPS for $1 s^{2} 2 s 3 d$ . (b) Black line, RMPS for $1 s^{2} 2 s 4 s$ ; red line, RMPS for $1 s^{2} 2 s 4 p$ ; blue line, RMPS for $1 s^{2} 2 s 4 d$ ; green line, RMPS for $1 s^{2} 2 s 4 f$ . In all cases the solid line shows the results for the triplet term and the dashed line shows the results for the singlet term. The active subshells are labeled on the plots ( $1 Mb = 10^{- 18} {cm}^{2}$ ).Reuse & Permissions
Figure 4
Total electron-impact-ionization cross sections for the $nl$ excited states of $B^{2 +}$ . (a) Solid line, RMPS for $1 s^{2} 3 s$ $^{2} S$ ; dashed line, RMPS for $1 s^{2} 3 p$ $^{2} P$ ; dot-dashed line, RMPS for $1 s^{2} 3 d$ $^{2} D$ . The solid squares show the TDCC results for the $1 s^{2} 3 s$ . (b) Solid line, RMPS for $1 s^{2} 4 s$ $^{2} S$ ; dashed line, RMPS for $1 s^{2} 4 p$ $^{2} P$ ; dot-dashed line, RMPS for $1 s^{2} 4 d$ $^{2} D$ ; double-dot dashed line, RMPS for $1 s^{2} 4 f$ $^{2} F$ . (c) Solid line, RMPS for $1 s^{2} 5 s$ $^{2} S$ ; dashed line, RMPS for $1 s^{2} 5 p$ $^{2} P$ ; dot-dashed line, RMPS for $1 s^{2} 5 d$ $^{2} D$ ; double-dot dashed line, RMPS for $1 s^{2} 5 f$ $^{2} F$ ; double-dashed dotted line, RMPS for $1 s^{2} 5 g$ $^{2} G$ ( $1 Mb = 10^{- 18} {cm}^{2}$ ).Reuse & Permissions
Figure 5
$n$ -scaled electron-impact-ionization cross sections vs threshold scaled energy, that is, cross section divided by $n^{4}$ for the $n$ -bundled excited states of (a) B, (b) $B^{+}$ , and (c) $B^{2 +}$ . In all plots the solid line shows the $n = 3$ RMPS data, the dashed line shows the $n = 4$ RMPS data and in panel (c) the solid circles show the $n = 5$ RMPS data ( $1 Mb = 10^{- 18} {cm}^{2}$ ).Reuse & Permissions
Figure 6
Total electron-impact-ionization cross sections for the $n$ bundled excited states of B, $B^{+}$ , and $B^{2 +}$ . (a) Solid line, B $n = 4$ RMPS; dashed line, B $n = 4$ Burgess-Vriens [Eq. (10)]. (b) Solid line, $B^{+}$ $n = 4$ RMPS; dashed line, $B^{+}$ $n = 4$ Burgess-Vriens [Eq. (10)]. (c) Solid line, $B^{2 +}$ $n = 5$ RMPS; dashed line, $B^{2 +}$ $n = 5$ Burgess-Vriens [Eq. (10)] ( $1 Mb = 10^{- 18} {cm}^{2}$ ).Reuse & Permissions

Physical Review A

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Electron-impact-ionization cross sections for excited states of $B^{q +}$ ( $q = 0 - 2$ ) and an investigation into $n$ scaling of ionization cross sections

Teck-Ghee Lee, S. D. Loch, C. P. Ballance, J. A. Ludlow, and M. S. Pindzola

Phys. Rev. A 82, 042721 – Published 29 October 2010

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Physical Review A

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Electron-impact-ionization cross sections for excited states of Bq+ (q=0–2) and an investigation into n scaling of ionization cross sections

Teck-Ghee Lee, S. D. Loch, C. P. Ballance, J. A. Ludlow, and M. S. Pindzola

Phys. Rev. A 82, 042721 – Published 29 October 2010

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Electron-impact-ionization cross sections for excited states of $B^{q +}$ ( $q = 0 - 2$ ) and an investigation into $n$ scaling of ionization cross sections