Switching classical trajectory Monte Carlo method to describe two-active-electron collisions

A. Jorge, Clara Illescas, L. Méndez, and B. Pons

Phys. Rev. A 94, 022710 – Published 17 August 2016

Abstract

We propose a classical trajectory Monte Carlo method to describe two-center collisions with two active electrons. The approach is based on switching between standard four-body and three-body descriptions and it is therefore easy to implement. We demonstrate the reliability of the approach for fundamental H+H and $H^{+} + H^{-}$ collisions that neither four-body nor three-body classical methods describe satisfactorily.

Received 31 May 2016

DOI:https://doi.org/10.1103/PhysRevA.94.022710

Physics Subject Headings (PhySH)

Scattering of atoms, molecules, clusters & ions

Few-body systems

Monte Carlo methods

Atomic, Molecular & Optical

Authors & Affiliations

A. Jorge¹, Clara Illescas¹, L. Méndez¹, and B. Pons²

¹Laboratorio Asociado al CIEMAT de Física Atómica y Molecular en Plasmas de Fusión, Departamento de Química, Módulo 13, Universidad Autónoma de Madrid, Cantoblanco E-28049 Madrid, Spain
²Université de Bordeaux, CNRS, CEA, CELIA, UMR5107, F-33405 Talence, France

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Issue

Vol. 94, Iss. 2 — August 2016

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Images

Figure 1
Evolution of electron capture transition probability as a function of $Z = v t$ in $H (1 s$ ) + $H (1 s$ ) collisions with $E = 30$ keV and $b = 1$ a.u. Results from switching (—) and 4b (- - -) CTMC calculations. In the inset, we zoom in on the $- 5 \leq Z \leq 100$ a.u. interval.
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Figure 2
Upper panel: Illustration of the switching between 4b- and $2 \times 3 b$ CTMC calculations in $H (1 s$ ) + $H (1 s$ ) collisions. The figure shows the time evolution of electron distances, $r_{1}$ (full line) and $r_{2}$ (dashed line), to the target nucleus, and the distance from the projectile to the target nucleus (dashed-dotted line), for a trajectory initially defined by $E = 30$ keV and $b = 1$ a.u. that leads to $H^{-}$ formation. The vertical line indicates the time when the switching takes place. Lower panels: Classical electron orbits before ( $- 50 < t < - 5$ a.u.) and after ( $5 < t < 50$ a.u.) the switching with respect to the nucleus they are bound to. In the “Before” panel the projectile is located at (1,0,–5) for clarity.
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Figure 3
Total cross section for negative-projectile ion formation [Eq. (1)] as a function of the incident energy $E$ in the laboratory frame. Present switching (—) and 4b (- - -) CTMC calculations. Previous 4b-CTMC results from Dimitriou et al. [38] ( $\cdot \cdot \cdot$ ) and Olson [36] (- $\cdot \cdot$ -). Two-center two-electron close-coupling calculations from Wang et al. [31] (- - $\cdot$ - -). Measurements from Hill et al. [28] ( $▴$ ) and McClure [26] ( $▪$ ).
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Figure 4
Illustration of the temporal evolution of mean monoelectronic energies $< E_{1}^{(T)} >$ (—, $•$ ), $< E_{2}^{(T)} >$ (- - -, $▴$ ), $< E_{2}^{(P)} >$ (- $\cdot$ - $\cdot$ ) and mean interelectronic repulsion, $< 1 / r_{12} >$ , (- $\cdot \cdot$ -, $▪$ ) for a nuclear trajectory with $E = 30$ keV and $b = 1$ a.u. in $H^{+}$ + $H^{-}$ collisions. The lines refer to averages over the electron pairs ( $e_{1}, e_{2}$ ) leading to direct neutralization, while the dots refer to averages over all $N^{2}$ electron pairs. The shaded area indicates the region where the switching between $2 \times 3b-$ and 4b-CTMC descriptions takes place.
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Figure 5
Total cross section for mutual neutralization in $H^{+}$ + $H^{-}$ collisions as a function of the collision energy $E$ . $H^{+}$ + $H^{-} (1 s^{2}) \to H (n l m$ )+ $H (n^{'} l^{'} m^{'}$ ) in the upper panel and $H (n l m$ )+ $H (1 s$ ) in the lower panel. Present CTMC results obtained with the switching (—) and 3b-IPM-CTMC (- $\cdot$ -) approaches. Coupled-channel calculations from Shingal and Bransden [30] (- - $\cdot$ - -), Wang et al. [31] (- $\cdot \cdot$ -), and Ling and Wang [55] ( $\cdot \cdot \cdot$ ). CB1-4B results from Mancev et al.[51] (- - - -). Experimental results from Schön et al. [40] ( $•$ ).
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