Interference patterns from post-collision interaction in below-threshold photoexcitation Auger processes

Xiao Wang and F. Robicheaux

Phys. Rev. A 98, 013421 – Published 27 July 2018

Abstract

We focus on the post-collision interaction in Auger processes where the photoelectron energy is near or below the ionization threshold. Time-dependent quantum and classical calculations are performed. When the photoelectron is more deeply bound, interference patterns can be seen in the angular and photoelectron energy distributions. These interference patterns are visible in quantum calculations, but not in purely classical calculations. A semiclassical analysis using actions from two-path trajectories gives the relative locations of the interference maxima very close to those from the full quantum calculations.

Received 25 May 2018
Corrected 21 May 2019

DOI:https://doi.org/10.1103/PhysRevA.98.013421

Physics Subject Headings (PhySH)

Autoionization & Auger processes

Rydberg atoms & molecules

Atomic, Molecular & Optical

Corrections

21 May 2019

Correction: Equation (4) contained a minor typographical error and has been fixed.

Authors & Affiliations

Xiao Wang¹ and F. Robicheaux^1,2,*

¹Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
²Purdue Quantum Center, Purdue University, West Lafayette, Indiana 47907, USA

^*robichf@purdue.edu

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Issue

Vol. 98, Iss. 1 — July 2018

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Images

Figure 1
Photoelectron energy distributions after PCI from both quantum and classical calculations. The initial photoelectron energy is $E_{1} = - 6.0 \times 10^{- 3}$ a.u., below the threshold. Auger electron energy is $E_{2} = 2.0$ a.u. above the threshold, and the Auger width is $Γ_{c} = 3.0 \times 10^{- 3}$ a.u. The inset figure is a magnification of quantum results at high density of Rydberg state.
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Figure 2
Quantum results of the angular ( $cos θ_{12}$ ) and photoelectron energy ( $E_{1 f}$ ) distributions (PED) at different initial photoelectron energy $E_{1}$ . The initial Auger electron energy is $E_{2} = 2.0$ a.u., and Auger width is $Γ_{c} = 0.003$ a.u. The photoelectron energy $E_{1}$ is given at the top left of each subfigure. Note that, the $E_{1 f}$ and PED scales are different in different subfigures. All calculations are performed at the same initial intensity in the source terms. Among different subfigures, the PED number is proportional to their absolute count of detections due to the same initial photon intensities. The dashed horizontal lines in the subfigures of $E_{1} = - 0.015$ and $- 0.02$ a.u. are plotted at $E_{1 f} = 0.01$ , 0.02, and 0.04 a.u. The small circles are the corresponding classical maxima presented later in the text.
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Figure 3
Quantum results of the PED at $E_{1} = - 0.006$ a.u., and different $Γ_{c}$ . The $Γ_{c}$ is given at the top left of each subfigure. The initial Auger electron energy is $E_{2} = 2.0$ a.u. Other properties are the same as those given in the caption of Fig. 2. The dashed horizontal line in the subfigure of $Γ_{c} = 3.3 \times 10^{- 4}$ a.u. is plotted at $E_{1 f} = 0.01$ a.u. The small circles are the corresponding classical maxima presented later in the text.
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Figure 4
The relation of $t_{2}$ versus $cos ω$ with a fixed $E_{1 f} = 0.02$ a.u. The $cos θ_{12}$ value, which is the angle difference in the asymptotic momentum of the two continuum electrons, is marked with different colors. The $ω$ is the angle difference between the launch directions of the two electrons, and $t_{2}$ is the time of Auger decay after launch of the photoelectron. Two X's are plotted at $(0.83, 0.45)$ and $(0.9989, 630)$ , which both give $cos θ_{12} = - 0.4$ . The triangle is plotted at $(0.987, 32.8)$ , which is the transition point that distinguishes the two paths, and is also the initial condition to achieve the classically maximum allowed $cos θ_{12} = 0.108$ .
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Figure 5
Illustrations for the two classical trajectories with final angle $cos θ_{12} = - 0.4$ and photoelectron energy $E_{1 f} = 0.02$ a.u. The nucleus is located at the origin. The red and blue lines are trajectories for photoelectron and Auger electron, respectively. The dashed red lines are photoelectron trajectories before the Auger decay. The figure (a) refers to an early Auger decay, and the figure (b) refers to a late Auger decay.
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Figure 6
The classical phases from the two paths versus different final value of $cos θ_{12}$ , at the same final energy of $E_{1 f} = 0.02$ a.u. The action difference reaches a local maximum around $cos θ_{12} = 0$ , and $δ S = 1.05$ , which is plotted in black dotted line. The $(cos θ_{12}, E_{1 f}) = (0, 0.02)$ is a constructive interference point as presented in Fig. 2. All other three black dotted lines represent the same phase differences $δ φ = 1.05$ , and are plotted at $cos θ_{12} = - 0.45$ , $- 0.67$ , $- 0.85$ , respectively.
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