Efficiency of core-level interatomic Coulombic decay in rare-gas dimers

Liping Liu, Přemysl Kolorenč, and Kirill Gokhberg

Phys. Rev. A 101, 033402 – Published 4 March 2020

Abstract

In this work we investigated the competition between the local Auger decay and core-level interatomic Coulombic decay (ICD) processes in core ionized rare-gas dimers. We computed the respective partial decay widths for the $4 d$ vacancy in ${Xe}_{2}$ , XeKr, and XeAr, as well as for the $3 d$ vacancy in ${Kr}_{2}$ . We found that the efficiency of ICD is strongly increased with decreasing interatomic distance and decreasing energy transfer in the decay step. The ICD-to-Auger ratio in the Franck-Condon region, where the decay occurs, is at most 0.26%. However, it reaches a few percentage points in larger clusters and becomes amenable for experimental observation. The small value of the branching ratio is due to large interatomic distances in the dimers (4–4.4 Å). Our results also indicate, in accordance with previous measurements, that in hydrogen-bonded and microsolvated clusters, where the distances between the monomers are 2–3 Å, core-level ICD should become an important pathway for charge redistribution following the absorption of hard x-rays.

Received 20 September 2019
Accepted 4 February 2020

DOI:https://doi.org/10.1103/PhysRevA.101.033402

Physics Subject Headings (PhySH)

Autoionization & Auger processes Electronic excitation & ionization

Atomic, Molecular & Optical

Authors & Affiliations

Liping Liu ^1,2, Přemysl Kolorenč³, and Kirill Gokhberg ²

¹Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China
²Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
³Charles University, Faculty of Mathematics and Physics, Institute of Theoretical Physics, V Holešovičkách 2, 18000 Prague, Czech Republic

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Vol. 101, Iss. 3 — March 2020

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Images

Figure 1
Potential-energy curves (PECs) of the ${Xe}_{2}, {Xe}^{+} (4 d^{- 1}) Xe$ and ${({Xe}_{2})}^{2 +}$ states. (bottom) The ground state of the xenon dimer. (top) The PECs of the decaying singly ionized ${Xe}^{+} (4 d^{- 1}) Xe$ states: ${}^{2}Σ_{g}$ (black solid line), ${}^{2}Σ_{u}$ (red solid line), ${}^{2}Δ_{g}$ (green dashed line), ${}^{2}Δ_{u}$ (blue dashed line), ${}^{2}Π_{g}$ (brown dotted line), ${}^{2}Π_{u}$ (violet dotted line). The PEC of the ${}^{2}Σ_{u}$ term lies above the PEC of the ${}^{2}Σ_{g}$ term. The PECs of the gerade and ungerade terms of the $Π$ and $Δ$ symmetry are very close and can be barely distinguished. (middle panel) ${({Xe}_{2})}^{2 +}$ final states which appear as six distinct groups, of which three comprise the two-site ICD final states (solid lines) and three the one-site Auger final states (dashed lines). The ICD states in order of increasing energy correspond respectively to the configurations ${Xe}^{+} (5 p^{- 1}) {Xe}^{+} (5 p^{- 1}), {Xe}^{+} (5 p^{- 1}) {Xe}^{+} (5 s^{- 1})$ , and ${Xe}^{+} (5 s^{- 1}) {Xe}^{+} (5 s^{- 1})$ . The Auger states in order of increasing energy correspond respectively to the configurations ${Xe}^{2 +} (5 p^{- 2}) Xe, {Xe}^{2 +} (5 p^{- 1} 5 s^{- 1}) Xe$ , and ${Xe}^{2 +} (5 s^{- 2}) Xe$ . The ground-state equilibrium distance $R_{eq} = 4.4$ Å of neutral ${Xe}_{2}$ is shown as a vertical dashed line.
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Figure 2
(bottom) Auger (horizontal lines at 125 meV) and ICD partial decay widths of the decaying singly ionized ${Xe}^{+} (4 d^{- 1}) Xe$ states. The Auger widths lie within a 6 meV band and appear as one line in the plot. The ICD widths of the ${Xe}^{+} (4 d^{- 1}) Xe$ states— ${}^{2}Σ_{g}$ (black solid line), ${}^{2}Σ_{u}$ (red solid line), ${}^{2}Δ_{g}$ (green dashed line), ${}^{2}Δ_{u}$ (blue dashed line), ${}^{2}Π_{g}$ (brown dotted line), ${}^{2}Π_{u}$ (violet dotted line)—show the characteristic $R^{- 6}$ behavior of the energy-transfer processes at large distances, while they deviate from it due to the effect of orbital overlap starting at 7 Å. The widths of the gerade and ungerade terms of the same linear symmetry are very close and can be barely distinguished. The plot of the $R^{- 6}$ function (dashed-dotted line) is included to accentuate the behavior of ICD widths at large $R$ . (top) ICD-to-Auger branching ratios. The ground-state equilibrium distance, $R_{eq}$ , of the neutral ${Xe}_{2}$ is shown as a vertical dashed line. The Franck-Condon region is marked by the dashed-dotted vertical lines.
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Figure 3
Potential-energy curves (PECs) of XeKr, ${Xe}^{+} (4 d^{- 1}) Kr$ and ${(XeKr)}^{2 +}$ states. (bottom) The ground state of XeKr. (top) The PECs of the decaying singly ionized ${Xe}^{+} (4 d^{- 1}) Kr$ states: ${}^{2}Σ$ (black solid line), ${}^{2}Δ$ (red dashed line), ${}^{2}Π$ (green dotted line). (middle panel) The Auger ${Xe}^{2 +} Kr$ (dashed lines), ICD ${Xe}^{+} {Kr}^{+}$ (solid lines), and ETMD ${XeKr}^{2 +}$ (dotted lines) final states. The Auger states in order of increasing energy correspond respectively to the ${Xe}^{2 +} (5 p^{- 2}) Kr, {Xe}^{2 +} (5 p^{- 1} 5 s^{- 1}) Kr$ , and ${Xe}^{2 +} (5 s^{- 2}) Kr$ configurations. The ICD states in order of increasing energy correspond, respectively, to the ${Xe}^{+} (5 p^{- 1}) {Kr}^{+} (4 p^{- 1}), {Xe}^{+} (5 s^{- 1}) {Kr}^{+} (4 p^{- 1}), {Xe}^{+} (5 p^{- 1}) {Kr}^{+} (4 s^{- 1})$ , and ${Xe}^{+} (5 s^{- 1}) {Kr}^{+} (4 s^{- 1})$ configurations. The ETMD states in order of increasing energy correspond respectively to the ${XeKr}^{2 +} (4 p^{- 2}), {XeKr}^{2 +} (4 p^{- 1} 4 s^{- 1})$ configurations. The ground-state equilibrium distance $R_{eq} = 4.3$ Å of neutral XeKr is shown as a vertical dashed line.
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Figure 4
Potential-energy curves (PECs) of XeAr, ${Xe}^{+} (4 d^{- 1}) Ar$ and ${(XeAr)}^{2 +}$ states. (bottom) The ground state of XeAr. (top) The PECs of the decaying singly ionized ${Xe}^{+} (4 d^{- 1}) Ar$ states: ${}^{2}Σ$ (black solid line), ${}^{2}Δ$ (red dashed line), ${}^{2}Π$ (green dotted line). (middle panel) The Auger ${Xe}^{2 +} Ar$ (dashed lines), ICD ${Xe}^{+} {Ar}^{+}$ (solid lines), and ETMD ${XeAr}^{2 +}$ (dotted lines) final states. The Auger states in order of increasing energy correspond respectively to the ${Xe}^{2 +} (5 p^{- 2}) Ar, {Xe}^{2 +} (5 p^{- 1} 5 s^{- 1}) Ar$ , and ${Xe}^{2 +} (5 s^{- 2}) Ar$ configurations. The ICD states in order of increasing energy correspond respectively to the ${Xe}^{+} (5 p^{- 1}) {Ar}^{+} (3 p^{- 1}), {Xe}^{+} (5 s^{- 1}) {Ar}^{+} (3 p^{- 1}), {Xe}^{+} (5 p^{- 1}) {Ar}^{+} (3 s^{- 1})$ , and ${Xe}^{+} (5 s^{- 1}) {Ar}^{+} (3 s^{- 1})$ configurations. The ETMD states in order of increasing energy correspond respectively to the ${XeAr}^{2 +} (3 p^{- 2}), {XeAr}^{2 +} (3 p^{- 1} 3 s^{- 1})$ configurations. The ground-state equilibrium distance $R_{eq} = 4.2$ Å of neutral XeAr is shown as a vertical dashed line.
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Figure 5
(bottom) Auger (horizontal lines at 125 meV) and ICD partial decay widths of the decaying singly ionized ${Xe}^{+} (4 d^{- 1}) Kr$ states. The ICD widths of the ${Xe}^{+} (4 d^{- 1}) Kr$ states— ${}^{2}Σ$ (black solid line), ${}^{2}Δ$ (red dashed line), ${}^{2}Π_{g}$ (green dotted line)—show the characteristic $R^{- 6}$ behavior of the energy-transfer processes at large distances, while they deviate from it due to the effect of orbital overlap starting at 6 Å. The plot of the $R^{- 6}$ function (dashed-dotted line) is included to accentuate the behavior of ICD widths at large $R$ . (top) ICD-to-Auger branching ratios. The ground-state equilibrium distance $R_{eq}$ of the neutral XeKr is shown as a vertical dashed line. The Franck-Condon region is marked by the dashed-dotted vertical lines.
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Figure 6
(bottom) Auger (horizontal lines at 125 meV) and ICD partial decay widths of the decaying singly ionized ${Xe}^{+} (4 d^{- 1}) Ar$ states. The ICD widths of the ${Xe}^{+} (4 d^{- 1}) Ar$ states— ${}^{2}Σ$ (black solid line), ${}^{2}Δ$ (red dashed line), ${}^{2}Π_{g}$ (green dotted line)—show the characteristic $R^{- 6}$ behavior of the energy-transfer processes at large distances, while they deviate from it due to the effect of orbital overlap starting at 6 Å. The plot of the $R^{- 6}$ function (dashed-dotted line) is included to accentuate the behavior of ICD widths at large $R$ . (top) ICD-to-Auger branching ratios. The ground-state equilibrium distance $R_{eq}$ of the neutral XeAr is shown as a vertical dashed line. The Franck-Condon region is marked by the dashed-dotted vertical lines.
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