Journal of Electron Spectroscopy and Related Phenomena 226 (2018) 26–34
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Auger decay including direct double processes of K-shell hollow states of Ne+ and the related hypersatellite radiative transitions
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Yongjun Lia, Liping Liua, Cheng Gaoa, Jiaolong Zenga,c, , Jianmin Yuana,b,c a
College of Liberal Arts and Science, National University of Defense Technology, Changsha, Hunan, 410073, PR China Graduate School of China Academy of Engineering Physics, Beijing 100193, PR China c IFSA Collaborative Innovation Center, Shanghai Jiao Tong University, Shanghai 200240, PR China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Hollow states Direct double Auger decay Auger spectra Hypersatellite radiative transitions
In this study, we theoretically investigated single and double Auger decay processes from the K−2V (V = 3s, 3p, 3d, 4s, 4p, 4d) hollow states of Ne+ in the framework of the first- and second-order perturbation theory implemented by the distorted wave approximation. The direct double Auger decay rates were calculated based on the separation of knock-out and shake-off mechanisms. Atomic data, including the transition energy, single and double Auger decay rates and natural lifetime width, are obtained and compared with the experimental and theoretical results available in the literature. The natural lifetime widths of the K−2V hollow states, including the contributions from single and direct double Auger decay, are in excellent agreement with a recent experiment. Using our theoretical results, we diagnosed the relative population fractions of the initial quantum states prepared in the experiment and interpreted the measured Auger spectra. There is an excellent agreement between the theoretical and experimental results. Finally, the hypersatellite Kα radiative transitions relevant to these hollow states were investigated using the natural lifetime widths determined by single and direct double Auger rates.
1. Introduction Hollow states are unique species in which at least two inner-shell electrons are removed [1,2]. The first experimental production of hollow atoms was performed by the excitation of highly charged ions in interaction with a metallic surface [3]. Since then, hollow atoms have been observed and studied in ion-surface collisions [4,5], electron-ion collisions [6,7] and in the interaction of synchrotron radiation [8,9]. Recently, with the development of X-ray free electron lasers (XFELs) such as the Linac Coherent Light Source [10] and Spring-8 Angstrom Compact free electron LAser [11], hollow states are also produced by the interaction of ultra-intensive X-ray pulses with matter, including atoms, molecules, clusters, and solids [12–14]. Cederbaum et al. [15] theoretically suggested that spectroscopy of hollow states is sensitive to the environment and it is a powerful tool for chemical analysis. The chemical sensitivity of double-core-hole (DCH) spectroscopy has been experimentally demonstrated by Berrah et al. [16], Salén et al. [17], and Nakano et al. [9]. The rich information related to DCH spectroscopy provides wide practical applications in many research fields [18–20]. For example, DCH spectroscopy provides a useful tool for diagnosing the intensity and duration of ultra-fast and
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ultra-intense XFEL pulses [21–23]. To investigate the interaction of XFELs with matter and the spectroscopy of hollow states, a lot of atomic data are required, including the Auger decay rates. Determination of accurate Auger decay rates of hollow states is in general challenging both experimentally and theoretically. Theoretically, it is difficult to properly and accurately describe the wave functions of hollow states, and therefore most past investigations of Auger decay of hollow states have been limited to few-electron systems, such as helium- and lithium-like atoms or ions [24]. The lifetime of hollow states is very short, and hence experimental investigation to obtain high-resolution signals is difficult [25–27]. One of the latest attractive experimental achievements is the double and triple measurements of the Auger decay for the K-shell resonance state of C+ [28]. These authors experimentally observed unambiguously a fourelectron Auger decay with simultaneous emission of three electrons. Recently, Goldsztejn et al. [29] experimentally investigated the Auger decay properties of the K−2V (V = 3s, 3p, 4s, 4p) hollow states of neon under the latest state-of-the-art experimental conditions. The hollow states in the experiment were produced by using synchrotron radiation with a photon energy of 2.3 keV. Such a photon can ionize one 1s electron of atomic neon and simultaneously promote another 1s
Corresponding author at: College of Liberal Arts and Science, National University of Defense Technology, Changsha, Hunan, 410073, PR China. E-mail address:
[email protected] (J. Zeng).
https://doi.org/10.1016/j.elspec.2018.05.003 Received 10 February 2018; Received in revised form 8 May 2018; Accepted 8 May 2018 Available online 16 May 2018 0368-2048/ © 2018 Elsevier B.V. All rights reserved.
Journal of Electron Spectroscopy and Related Phenomena 226 (2018) 26–34
Y. Li et al.
electron to a valence orbital, resulting in the production of hollow states. They obtained a width of natural lifetime broadening of 701 ± 11 meV for these hollow states. To the best of our knowledge, no theoretical investigations reported the Auger decay properties of these hollow states. In this work, we theoretically investigated the complete Auger decay of the K−2V (V = 3s, 3p, 3d, 4s, 4p, 4d) hollow states of the singly charged ion Ne+, including single and double Auger decay processes. By including contributions from the direct double Auger decay (DDAD) processes, the predicted natural lifetime widths of these hollow states are in better agreement with the recent experiment [29] than by only considering the single Auger decays (SAD). Besides these K−2V hollow states of Ne+, some other hollow states, such as 1s02s22p6 of Ne2+, and some single hole states, such as 1s2s22p6, 1s2s22p53p, and 1s2s2p63s, of Ne+ were produced in the measurement as well, which makes it difficult to theoretically interpret the experiment. Among these hollow states, 1s02s22p6 hollow states of Ne2+ have been investigated [1,30–36], but only limited to SAD processes. By comparing the theoretical Auger spectra with the experimental spectra, we diagnosed the population fractions of the initial quantum states prepared in the experiment [29]. Using the predicted natural lifetime widths, we also investigated the hypersatellite radiative transitions related to the hollow states of K−2V.
electron. The wave function of the free electron is obtained in the same central potential as that of the bound orbital of |Ψm〉. In addition to SAD, DDAD is also possible with two electrons being simultaneously ejected. In the second-order perturbation theory, the DDAD rate is expressed as
2. Theoretical method
where σmf(ε0) is the electron impact ionization cross-section from the middle state m to the final state f with the incident energy ε0 determined by energy conservation. E , E0−E , Ψf2 + E0, Ψm+ represents the overlap between the wave functions of the initial and final states. In our calculations, the interactions among the fine-structure levels belonging to the following configurations are included for singly charged ion Ne+: (valence electron excitations) 1s22s22p5, 1s22s2p6, 1s22s22p4nl, 1s22s2p5nl, 1s22s02p6nl, 1s22s22p33ln′l′, 1s22s2p43ln′l′, and 1s22s02p53ln′l′, (single K-shell excitations) 1s2s22p6, 1s2s22p5nl, 1s2s2p6nl, 1s2s22p43ln′l′, 1s2s2p53ln′l′, and 1s2s02p63ln′l′, and (double K-shell excitations) 1s02s22p6nl, 1s02s22p53ln′l′, and 1s02s2p63ln′l′ (3l = 3s, 3p, 3d, nl or n′l′ = 3s, 3p, 3d, 4s, 4p, 4d, and 4f). For Ne2+, the following configurations are included: (valence electron excitations) 1s22s22p4, 1s22s2p5, 1s22s02p6, 1s22s22p3nl, 1s22s2p4nl, 1s22s02p5nl, 1s22s22p23ln′l′, 1s22s2p33ln′l′, and 1s22s02p43ln′l′, (single K-shell excitations) 1s2s22p5, 1s2s2p6, 1s2s22p4nl, 1s2s2p5nl, 1s2s02p6nl, 1s2s22p33ln′l′, 1s2s2p43ln′l′, and 1s2s02p53ln′l′, and (double K-shell excitations) 1s02s22p6, 1s02s22p5nl, 1s02s2p6nl, 1s02s22p43ln′l′, 1s02s2p53ln′l′, and 1s02s02p63ln′l′. The same excitation rules apply for the configuration interaction of Ne3+. The orbital wave functions were obtained by optimizing on the 1s-vacancy states of 1s2s22p5, 1s2s2p6, 1s2s22p43l, 1s2s2p53l and 1s2s02p63l (3l = 3s, 3p, 3d). The continuum wavefunctions are calculated in the framework of the distorted wave approximation. The wavefunctions and all quantities required in this work are obtained by using the Flexible Atomic Code [39]. The convergence of the wavefunctions has been checked carefully to ensure the convergence of our results. From inspection of the configurations included in our calculations, one can see that we have constructed a complete Auger pathways for both SAD and DDAD processes. Not only the main KK-KLL and KK-KLV Auger processes but also three electron Auger of the shake-up processes and KK-LLL processes, where two L-shell electrons simultaneously fill both K-vacancies and a third L-shell electron is emitted with high kinetic energy, have been included in this work. Although the KK-LLL processes are weak compared with the main channels, the signal of the three electron Auger processes is experimentally observed in collisions of bare ions on a metal surface [4]. Recently, a similar three electron Auger processes was observed in the Auger decay of argon with double 2p vacancies, where the double vacancies are filled by two valence electrons and a third electron is ejected simultaneously [46].
(6) where |Ψ2f + is the wave function of the final state in the DDAD process. Summation–integration of the intermediate states represents summation over bound states of one higher ionization stage and integration over a complete set of continuum wave functions of the free electron. According to the knock-out and shake-off mechanisms, the DDAD rate can be simplified as [41–45] 2 AKO =
N
N
2 ASO =
1
∑ HD (i) + ∑ r i=1
i
