#
Double K-Shell Ionization of Ar by 197-MeV/u Xe^{54+} Ion Impact

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## Abstract

**:**

^{54+}ion at 197 MeV/u. The X-ray spectra of multi-ionized argon are measured at the observation angles of 90° and 145° with respect to the projectile beam. The target K X-ray satellite and hypersatellite lines are analyzed with a fitting model and the cross-section ratio of double to single K-shell ionization is derived. The experimental results are compared to the relativistic time-dependent, two-center calculations, and a reasonable agreement is reached.

## 1. Introduction

^{17+}[4,16], 2.0-6.0 MeV/u Si

^{14+}[16], 5 MeV/u F

^{9+}, Mg

^{12+}, and Al

^{13+}ions [16], respectively. Experimental studies of such a process for argon were also carried out with gaseous targets by Schulz et al. and by Wohrer et al. by employing 0.5 MeV/u S

^{16+}[17] and 7.0 MeV/u Fe

^{26+}beams [18], respectively. More recently, Hillenbrand et al. presented a study of double K-shell vacancies in xenon atoms in symmetric collisions with 15–50-MeV/u Xe

^{54+}ions [19]. In these cases, the ion velocity v

_{p}is lower than or close to the classical velocity of the target atomic electron v

_{K}; the formation mechanisms of double K-shell vacancies in atoms are complicated, due to the contributions of the direct ionization and electron transfer, while the situation gets simpler when v

_{p}is far greater than v

_{K}. The two K-shell electrons of the target atom are considered to be removed dominantly by two independent direct single-ionization events [14]. The experimental study of this process is important for mapping the limits of the applicability of the independent electron approximation, which is usually considered to be valid for multiple inner-shell ionization. This requires the relativistic energies for the incident heavy ions according to the classical velocity of the K-shell electrons for atoms with the medium atomic numbers (Z). However, the availability of the relativistic heavy ions made these studies scarce.

^{54+}ions through the X-ray spectroscopy method at a heavy-ion storage ring equipped with an internal gas-jet target, where the corresponding v

_{p}/v

_{K}ranges from 1.2 to 2.2 [15]. In this paper, we report the results of an X-ray spectroscopy study of the argon atoms with the double K-shell vacancies produced in single collisions with relativistic (197-MeV/u) bare xenon ions. The present work is a continuation of our previous study, and its main goal is to explore the creation of K- and L-shell vacancies in argon atoms colliding with heavy bare ions in the higher v

_{p}/v

_{K}region, as well as the filling processes of the K-shell vacancies. The experiment and data analysis methods are described in the second and third sections, respectively. The results and discussions are presented in Section 4, and finally, a conclusion of the present work and a brief outlook are given in Section 5.

## 2. Experiment

^{7}Xe

^{54+}ions with the energy of 197 MeV/u was injected into the experimental ring (CSRe); it was cooled by the electron cooler and then collided with the argon gas-jet target. The beam current was about 100–600 μA, and the target thickness was around 10

^{12}–10

^{13}atoms/cm

^{2}during the measurement. The beam energy loss, due to the interaction with the target, was compensated by the continuous electron cooling. The projectile ions that capture one electron were separated from the circulating beam due to the change in their magnetic stiffness.

^{55}Fe,

^{133}Ba,

^{152}Eu, and

^{241}Am before and after the experiments. The energy resolutions (i.e., full width at half maximum) of the present detectors are both about 181 eV at around 3.0 keV.

## 3. Data Analysis Methods

#### 3.1. Spectra Fitting of K X-ray

^{d}and Kβ

^{d}, at 2.957 keV and 3.191 keV, are indicated by the vertical lines, respectively [22]. The clear shift of the experimental peaks to higher energies indicates high ionizations of the argon atoms. The energy intervals between the Kα

^{s}, Kα

^{h,s}, Kβ

^{s}, and Kβ

^{h,s}peaks are close to the resolution of the detectors (~180 eV) [23]. The origin of the Kα

^{s}, Kβ

^{s}satellite and Kα

^{h,s}, Kβ

^{h,s}hypersatellite peaks is described in detail in our previous paper [15]. The Kα

^{s}, Kβ

^{s}satellite and Kα

^{h,s}, Kβ

^{h,s}hypersatellite peaks come from the transitions of the following types: ${K}^{-1}{L}^{-{n}_{L}}{M}^{-{n}_{M}}\to {K}^{0}{L}^{-\left({n}_{L}+1\right)}{M}^{-{n}_{M}}$, ${K}^{-1}{L}^{-{n}_{L}}{M}^{-{n}_{M}}\to {K}^{0}{L}^{-{n}_{L}}{M}^{-\left({n}_{M}+1\right)}$, ${K}^{-2}{L}^{-{n}_{L}}{M}^{-{n}_{M}}\to {K}^{-1}{L}^{-\left({n}_{L}+1\right)}{M}^{-{n}_{M}}$, and ${K}^{-2}{L}^{-{n}_{L}}{M}^{-{n}_{M}}\to {K}^{-1}{L}^{-{n}_{L}}{M}^{-\left({n}_{M}+1\right)}$, respectively.

^{s}, Kα

^{h,s}, Kβ

^{s}, and Kβ

^{h,s}peaks are fitted by four Gaussian distributions with the following parameters: (a) the positions of these four peaks are all expressed in terms of the mean L-vacancy number ${n}_{L}^{x}$ at the time of X-ray emission; (b) the full widths at half maximum (FWHM) of the Kα

^{s}and Kα

^{h,s}peaks are set to the same because of the identical peak widths of Kα

^{s}and Kα

^{h,s}for the same ${n}_{L}^{x}$, as derived by convolution and fitting [23]; so, the same occurred for the Kβ

^{s}and Kβ

^{h,s}peaks for the same reason. Therefore, a total of seven parameters (four peak intensities, two peak widths, and ${n}_{L}^{x}$) are used.

^{s}, Kα

^{h,s}, Kβ

^{s}, and Kβ

^{h,s}as a function of the vacancy number in the L-shell were calculated using the GRASP 2K program [25]. The energy shifts caused by M-shell vacancies are assumed to be proportional to their number and given by the difference between the calculated results when the M-shell is full and when there is only one M-vacancy. The binomial population distributions of the number of the L- and M-shell vacancies in the target atoms at the time of the K-shell radiations are assumed [26]. The average numbers of L-vacancy ${n}_{L}^{x}$ and M-vacancy ${n}_{M}^{x}$ were associated by a scaling formula [27]. The results were the convolutions of the population distributions of the number of the L- and M-shell vacancies and Gaussians for a detector resolution of 181 eV. The weight center energies of the K

^{−1}L

^{0}→K

^{0}L

^{−1}and K

^{−1}L

^{0}M

^{0}→ K

^{0}L

^{0}M

^{−1}argon transitions are calculated to be 3.131 and 3.1416 keV, respectively. The mean energy of Kα

^{s}, Kα

^{h,s}, Kβ

^{s}, and Kβ

^{h,s}as a function of the spectator L-vacancy number ${n}_{L}^{x}$ are obtained as follows:

^{s}and Kβ

^{h,s}peaks shift much more than the Kα

^{s}and Kα

^{h,s}peaks. In addition, the Gaussian profiles of the Kβ

^{s}and Kβ

^{h,s}peaks broadened more than the Kα

^{s}and Kα

^{h,s}peaks. This is due to the fact that the L-vacancies affect the transitions from the upper M-shell more than those from the L-shell.

#### 3.2. Fluorescence Yields of Argon with Multiple Vacancy

^{h,s}and Kα

^{s}X-rays, the fluorescence yields of argon with multiple vacancies are required. The fluorescence yields ${\omega}_{K{a}^{h,s}}$ and ${\omega}_{K{a}^{s}}$ for argon with different spectator vacancies in the K-shell, L-shell, and M-shell should be undertaken for each parent defect configuration and are currently not available. Therefore, the fluorescence yields of multivacancy configurations are derived using a statistical weighting procedure developed by Larkins [28]. The original radiative and radiationless transition rates of a single K vacancy are obtained from the tabulated data [29,30]. The relationship between the initial vacancy distribution of argon atoms by projectile impacts and their time evolutions by taking into account multi-step vacancy rearrangement processes is evaluated by the model developed by Horvat et al. [31]. The population distributions of the number of target atom L- and M-shell vacancies from collisions are also assumed to be binomial. According to the scaling formula, the average numbers of the spectator L-vacancy ${n}_{L}^{0}$ and M-vacancy ${n}_{M}^{0}$ are associated [27].

^{h,s}radiation is larger than that for the Kα

^{s}radiation if they have the same initial ${n}_{L}^{0}$. This is due to the fact that the K-shell is filled faster for the double K-vacancies than for the single K-vacancy.

^{−1}states originating from the cascade decay of the ${K}^{-2}{L}^{-{n}_{L}}$ states.

## 4. Results and Discussion

^{h,s})/I(Kα

^{s}). Taking the relative intensities of the X-ray emission listed in Table 1 and the fluorescence yields deduced in Section 3, the ionization cross-section ratios for argon collided by the 197 MeV/u Xe

^{54+}ion were obtained and are listed in Table 2. The experimental mean number of the L-vacancies produced by collision ${n}_{L}^{0}$(${K}^{-2}{L}^{-{n}_{L}}$) is also shown in in Table 2. The mean number of L-vacancies of the ${K}^{-1}{L}^{-{n}_{L}}$ state in collision ${n}_{L}^{0}$(${K}^{-1}{L}^{-{n}_{L}}$) is not given here because we do not try to distinguish between the contributions of the ${K}^{-1}{L}^{-{n}_{L}}$ states produced in collision and those originating from the cascading of the ${K}^{-2}{L}^{-{n}_{L}}$ states under the current experimental resolution.

_{P}is 77.4 a.u, which is about 4.3 times the velocity of the atom’s K-shell electrons, but the perturbation strength from the projectile ion κ (κ = Z

_{P}/v

_{P,}Z

_{P}is the nuclear charge of the projectile) is 0.70, which is close to 1. Thereby the non-perturbative relativistic coupled-channel (RCC) method based on the independent electron model and the two-center atomic-like Dirac–Fock–Sturm orbitals as a basis set are adopted to calculate the cross-sections of single and double K-shell ionizations [32]. The calculation results are also shown Table 2. The experimental ratio R

_{21}for the double-to-single target K-shell vacancy production cross-section is slightly greater, but it agrees reasonably with the theoretical result. This indicates that the independent electron approximation is still suitable for the process of K-shell multiple ionization in the current collision system.

## 5. Conclusions

^{s}, Kα

^{h,s}, Kβ

^{s}, and Kβ

^{h,s}X-rays of multiple ionized argon atoms were measured in single collisions of 197-MeV/u Xe

^{54+}ions with an argon target. The double K-shell ionization processes of the argon atoms were investigated by means of the intensity ratios I(Kα

^{h,s})/I(Kα

^{s}) from a fitting model, combined with the evaluation of the fluorescence yields of the multi-vacancy state atoms and the vacancy rearrangement process. The relative yield of the double K-shell vacancies of the argon atoms with respect to single the K-shell ionized ones was determined to be 12%. The experimental cross-section ratio shows a reasonable agreement with the calculated value from the relativistic time-dependent two-center theory. However, the mean number of the spectator L-vacancies extracted from the experiments is a number that is nearly one less than that of the theory. More precise experiments with high-resolution detectors are expected to provide a more stringent test of the theory.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- McGuire, J.H.; Berrah, N.; Bartlett, R.J.; Samson, J.A.; Tanis, J.A.; Cocke, C.L.; Schlachter, A.S. The ratio of cross sections for double to single ionization of helium by high energy photons and charged particles. J. Phys. B At. Mol. Opt. Phys.
**1995**, 28, 913–940. [Google Scholar] [CrossRef] - Awaya, Y.; Katou, T.; Kumagai, H.; Tonuma, T.; Tendow, Y.; Izumo, K.; Hashizume, A.; Takahashi, T.; Hamada, T. Ratio of single K-shell ionization cross section to double K-shell ionization cross section in heavy-ion-atom collisions. Phys. Lett. A
**1980**, 75, 478–480. [Google Scholar] [CrossRef] - Hall, J.; Richard, P.; Gray, T.J.; Jones, K.; Johnson, B.; Gregory, D. Ratios of double to single K-vacancy production in heavy ion-atom collisions. Phys. Lett. A
**1982**, 75, 129–132. [Google Scholar] [CrossRef] - Hall, J.; Richard, P.; Philip, L.P.; Gregory, D.C.; Miller, P.D.; Moak, C.D.; Jones, C.M.; Alton, G.D.; Bridwell, L.B.; Sofield, C.J. Energy systematics of single and double K-shell-vacancy production in titanium bombarded by chlorine ions. Phys. Rev. A
**1986**, 33, 914–920. [Google Scholar] [CrossRef] [PubMed] - Kobal, M.; Kavčič, M.; Budnar, M.; Dousse, J.C.; Maillard, Y.P.; Mauron, O.; Raboud, P.A.; Tökési, K. Double-K-shell ionization of Mg and Si induced in collisions with C and Ne ions. Phys. Rev. A
**2004**, 70, 062720. [Google Scholar] [CrossRef] [Green Version] - Briand, J.P.; Chevallier, P.; Tavernier, M.; Rozet, J.P. Observation of K Hypersatellites and KL Satellites in the X-ray Spectrum of Doubly K-Ionized Gallium. Phys. Rev. Lett.
**1971**, 27, 777–779. [Google Scholar] [CrossRef] - Watson, R.L.; Horvat, V.; Peng, Y. Kα X-ray satellite and hypersatellite spectra of vanadium metal and oxides excited in heavy-ion collisions. Phys. Rev. A
**2008**, 78, 062702. [Google Scholar] [CrossRef] - Horvat, V.; Watson, R.L.; Peng, Y. Kα satellite and hypersatellite distributions of Ar excited in heavy-ion collisions. Phys. Rev. A
**2009**, 79, 012708. [Google Scholar] [CrossRef] - Maillard, Y.P.; Dousse, J.C.; Hoszowska, J.; Berset, M.; Mauron, O.; Raboud, P.A.; Kavčič, M.; Rzadkiewicz, J.; Banaś, D.; Tökési, K. Hypersatellite X-ray decay of 3d hollow-K-shell atoms produced by heavy-ion impact. Phys. Rev. A
**2018**, 98, 012705. [Google Scholar] [CrossRef] [Green Version] - Köhrbrück, R.; Stolterfoht, N.; Schippers, S.; Hustedt, S.; Heiland, W.; Lecler, D.; Kemmler, J.; Bleck-Neuhaus, J. Electron emission following the interaction of highly charged ions with a Pt(110) target. Phys. Rev. A
**1993**, 48, 3731–3740. [Google Scholar] [CrossRef] - Woods, C.W.; Kauffman, R.L.; Jamison, K.A.; Stolterfoht, N.; Richard, P. K-shell Auger-electron hypersatellites of Ne. Phys. Rev. A
**1975**, 12, 1393–1398. [Google Scholar] [CrossRef] - Wölfli, W.; Stoller, C.; Bonani, G.; Suter, M.; Stöckli, M. Two-Electron-One-Photon Transitions in Heavy-Ion Collisions. Phys. Rev. Lett.
**1975**, 35, 656–659. [Google Scholar] [CrossRef] - Folkerts, L.; Das, J.; Bergsma, S.W.; Morgenstern, R. Three-electron Auger processes observed in collisions of bare ions on a metal surface. Phys. Lett. A
**1992**, 163, 73–76. [Google Scholar] [CrossRef] - McGuire, J.H.; Weaver, L. Independent electron approximation for atomic scattering by heavy particles. Phys. Rev. A
**1977**, 16, 41–47. [Google Scholar] [CrossRef] - Shao, C.; Yu, D.; Cai, X.; Chen, X.; Ma, K.; Evslin, J.; Xue, Y.; Wang, W.; Kozhedub, Y.S.; Lu, R.; et al. Production and decay of K-shell hollow krypton in collisions with 52-197-MeV/u bare xenon ions. Phys. Rev. A
**2017**, 96, 012708. [Google Scholar] [CrossRef] [Green Version] - Hall, J.; Richard, P.; Gray, T.J.; Lin, C.D.; Jones, K.; Johnson, B.; Gregory, D. Double K-shell-to-K-shell electron transfer in ion-atom collisions. Phys. Rev. A
**1981**, 24, 2416. [Google Scholar] [CrossRef] - Schulz, M.; Justiniano, E.; Konrad, J.; Schuch, R.; Salin, A. K-shell to K-shell charge transfer in collisions of bare decelerated S ions with Ar. J. Phys. B At. Mol. Opt. Phys.
**1987**, 20, 2057–2073. [Google Scholar] [CrossRef] - Wohrer, K.; Chetioui, A.; Rozet, J.P.; Jolly, A.; Stephan, C. K-K transfer cross sections in near-symmetric Fe
^{26+}ion-atom collisions at intermediate velocity. J. Phys. B At. Mol. Opt. Phys.**1984**, 17, 1587. [Google Scholar] [CrossRef] - Hillenbrand, P.M.; Hagmann, S.; Kozhedub, Y.S.; Benis, E.P.; Brandau, C.; Chen, R.J.; Dmytriiev, D.; Forstner, O.; Glorius, J.; Grisenti, R.E.; et al. Single and double K-shell vacancy production in slow Xe
^{54+,53+}-Xe collisions. Phys. Rev. A**2022**, 105, 022810. [Google Scholar] [CrossRef] - Xia, J.W.; Zhan, W.L.; Wei, B.W.; Yuan, Y.J.; Song, M.T.; Zhang, W.Z.; Yang, X.D.; Yuan, P.; Gao, D.Q.; Zhao, H.W.; et al. The heavy ion cooler-storage-ring project (HIRFL-CSR) at Lanzhou. Nucl. Instr. Meth. Phys. Res. Sec. A
**2002**, 488, 11–25. [Google Scholar] [CrossRef] - Shao, C.; Lu, R.; Cai, X.; Yu, D.; Ruan, F.; Xue, Y.; Zhang, J.; Torpokov, D.K.; Nikolenko, D. HIRFL–CSR internal cluster target. Nucl. Instrum. Meth. Sec. B
**2013**, 317, 617–622. [Google Scholar] [CrossRef] - Deslattes, R.D.; Kessler, E.G.; Indelicato, P.; de Billy, L.; Lindroth, E.; Anton, J. X-ray transition energies: New approach to a comprehensive evaluation. Rev. Mod. Phys.
**2003**, 75, 35–99. [Google Scholar] [CrossRef] - Ma, K.; Jiao, Z.; Jiang, F.; Ye, J.; Lv, H.; Chen, Z. Theoretical calculation of Kα and Kβ X-ray satellite and hypersatellite structures for hollow argon atoms. Acta Phys. Sin.
**2018**, 67, 173201. [Google Scholar] - Banaś, D.; Pajek, M.; Semaniak, J.; Braziewicz, J.; Kubala-Kukuś, A.; Majewska, U.; Czyżewski, T.; Jaskóła, M.; Kretschmer, W.; Mukoyama, T. Multiple ionization effects in low-resolution X-ray spectra induced by energetic heavy ions. Nucl. Instrum. Methods Phys. Res. Sec. B
**2002**, 195, 233–246. [Google Scholar] [CrossRef] - Jönsson, P.; Gaigalas, G.; Bieroń, J.; Fischer, C.F.; Grant, I.P. New Version: Grasp2k Relativistic Atomic Structure Package. Comput. Phys. Commun.
**2013**, 184, 2197–2203. [Google Scholar] [CrossRef] [Green Version] - Watson, R.L.; Jenson, F.E.; Chiao, T. Z dependence of Kα X-ray satellite structure in heavy-ion—atom collisions. Phys. Rev. A
**1974**, 10, 1230–1244. [Google Scholar] [CrossRef] - Sulik, B.; Kádár, I.; Ricz, S.; Varga, D.; Végh, J.; Hock, G.; Berényi, D. A Simple Theoretical Approach to Multiple Ionization and Its Application for 5.1 and 5.5 MeV/u X
^{q+}-Ne Collisions. Nucl. Instrum. Methods Phys. Res. Sec. B**1987**, 28, 509–518. [Google Scholar] [CrossRef] - Larkins, F.P. Dependence of Fluorescence Yield on Atomic Configuration. J. Phys. B At. Mol. Opt. Phys.
**1971**, 4, L29–L32. [Google Scholar] [CrossRef] - Scofield, J.H. Relativistic Hartree-Slater Values for K and L X-ray Emission Rates. At. Data Nucl. Data Tables
**1974**, 14, 121–137. [Google Scholar] [CrossRef] - Chen, M.H.; Crasemann, B.; Mark, H. Relativistic Radiationless Transition Probabilities for Atomic K-and L-Shells. At. Data Nucl. Data Tables
**1979**, 24, 13–37. [Google Scholar] [CrossRef] - Horvat, V.; Watson, R.L.; Blackadar, J.M. Target-Atom Inner-Shell Vacancy Distributions Created in Collisions with Heavy Ion Projectiles. Nucl. Instrum. Methods Phys. Res. Sec. B
**2000**, 170, 336–346. [Google Scholar] [CrossRef] - Kozhedub, Y.S.; Shabaev, V.M.; Tupitsyn, I.I.; Gumberidze, A.; Hagmann, S.; Plunien, G.; Stöhlker, T. Relativistic Calculations of X-ray Emission Following a Xe-Bi
^{83+}Collision. Phys. Rev. A**2014**, 90, 042709. [Google Scholar] [CrossRef] [Green Version] - Carlson, T.A.; Nestor, C.W. Calculation of Electron Shake-Off Probabilities as the Result of X-ray Photoionization of the Rare Gases. Phys. Rev. A
**1973**, 8, 2887–2894. [Google Scholar] [CrossRef]

**Figure 1.**Measured spectra of X-rays emitted from argon target in the collisions with 197-MeV/u Xe

^{54+}ions, obtained by the Si(Li) detector at the 90° observation angle. The measured data are represented by open circles, while the fitted transitions are represented by dashed curves. The fitted background is shown as gray dotted line.

**Figure 2.**(

**a**) Calculated average numbers of spectator L-shells at the time of X-ray emission ${n}_{L}^{x}$ versus that of spectator L-shells produced in the collision ${n}_{L}^{0}$ for argon. (

**b**) The calculated fluorescence yields ${\omega}_{K{a}^{s}}$, ${\omega}_{K{a}^{h,s}}$ and ${\omega}_{K{a}^{s}}^{\prime}$ versus ${n}_{L}^{0}$ for argon. The experimental results are represented by solid symbols with vertical and horizontal lines indicating their coordinates.

**Table 1.**The determined relative intensities I(Kα

^{h,s})/I(Kα

^{s}), the energy, and FWHM of Kα

^{s}, Kα

^{h,s}, Kβ

^{s}and Kβ

^{h,s}peaks, as well as the average number of spectator L-vacancies ${n}_{L}^{x}$ of argon in collision with 197-MeV/u Xe

^{54+}ion. The data include measurements at both the Si(Li) at the 90° observation angle and the germanium detectors at the 145° observation angle.

Results | Detection Angle of 90° | Detection Angle of 145° |
---|---|---|

$\mathrm{I}\left(K{a}^{h,s}\right)/\mathrm{I}\left(K{a}^{s}\right)$ | 0.107 ± 0.02 | 0.119 ± 0.02 |

$\mathrm{E}\left(K{a}^{s}\right)$/FWHM (keV) | 3.0007/0.199 | 3.0037/0.206 |

$\mathrm{E}\left(K{a}^{h,s}\right)$/FWHM (keV) | 3.1778/0.199 | 3.1808/0.206 |

$\mathrm{E}\left(K{\beta}^{s}\right)$/FWHM (keV) | 3.3058/0.238 | 3.3132/0.244 |

$\mathrm{E}\left(K{\beta}^{h,s}\right)$/FWHM (keV) | 3.5371/0.238 | 3.5448/0.244 |

${n}_{L}^{x}$ | 2.34 ± 0.3 | 2.49 ± 0.3 |

**Table 2.**Comparison of our experimental results with theory for target single and double K-shell vacancy production. The uncertainty of intensity ratio comes from the uncertainties of the fitting parameters. The uncertainty of the deduced mean L-vacancies is estimated by detection error and fitting error.

Projectile | Experiment | Theory (RCC) | ||||
---|---|---|---|---|---|---|

${\mathit{\sigma}}_{{\mathit{K}}^{-2}}{/\mathit{\sigma}}_{{\mathit{K}}^{-1}}$ | ${\mathit{n}}_{\mathit{L}}^{0}$$\left({\mathit{K}}^{-2}{\mathit{L}}^{-{\mathit{n}}_{\mathit{L}}}\right)$ | ${\mathit{\sigma}}_{{\mathit{K}}^{-2}}\left(\mathbf{kbarn}\right)$ | ${\mathit{\sigma}}_{{\mathit{K}}^{-1}}\phantom{\rule{0ex}{0ex}}\left(\mathbf{kbarn}\right)$ | ${\mathit{\sigma}}_{{\mathit{K}}^{-2}}{/\mathit{\sigma}}_{{\mathit{K}}^{-1}}$ | ${\mathit{n}}_{\mathit{L}}^{0}$$\left({\mathit{K}}^{-2}{\mathit{L}}^{-{\mathit{n}}_{\mathit{L}}}\right)$ | |

197 MeV/u Xe^{54+} | 0.12 ± 0.02 | 2.4 ± 0.3 | 289 | 2709 | 0.1067 | 3.56 |

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**MDPI and ACS Style**

Shao, C.; Yu, D.; Kozhedub, Y.S.; Ma, K.; Song, Z.; Wang, W.; Xue, Y.; Zhang, M.; Liu, J.; Yang, B.;
et al. Double *K*-Shell Ionization of Ar by 197-MeV/u Xe^{54+} Ion Impact. *Atoms* **2022**, *10*, 155.
https://doi.org/10.3390/atoms10040155

**AMA Style**

Shao C, Yu D, Kozhedub YS, Ma K, Song Z, Wang W, Xue Y, Zhang M, Liu J, Yang B,
et al. Double *K*-Shell Ionization of Ar by 197-MeV/u Xe^{54+} Ion Impact. *Atoms*. 2022; 10(4):155.
https://doi.org/10.3390/atoms10040155

**Chicago/Turabian Style**

Shao, Caojie, Deyang Yu, Yury S. Kozhedub, Kun Ma, Zhangyong Song, Wei Wang, Yingli Xue, Mingwu Zhang, Junliang Liu, Bian Yang,
and et al. 2022. "Double *K*-Shell Ionization of Ar by 197-MeV/u Xe^{54+} Ion Impact" *Atoms* 10, no. 4: 155.
https://doi.org/10.3390/atoms10040155