Theoretical calculation of K_{α} and K_{β} X-ray satellite and hypersatellite structures for hollow argon atoms

Ma Kun^{1}, Jiao Zheng^{1}, Jiang Feng-Jian^{1}, Ye Jian-Feng^{1}, Lv Hai-Jiang^{1}, Chen Zhan-Bin^{2,3}

1. School of Information Engineering, Huangshan University, Huangshan 245041, China; 2. School of Science, Hunan University of Technology, Zhuzhou 412007, China; 3. College of Science, National University of Defense Technology, Changsha 410073, China

Abstract A systematical knowledge of the satellite and hypersatellite structures of X-ray transitions is of great interest for various research areas, such as the explanation of the X-ray radiation from universe, plasma diagnostics, extreme ultraviolet (EUV) and X-ray sources and so on. Among these researches, the detailed explanation of the complex structures of X-ray satellites and hypersatellites are crucial for understanding the X-ray emission mechanism and the hollow atom formation mechanism. In this paper, the K_{α} and K_{β} X-ray satellite and hypersatellite structure are theoretically studied for hollow argon atoms with the relativistic multiconfiguration Dirac-Fock (MCDF) method, which includes the Breit and quantum electro-dynamics (QED) corrections. To check the applicability of the method, the transition energies and rates of the diagram lines for Ar are calculated,. and the results are in agreement with previously published data. Then the MCDF calculations of the transition energies and probabilities of K_{α 1, 2} (K →L_{3, 2}) and K_{β 1, 3} (K → M_{3, 2}) X-ray satellites and hypersatellites, which originate from the argon atoms with additional vacancies in the L shell, are carried out. To obtain the overall profile of the K X-ray spectrum, the diagram lines are integrated with the satellites and hypersatellites on the assumption that the intensity is proportional to the corresponding transition probability and each discrete line has a Gaussian distribution profile with a full width at half maximum (FWHM) value of 20 eV. From the convoluted profile, we can obtain the dependence of the average transition energy and relative transition intensity of the satellites and hypersatellites on the initial hollow configuration. It is found that the transition energy shift increases linearly with the number of spectator vacancies in the L shell increasing. For instance, the energy shift of the K_{α} satellite caused by L-shell hole is about 20 eV, and that of the K_{β} satellite is 48 eV. While for hypersatellite, the energy shift increases greatly due to the double ionization in the K shell. The energy shift increment of K_{α} and K_{β} hypersatellites corresponding to L vacancy are 21 and 52 eV, respectively. Finally, four simple empirical formulae for estimating the energy shifts of the K_{α}, K_{β} X-ray satellites and hypersatellite for Ar atom with any number of L-shells vacancies are deduced by using the least square method. These results are useful in explaining various K X-ray spectra and better understanding the collision process.

Fund:Project supported by the Natural Science Foundation of Anhui Province, China (Grant No. 1808085QA22), the Key Project for Young Talents in College of Anhui Province, China (Grant No. gxyqZD2016301), the Natural Science Foundation of the Higher Education Institutions of Anhui Province, China (Grant No. KJHS2015B01), and the Natural Science Research Project of Huangshan University, China (Grant No. 2016xskq003).

Ma Kun,Jiao Zheng,Jiang Feng-Jian et al.. Theoretical calculation of K_{α} and K_{β} X-ray satellite and hypersatellite structures for hollow argon atoms[J]. Acta Physica Sinica, 2018, 67(17):
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doi:10.7498/aps.67.20180553.

Briand J P, Chevallier P, Tavernier M, Rozet J P 1971 Phys. Rev. Lett. 27 777

[2]

Kozio K 2014 J. Quant. Spectrosc. Ra. 149 138

[3]

Wang X L, Dong C D, Su M G 2012 Nucl. Instr. Meth. B 280 93

[4]

Yerokhin V A, Surzhykov A, Fritzsche S 2014 Phys. Rev. A 90 022509

[5]

Steinbrügge R, Bernitt S, Epp S W, Rudolph J K, Beilmann C, Bekker H, Eberle S, Müller A, Versolato O O, Wille H C, Yava H, Ullrich J, Crespo López-Urrutia J R 2015 Phys. Rev. A 91 032502

[6]

Czarnota M, Bana D, Berset M, Chmielewska D, Dousse J C, Hoszowska J, Maillard Y P, Mauron O, Pajek M, Polasik M, Raboud P A, Rzadkiewicz J, Słabkowska K, Sujkowski Z 2013 Phys. Rev. A 88 052505

[7]

Yuan Y J, Yang J C, Xia J W, et al. 2013 Nucl. Instrum. Methods Phys. Res. Sect. B 317 214

[8]

Shao C J, Yu D Y, Cai X H, Chen X, Ma K, Evslin J, Xue Y L, Wang W, Kozhedub Y S, Lu R C, Song Z Y, Zhang M W, Liu J L, Yang B, Guo Y P, Zhang J M, Ruan F F, Wu Y H, Zhang Y Z, Dong C Z, Chen X M, Yang Z H 2017 Phys. Rev. A 96 012708

[9]

Chen X, Ma K, Dong C Z, Zhang D H, Shao C J, Yu D Y, Cai X H 2015 Nucl. Instr. Meth. B 362 14

[10]

Liang T, Ma K, Chen X, Xie L Y, Dong C Z, Shao C J, Yu D Y, Cai X H 2015 Acta Phys. Sin. 64 153401 (in Chinese)[梁腾, 马堃, 陈曦, 颉录有, 董晨钟, 邵曹杰, 于得洋, 蔡晓红 2015 物理学报 64 153401]

[11]

Liang T, Ma K, Wu Z W, Zhang D H, Dong C Z, Shi Y L 2016 Acta Phys. Sin. 65 143401 (in Chinese)[梁腾, 马堃, 武中文, 张登红, 董晨钟, 师应龙 2016 物理学报 65 143401]

[12]

Grant I P 1970 Adv. Phys. 19 747

[13]

Jönsson P, He X, Fischer C F, Grant I P 2007 Comput. Phys. Commun. 177 597