Fully relativistic distorted-wave method of studying electron-atom collision excitation process

LI Wenbo; LI Bingbing; CHEN Hao; XIE Luyou; WU Zhongwen; DING Xiaobin; ZHANG Denghong; JIANG Jun; DONG Chenzhong

doi:10.7498/aps.74.20241467

Abstract

The electron-atom (ion) collision excitation process is one of the most common inelastic scattering processes. It is of great significance in the fields of astrophysics and laboratory plasma. The relativistic distorted-wave method is a widely used theoretical tool for studying electron-atom (ion) collisions, with the aim of obtaining scattering parameters, such as impact cross sections and rate coefficients.In recent years, we have developed a set of fully relativistic distorted-wave methods and programs of studying the electron-atom collision excitation processes. This method is based on the multi-configuration Dirac-Hartree-Fock (MCDHF) method, together with the corresponding packages GRASP 92/2K/2018 and RATIP. In the present work, continuum state wave functions, total and differential cross sections, state multipoles, integral and differential Stokes parameters of the radiation photon after the impact excitation processes of polarized electrons and atoms are calculated. The influences of electron correlation effects, Breit interaction, and plasma screening effects on the excitation cross sections are discussed. The present methods and programs possess several advantages below.1) In the calculations of the continuum electron wave functions, the direct interaction and exchange interaction between the bound electron and the continuum electron are both included. Then, the anti-symmetrized coupling wave function, which is composed of the continuum electron wave function and the continuum ion wave function, is utilized as the wave function of the system. This method is employed to study the low-energy electron scattering process and medium energy electron scattering process.2) In this method, the target state wave function is obtained form the MCDHF theory and the corresponding GRASP packages. The MCDHF method has the advantage of being able to consider the electron correlation effects, including valence-valence, core-valence, and core-core correlations, as well as the influence of Breit interaction and quantum electrodynamics effect on the target state wave function. Furthermore, the calculation of the collision excitation matrix elements also includes the contribution of the Breit interaction. Consequently, the present method integrates the advantages of both the MCDHF method and distorted-wave method, thus is made suitable for studying the scattering processes of highly charged ions. In addition, it facilitates the study of the influence of higher-order effects on the collision dynamics, thereby obtaining high-precision theoretical data.3) The current method and program can also be utilized to study the scattering cross section of electron-atom collision excitation processes, as well as the influence of plasma screening effects on collision excitation. Furthermore, the state multipoles, differential Stokes parameters, integral Stokes parameters, and orientation parameters of electron-complex atom collision excitation can be studied in detail by using the present method and program.

Keywords:

Authors and contacts

Key Laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070 China

Corresponding author: JIANG Jun, phyjiang@yeah.net ; DONG Chenzhong, dongcz@nwnu.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2022YFA1602500) and the National Natural Science Foundation of China (Grant Nos. 12064041, 12174315, 12274352, 12364034, 12174316, 12374384).

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References

[1]	Fontes C J, Sampson D H, Zhang H L 1993 Phys. Rev. A 47 1009 Google Scholar
[2]	Fontes C J, Zhang H L, Sampson D H 1999 Phys. Rev. A 59 295 Google Scholar
[3]	Ren C, Wu Z W, Jiang J, Xie L Y, Zhang D H, Dong C Z 2018 Phys. Rev. A 98 012711 Google Scholar
[4]	Jakubowicz H, Moores D L 1981 J. Phys. B: Atom. Mol. Phys. 14 3733 Google Scholar
[5]	Bartschat K, Burke P G 1987 J. Phys. B: Atom. Mol. Phys. 20 3191 Google Scholar
[6]	Teng H G 2000 J. Phys. B: Atom. Mol. Phys. 33 L553 Google Scholar
[7]	Wu D, Loch S D, Pindzola M S, Balance C P 2012 Phys. Rev. A 85 012711 Google Scholar
[8]	Liu P F, Liu Y P, Zeng J L, Yuan J M 2014 Phys. Rev. A 89 042704 Google Scholar
[9]	蒋军2007 硕士学位论文(兰州: 西北师范大学) Jiang J 2007 M. S. Thesis (Lanzhou: Northwest Normal University
[10]	Suckewer S, Hinnov E 1978 Phys. Rev. Lett. 41 756 Google Scholar
[11]	Eichler J 1990 Phys. Rep. 193 165 Google Scholar
[12]	Vane C R, Datz S, Dittner P F, Giese J, Jones N L, Krause H F, Rosseel T M, Peterson R S 1994 Phys. Rev. A 49 1847 Google Scholar
[13]	Wan J J, Dong C Z, Ding X B, Ma X W, Rzadkiewicz J, Stöhlker T, Fritzsche S 2009 Phys. Rev. A 79 022707 Google Scholar
[14]	Eichler J, Stöhlker T 2007 Phys. Rep. 439 1 Google Scholar
[15]	Biswas S, Monti J M, Tachino C A, Rivarola R D, Tribedi L C 2015 J. Phys. B: At. Mol. Opt. Phys. 48 115206 Google Scholar
[16]	Abdurakhmanov I B, Kadyrov A S, Avazbaev S K, Bray I 2016 J. Phys. B: At. Mol. Opt. Phys. 49 115203 Google Scholar
[17]	Zhang S B, Wang J G, Janev R K 2010 Phys. Rev. Lett. 104 023203 Google Scholar
[18]	Fang X, Liu X W 2013 Mon. Not. R. Astron. Soc. 429 2791 Google Scholar
[19]	Menchero L F, Zatsarinny O, Bartschat K 2017 J. Phys. B: At. Mol. Opt. Phys. 50 065203 Google Scholar
[20]	Cheung C, Safronova M, Porsev S 2021 Symmetry 13 621 Google Scholar
[21]	Wu Z W, He Z M, Tian Z Q, Dong C Z, Fritzsche S 2022 Phys. Rev. A 105 062813 Google Scholar
[22]	Li F H, Li J T, Zheng Y, Guo L X, Liu W, Liu Z Y 2023 IEEE T. Plasma Sci. 51 3579 Google Scholar
[23]	Yan J, Liu Y P, Hou Y, Gao C, Wu J H, Zeng J L, Yuan J M 2023 Chin. Phys. B 32 063101 Google Scholar
[24]	Zeng J L, Jiang X B, Gao C, Wu J H, Yuan J M 2024 Results Phys. 58 107522 Google Scholar
[25]	刘丽娟2012 硕士学位论文(兰州: 西北师范大学) Liu L J 2012 M. S. Thesis (Lanzhou: Northwest Normal University
[26]	Silver J D, Varney A J, Margolis H S, et al. 1994 Rev. Sci. Instrum. 65 1072 Google Scholar
[27]	Biedermann C, Förster A, Fußmann G, Radtke R 1997 Phys. Scr. T73 360 Google Scholar
[28]	Crespo López-Urrutia J R, Dorn A, Moshammer R, Ullrich J 1999 Phys. Scr. T80B 502 Google Scholar
[29]	Beiersdorfer P, Brown G V 2015 Phys. Rev. A 91 032514 Google Scholar
[30]	Hu Z M, Han X Y, Li Y M, Kato D, Tong X M, Nakamura N 2012 Phys. Rev. Lett. 108 073002 Google Scholar
[31]	Yan C L, Lu Q, Xie Y M, Li B L, Fu N, Zou Y, Chen C, Xiao J 2022 Phys. Rev. A 105 032820 Google Scholar
[32]	Dunn G H, Djurić N, Chung Y S, Bannister M, Smith A C H 1995 Nucl. Instr. Meth. Phys. Res. B 98 107 Google Scholar
[33]	Taylor P O, Dunn G H 1973 Phys. Rev. A 8 2304 Google Scholar
[34]	Rogers W T, Olsen J Q, Dunn G H 1978 Phys. Rev. A 18 1353 Google Scholar
[35]	Huber B A, Ristori C, Hervieux P A, Maurel M, Guet C, Andrä H J 1991 Phys. Rev. Lett. 67 1407 Google Scholar
[36]	Huber B A, Ristori C, Guet C, Küchler D, Johnson W R 1994 Phys. Rev. Lett. 73 2301 Google Scholar
[37]	Srigengan B, Williams I D, Newell W R 1996 J. Phys. B: At. Mol. Opt. Phys. 29 L605 Google Scholar
[38]	Bannister M E, Djurić N, Woitke O, Dunn G H, Chung Y S, Smith A C H, Wallbank B, Berrington K A 1999 Int. J. Mass Spectrom. 192 39 Google Scholar
[39]	Phaneuf R A, Havener C C, Dunn G H, Müller A 1999 Rep. Prog. Phys. 62 1143 Google Scholar
[40]	Wallbank B, Bannister M E, Krause H F, Chung Y S, Smith A C H, Djurić N, Dunn G H 2007 Phys. Rev. A 75 052703 Google Scholar
[41]	Smirnov Yu M 2015 J. Phys. B: At. Mol. Opt. Phys. 48 165204 Google Scholar
[42]	Smirnov Yu M 2016 J. Phys. B: At. Mol. Opt. Phys. 49 175204 Google Scholar
[43]	Smirnov Yu M 2017 Russ. J. Phys. Chem. B 11 873 Google Scholar
[44]	Huang Z K, Wen W Q, Wang S X, et al. 2020 Phys. Rev. A 102 062823 Google Scholar
[45]	Wang S X, Huang Z K, Wen W Q, et al. 2022 Phys. Rev. A 106 042808 Google Scholar
[46]	邵林, 黄忠魁, 汶伟强, 汪书兴, 黄厚科, 马万路, 刘畅, 汪寒冰, 陈冬阳, 刘鑫, 周晓鹏, 赵冬梅, 张少锋, 朱林繁, 马新文 2024 73 123402 Google Scholar Shao L, Huang Z K, Wen W Q, Wang S X, Huang H K, Ma W L, Liu C, Wang H B, Chen D Y, Liu X, Zhou X P, Zhao D M, Zhang S F, Zhu L F, Ma X W 2024 Acta Phys. Sin. 73 123402 Google Scholar
[47]	Liu X J, Zhu L F, Yuan Z S, Li W B, Cheng H D, Huang Y P, Zhong Z P, Xu K Z, Li J M 2003 Phys. Rev. Lett. 91 193203 Google Scholar
[48]	Du X J, Xu Y C, Wang L H, Li T J, Ma Z R, Wang S X, Zhu L F 2022 Phys. Rev. A 105 012812 Google Scholar
[49]	Wang D H, Wang S X, Nie Z W, Wang L H, Xu Y C, Du X J, Zhu L F 2022 Plasma Sources Sci. Technol. 31 045012 Google Scholar
[50]	Dörner R, Mergel V, Jagutzki O, Spielberger L, Ullrich J, Moshammer R, Schmidt-Böcking H 2000 Phys. Rep. 330 95 Google Scholar
[51]	Xia Z H, Ren B, Zhang R T, Wei L, Han J, Meng T, Wang J, Ma P, Zhang Y, Tu B, Xiao J, Yao K, Zou Y, Zhu X L, Guo D L, Ma X, Wei B 2022 Astrophysical J. 933 207 Google Scholar
[52]	Ren B, Ma P, Zhang Y, Wei L, Han J, Xia Z, Wang J, Meng T, Yu W, Zou Y, Yang C L, Wei B 2022 Phys. Rev. A 106 012805 Google Scholar
[53]	Uhlmann L J, Dall R G, Truscott A G, Hoogerland M D, Baldwin K G H, Buckman S J 2005 Phys. Rev. Lett. 94 173201 Google Scholar
[54]	Łukomski M, MacAskill J A, Seccombe D P, McGrath C, Sutton S, Teeuwen J, Kedzierski W, Reddish T J, McConkey J W, van Wijngaarden W A 2005 J. Phys. B: At. Mol. Opt. Phys. 38 3535 Google Scholar
[55]	Byron L J, Dall R G, Truscott A G 2010 Phys. Rev. A 81 013405 Google Scholar
[56]	Daw A, Gardner L D, Janzen P H, Kohl J L 2006 Phys. Rev. A 73 032709 Google Scholar
[57]	Knehr E, Kuzmin A, Doerner S, Wuensch S, Ilin K, Schmidt H, Siegel M 2020 Appl. Phys. Lett. 117 132602 Google Scholar
[58]	Heddle D W O, Samuel M J 1970 J. Phys. B: Atom. Mol. Phys. 3 1593 Google Scholar
[59]	Stewart Jr M D, Chilton J E, Boffard J B, Lin C C 2002 Phys. Rev. A 65 032704 Google Scholar
[60]	McCarthy I E, Weigold E 1988 Rep. Prog. Phys. 51 299 Google Scholar
[61]	McCarthy I E, Weigold E 1991 Rep. Prog. Phys. 54 789 Google Scholar
[62]	Fursa D V, Bray I 1995 Phys. Rev. A 52 1279 Google Scholar
[63]	Bray I, Fursa D V 1996 Phys. Rev. Lett. 76 2674 Google Scholar
[64]	Bartschat K, Zatsarinny O 2015 Phys. Scr. 90 054006 Google Scholar
[65]	Zhao G P, Liu L, Chang Z, Wang J G, Janev R K 2018 J. Phys. B: At. Mol. Opt. Phys. 51 085201 Google Scholar
[66]	Liu Y D, Jia C C, Ma M X, Gao X, Liu L, Wu Y, Chen X J, Wang J G 2024 Chin. Phys. B 33 083401 Google Scholar
[67]	杨威, 蔡晓红, 于得洋 2005 54 2128 Google Scholar Yang W, Cai X H, Yu D Y 2005 Acta Phys. Sin. 54 2128 Google Scholar
[68]	Whiteford A D, Badnell N R, Ballance C P, O’Mullane M G, Summers H P, Thomas A L 2001 J. Phys. B: At. Mol. Opt. Phys. 34 3179 Google Scholar
[69]	Fan Q P, Wang W H, Hu F, Cao L F, Zhang Q Q, Liu Y W, Jiang G 2014 Chin. Phys. B 23 113401 Google Scholar
[70]	Chen Y Q, Jiang X W, Yao L F, Jiang W, Liu H N, Zhang Y 2023 Plasma Sources Sci. Technol. 32 045017 Google Scholar
[71]	Bar-Shalom A, Klapisch M, Oreg J 1988 Phys. Rev. A 38 1773 Google Scholar
[72]	Meng F C, Chen C Y, Wang Y S, Zou Y M 2007 Chinese Phys. Lett. 24 3404 Google Scholar
[73]	Gu M F 2008 Can. J. Phys. 86 675 Google Scholar
[74]	Podpaly Y, Clementson J, Beiersdorfer P, Williamson J, Brown G V, Gu M F 2009 Phys. Rev. A 80 052504 Google Scholar
[75]	Ma Y L, Liu L, Xie L Y, Wu Y, Zhang D H, Dong C Z, Qu Y Z, Wang J G 2022 Chin. Phys. B 31 043401 Google Scholar
[76]	Zhang C Y, Wu S J, Wang K, Si R, Yao K, Huang Z K, Wen W Q, Ma X W, Chen C Y, Badnell N R 2023 Phys. Rev. A 108 022801 Google Scholar
[77]	杜贵锋2011 硕士学位论文(兰州: 西北师范大学) Du G F 2011 M. S. Thesis (Lanzhou: Northwest Normal University
[78]	杨宁选2009 硕士学位论文(兰州: 西北师范大学) Yang N X 2009 M. S. Thesis (Lanzhou: Northwest Normal University
[79]	Macek J, Jaecks D H 1971 Phys. Rev. A 4 2288 Google Scholar
[80]	Bartschat K, Blum K, Hanne G F, Kessler J 1981 J. Phys. B: Atom. Mol. Phys. 14 3761 Google Scholar
[81]	Bartschat K, Scott N S, Blum K, Burke P G 1984 J. Phys. B: Atom. Mol. Phys. 17 269 Google Scholar
[82]	Khalid S M, Kleinpoppen H 1984 J. Phys. B: Atom. Mol. Phys. 17 243 Google Scholar
[83]	Raeker A, Blum K, Bartschat K 1993 J. Phys. B: Atom. Mol. Phys. 26 1491 Google Scholar
[84]	Kłosowski Ł, Piwiski M, Dziczek D, Wiśniewska K, Chwirot S 2007 Meas. Sci. Technol. 18 3801 Google Scholar
[85]	Kłosowski Ł, Piwiski M, Dziczek D, Pleskacz K, Chwirot S 2009 Phys. Rev. A 80 062709 Google Scholar
[86]	Hussey M, Murray A, MacGillivray W, King G C 2007 Phys. Rev. Lett. 99 133202 Google Scholar
[87]	Percival A K, Jhumka S, Hussey M, Murray A J 2011 J. Phys. B: At. Mol. Opt. Phys. 44 105203 Google Scholar
[88]	Polasik M 1989 Phys. Rev. A 39 616 Google Scholar
[89]	Wu Z W, Tian Z Q, Dong C Z, Surzhykov A, Fritzsche S 2023 New J. Phys. 25 093039 Google Scholar
[90]	Ding X B, Koike F, Murakami I, Kato D, Sakaue H A, Dong C Z, Nakamura N 2012 J. Phys. B: At. Mol. Opt. Phys. 45 035003 Google Scholar
[91]	Wang K, Li S, Jönsson P, Fu N, Dang W, Guo X L, Chen C Y, Yan J, Chen Z B, Si R 2017 J. Quant. Spectrosc. Radiat. Transf. 187 375 Google Scholar
[92]	颉录有2008 博士学位论文(兰州: 西北师范大学) Xie L Y 2008 Ph. D. Dissertation (Lanzhou: Northwest Normal University
[93]	武中文2012 硕士学位论文(兰州: 西北师范大学) Wu Z W 2012 M. S. Thesis 2012 (Lanzhou: Northwest Normal University
[94]	Parpia F A, Fischer C F, Grant I P 1996 Compt. Phys. Commun. 94 249 Google Scholar
[95]	Jönsson P, Gaigalas G, Bieroń J, Fischer C F, Grant I P 2013 Compt. Phys. Commun. 184 2197 Google Scholar
[96]	Fischer C F, Gaigalas G, Jönsson P, Bieroń J 2019 Compt. Phys. Commun. 237 184 Google Scholar
[97]	Fritzsche S, Fischer C F, Dong C Z 2000 Compt. Phys. Commun. 124 340 Google Scholar
[98]	Fritzsche S 2012 Compt. Phys. Commun. 183 1525 Google Scholar
[99]	Carse G D, Walker D W 1973 J. Phys. B: Atom. Mol. Phys. 6 2529 Google Scholar
[100]	Walker D W 1974 J. Phys. B: Atom. Mol. Phys. 7 97 Google Scholar
[101]	Dong C Z, Xie L Y, Zhou X X, Ma X W, Fritzsche S 2003 Hyperfine Interact. 146 161 Google Scholar
[102]	Li J G, Dong C Z, Yu Y J, Ding X B, Fritzsche S, Fricke B 2007 Sci. China Phys. Mech. 50 707 Google Scholar
[103]	Xie L Y, Wang J G, Janev R K, Qu Y Z, Dong C Z 2012 Eur. Phys. J. D 66 125 Google Scholar
[104]	Grant I P, McKenzie B J, Norrington P H, Mayers D F, Pyper N C 1980 Compt. Phys. Commun. 21 207 Google Scholar
[105]	Dyall K G, Grant I P, Johnson C T, Parpia F A, Plummer E P 1989 Compt. Phys. Commun. 55 425 Google Scholar
[106]	Jiang J, Dong C Z, Xie L Y, Wang J G, Yan J, Fritzsche S 2007 Chin. Phys. Lett. 24 691 Google Scholar
[107]	Li B W, Dong C Z, Jiang J, Wang J G 2010 Eur. Phys. J. D 59 201 Google Scholar
[108]	Jiang J, Dong C Z, Xie L Y, Wang J G 2008 Phys. Rev. A 78 022709 Google Scholar
[109]	马小云2013 硕士学位论文(兰州: 西北师范大学) Ma X Y 2013 M. S. Thesis (Lanzhou: Northwest Normal University
[110]	Grant I P 1970 Adv. Phys. 19 747 Google Scholar
[111]	Rodrigues G C, Ourdane M A, Bieroń J, Indelicato P, Lindroth E. 2000 Phys. Rev. A 63 012510 Google Scholar
[112]	Dong C Z, Fritzsche S 2005 Phys. Rev. A 72 012507 Google Scholar
[113]	Fischer C F, Godefroid M, Brage T, Jönsson P, Gaigalas G 2016 J. Phys. B: At. Mol. Opt. Phys. 49 182004 Google Scholar
[114]	Andersen N, Broad J T, Campbell E E B, Gallagher J W, Hertel I V 1997 Phys. Rep. 278 107 Google Scholar
[115]	Jung R O, Boffard J B, Anderson L W, Lin C C 2005 Phys. Rev. A 72 022723 Google Scholar
[116]	Jiang J, Dong C Z, Xie L Y, Zhou X X, Wang J G 2008 J. Phys. B: At. Mol. Opt. Phys. 41 245204 Google Scholar
[117]	Goeke J, Hanne G F, Kessler J 1989 J. Phys. B: Atom. Mol. Phys. 22 1075 Google Scholar
[118]	Beiersdorfer P, Osterheld A L, Chen M H, Henderson J R, Knapp D A, Levine M A, Marrs R E, Reed K J, Schneider M B, Vogel D A 1990 Phys. Rev. Lett. 65 1995 Google Scholar
[119]	Takács E, Meyer E S, Gillaspy J D, Roberts J R, Chantler C T, Hudson L T, Deslattes R D, Brown C M, Laming J M, Dubau J, Inal M K 1996 Phys. Rev. A 54 1342 Google Scholar
[120]	Dyl D, Dziczek D, Piwinski M, Gradziel M, Srivastava R, Dygdala R S, Chwirot S 1999 J. Phys. B: Atom. Mol. Phys. 32 837 Google Scholar
[121]	Srivastava R, Blumy K, McEachranz R P, Stauffer A D 1996 J. Phys. B: Atom. Mol. Phys. 29 3513 Google Scholar
[122]	Sohn M, Hanne G F 1992 J. Phys. B: Atom. Mol. Phys. 25 4627 Google Scholar
[123]	李博文, 蒋军, 董晨钟, 王建国, 丁晓彬 2009 58 5274 Google Scholar Li B W, Jiang J, Dong C Z, Wang J G, Ding X B 2009 Acta Phys. Sin. 58 5274 Google Scholar
[124]	Whitten B L, Lane N F, Weisheit J C 1984 Phys. Rev. A 29 945 Google Scholar
[125]	Murillo M S, Weisheit J C 1998 Phys. Rep. 302 1 Google Scholar
[126]	Hu F 2021 Radiat. Phys. Chem. 180 109293 Google Scholar
[127]	Pindzola M S, Loch S D, Colgan J, Fontes C J 2008 Phys. Rev. A 77 062707 Google Scholar
[128]	Jiang J, Dong C Z, Xie L Y 2014 Chin. Phys. Lett. 31 023401 Google Scholar

Cited By

图 1 极化电子与光子Stokes参数测量示意图

Figure 1. Schematic diagram of polarized electron and photon Stokes parameter measurement.

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图 2 Xe原子的激发截面随入射电子能量的变化, 方形为模型A的结果, 三角形为模型B的结果, 带误差条的圆形为Jung 等^[115]的实验结果(数据图片来自于文献[116])

Figure 2. Excitation cross section of Xe atom varies with the energy of incident electron. The square represents the results of model A, the triangle represents the results of model B, and the circle with error bars represents the experiment results of Jung et al^[115]. From Ref. [116].

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图 3 入射电子能量为8 eV时, 不同计算模型下Hg原子¹S₀ - ³P₁电子碰撞激发微分截面, 其中SC为模型I单组态近似的计算结果, 6l为模型II的计算结果, 7l为模型III的计算结果, Experiment为Goeke等^[117]的实验结果

Figure 3. Differential cross sections of electron collision excitation of Hg atom ¹S₀ -³P₁ under different calculation models, when the incident electron energy is 8 eV. The SC represents the calculation results of single configuration approximation of model I, 6l represents the calculation results of model II, 7l represents the calculation results of model III, Experiment represents the results of Goeke et al^[117].

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图 4 从基态2p⁶ J = 0到2p⁵3s J = 2的磁能级之间的激发截面(数据图片来自于文献[108])

Figure 4. Excitation cross sections from ground state 2p⁶ J = 0 to 2p⁵3s J = 2 magnetic energy levels. From Ref. [108].

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图 5 入射电子能量为45 eV时, 电子与Ca原子从基态到¹P₁的碰撞激发微分Stokes参数P₁, P₂和–P₃, 其中$ \kappa $为最大分波量子数, Experiment为Dyl等^[120]的实验结果

Figure 5. Collision excitation differential Stokes parameters P₁, P₂ and –P₃ of electron and Ca atom from ground state to ¹P₁, when the incident electron energy is 45 eV. $ \kappa $ is the maximum partial wave quantum number, and Experiment represents the results of Dyl et al^[120].

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图 6 入射电子能量为8 eV时, 不同关联模型下计算的Hg原子¹S₀ -³P₁归一化的态多极, 其中SC为利用单组态计算的结果, MC 6l为考虑了6l关联轨道的计算结果, MC 7l为考虑了7l关联轨道的计算结果, Experiment为Sohn等^[122]的实验结果

Figure 6. Normalized state multipoles of Hg atom ¹S₀ -³P₁ calculated under different correlation models, when the incident electron energy is 8 eV. The SC represents the calculation results using a single configuration, MC 6l represents the calculation results considering the 6l correlation orbit, MC 7l represents the calculation results considering the 7l correlation orbit, and Experiment refers to the results of Sohn et al^[122].

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图 7 入射电子能量为15 eV时, 不同关联模型下计算的Hg原子¹S₀ -³P₁归一化的态多极, 其中SC为利用单组态计算的结果, MC 6l为考虑了6l关联轨道的计算结果, MC 7l为考虑了7l关联轨道的计算结果, RDW R 为Srivastava等^[121]的理论结果, Experiment为Sohn等^[122]的实验结果

Figure 7. Normalized state multipoles of Hg atom ¹S₀ -³P₁ calculated under different correlation models, when the incident electron energy is 15 eV. The SC represents the calculation results using a single configuration, MC 6l represents the calculation results considering the 6l correlation orbit, MC 7l represents the calculation results considering the 7l correlation orbit, RDW R represents the theoretical results of Srivastava et al^[121], and Experiment refers to the results of Sohn et al^[122].

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图 8 从基态1s² ¹S₀ 到 1s2p ¹P₁和³P₁的激发截面随屏蔽长度的变化(数据图片来自于文献[128])

Figure 8. Excitation cross sections from ground state 1s² ¹S₀ to 1s2p ¹P₁ and ³P₁ vary with shielding length. From Ref. [128].

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[1]	Fontes C J, Sampson D H, Zhang H L 1993 Phys. Rev. A 47 1009 Google Scholar
[2]	Fontes C J, Zhang H L, Sampson D H 1999 Phys. Rev. A 59 295 Google Scholar
[3]	Ren C, Wu Z W, Jiang J, Xie L Y, Zhang D H, Dong C Z 2018 Phys. Rev. A 98 012711 Google Scholar
[4]	Jakubowicz H, Moores D L 1981 J. Phys. B: Atom. Mol. Phys. 14 3733 Google Scholar
[5]	Bartschat K, Burke P G 1987 J. Phys. B: Atom. Mol. Phys. 20 3191 Google Scholar
[6]	Teng H G 2000 J. Phys. B: Atom. Mol. Phys. 33 L553 Google Scholar
[7]	Wu D, Loch S D, Pindzola M S, Balance C P 2012 Phys. Rev. A 85 012711 Google Scholar
[8]	Liu P F, Liu Y P, Zeng J L, Yuan J M 2014 Phys. Rev. A 89 042704 Google Scholar
[9]	蒋军2007 硕士学位论文(兰州: 西北师范大学) Jiang J 2007 M. S. Thesis (Lanzhou: Northwest Normal University
[10]	Suckewer S, Hinnov E 1978 Phys. Rev. Lett. 41 756 Google Scholar
[11]	Eichler J 1990 Phys. Rep. 193 165 Google Scholar
[12]	Vane C R, Datz S, Dittner P F, Giese J, Jones N L, Krause H F, Rosseel T M, Peterson R S 1994 Phys. Rev. A 49 1847 Google Scholar
[13]	Wan J J, Dong C Z, Ding X B, Ma X W, Rzadkiewicz J, Stöhlker T, Fritzsche S 2009 Phys. Rev. A 79 022707 Google Scholar
[14]	Eichler J, Stöhlker T 2007 Phys. Rep. 439 1 Google Scholar
[15]	Biswas S, Monti J M, Tachino C A, Rivarola R D, Tribedi L C 2015 J. Phys. B: At. Mol. Opt. Phys. 48 115206 Google Scholar
[16]	Abdurakhmanov I B, Kadyrov A S, Avazbaev S K, Bray I 2016 J. Phys. B: At. Mol. Opt. Phys. 49 115203 Google Scholar
[17]	Zhang S B, Wang J G, Janev R K 2010 Phys. Rev. Lett. 104 023203 Google Scholar
[18]	Fang X, Liu X W 2013 Mon. Not. R. Astron. Soc. 429 2791 Google Scholar
[19]	Menchero L F, Zatsarinny O, Bartschat K 2017 J. Phys. B: At. Mol. Opt. Phys. 50 065203 Google Scholar
[20]	Cheung C, Safronova M, Porsev S 2021 Symmetry 13 621 Google Scholar
[21]	Wu Z W, He Z M, Tian Z Q, Dong C Z, Fritzsche S 2022 Phys. Rev. A 105 062813 Google Scholar
[22]	Li F H, Li J T, Zheng Y, Guo L X, Liu W, Liu Z Y 2023 IEEE T. Plasma Sci. 51 3579 Google Scholar
[23]	Yan J, Liu Y P, Hou Y, Gao C, Wu J H, Zeng J L, Yuan J M 2023 Chin. Phys. B 32 063101 Google Scholar
[24]	Zeng J L, Jiang X B, Gao C, Wu J H, Yuan J M 2024 Results Phys. 58 107522 Google Scholar
[25]	刘丽娟2012 硕士学位论文(兰州: 西北师范大学) Liu L J 2012 M. S. Thesis (Lanzhou: Northwest Normal University
[26]	Silver J D, Varney A J, Margolis H S, et al. 1994 Rev. Sci. Instrum. 65 1072 Google Scholar
[27]	Biedermann C, Förster A, Fußmann G, Radtke R 1997 Phys. Scr. T73 360 Google Scholar
[28]	Crespo López-Urrutia J R, Dorn A, Moshammer R, Ullrich J 1999 Phys. Scr. T80B 502 Google Scholar
[29]	Beiersdorfer P, Brown G V 2015 Phys. Rev. A 91 032514 Google Scholar
[30]	Hu Z M, Han X Y, Li Y M, Kato D, Tong X M, Nakamura N 2012 Phys. Rev. Lett. 108 073002 Google Scholar
[31]	Yan C L, Lu Q, Xie Y M, Li B L, Fu N, Zou Y, Chen C, Xiao J 2022 Phys. Rev. A 105 032820 Google Scholar
[32]	Dunn G H, Djurić N, Chung Y S, Bannister M, Smith A C H 1995 Nucl. Instr. Meth. Phys. Res. B 98 107 Google Scholar
[33]	Taylor P O, Dunn G H 1973 Phys. Rev. A 8 2304 Google Scholar
[34]	Rogers W T, Olsen J Q, Dunn G H 1978 Phys. Rev. A 18 1353 Google Scholar
[35]	Huber B A, Ristori C, Hervieux P A, Maurel M, Guet C, Andrä H J 1991 Phys. Rev. Lett. 67 1407 Google Scholar
[36]	Huber B A, Ristori C, Guet C, Küchler D, Johnson W R 1994 Phys. Rev. Lett. 73 2301 Google Scholar
[37]	Srigengan B, Williams I D, Newell W R 1996 J. Phys. B: At. Mol. Opt. Phys. 29 L605 Google Scholar
[38]	Bannister M E, Djurić N, Woitke O, Dunn G H, Chung Y S, Smith A C H, Wallbank B, Berrington K A 1999 Int. J. Mass Spectrom. 192 39 Google Scholar
[39]	Phaneuf R A, Havener C C, Dunn G H, Müller A 1999 Rep. Prog. Phys. 62 1143 Google Scholar
[40]	Wallbank B, Bannister M E, Krause H F, Chung Y S, Smith A C H, Djurić N, Dunn G H 2007 Phys. Rev. A 75 052703 Google Scholar
[41]	Smirnov Yu M 2015 J. Phys. B: At. Mol. Opt. Phys. 48 165204 Google Scholar
[42]	Smirnov Yu M 2016 J. Phys. B: At. Mol. Opt. Phys. 49 175204 Google Scholar
[43]	Smirnov Yu M 2017 Russ. J. Phys. Chem. B 11 873 Google Scholar
[44]	Huang Z K, Wen W Q, Wang S X, et al. 2020 Phys. Rev. A 102 062823 Google Scholar
[45]	Wang S X, Huang Z K, Wen W Q, et al. 2022 Phys. Rev. A 106 042808 Google Scholar
[46]	邵林, 黄忠魁, 汶伟强, 汪书兴, 黄厚科, 马万路, 刘畅, 汪寒冰, 陈冬阳, 刘鑫, 周晓鹏, 赵冬梅, 张少锋, 朱林繁, 马新文 2024 73 123402 Google Scholar Shao L, Huang Z K, Wen W Q, Wang S X, Huang H K, Ma W L, Liu C, Wang H B, Chen D Y, Liu X, Zhou X P, Zhao D M, Zhang S F, Zhu L F, Ma X W 2024 Acta Phys. Sin. 73 123402 Google Scholar
[47]	Liu X J, Zhu L F, Yuan Z S, Li W B, Cheng H D, Huang Y P, Zhong Z P, Xu K Z, Li J M 2003 Phys. Rev. Lett. 91 193203 Google Scholar
[48]	Du X J, Xu Y C, Wang L H, Li T J, Ma Z R, Wang S X, Zhu L F 2022 Phys. Rev. A 105 012812 Google Scholar
[49]	Wang D H, Wang S X, Nie Z W, Wang L H, Xu Y C, Du X J, Zhu L F 2022 Plasma Sources Sci. Technol. 31 045012 Google Scholar
[50]	Dörner R, Mergel V, Jagutzki O, Spielberger L, Ullrich J, Moshammer R, Schmidt-Böcking H 2000 Phys. Rep. 330 95 Google Scholar
[51]	Xia Z H, Ren B, Zhang R T, Wei L, Han J, Meng T, Wang J, Ma P, Zhang Y, Tu B, Xiao J, Yao K, Zou Y, Zhu X L, Guo D L, Ma X, Wei B 2022 Astrophysical J. 933 207 Google Scholar
[52]	Ren B, Ma P, Zhang Y, Wei L, Han J, Xia Z, Wang J, Meng T, Yu W, Zou Y, Yang C L, Wei B 2022 Phys. Rev. A 106 012805 Google Scholar
[53]	Uhlmann L J, Dall R G, Truscott A G, Hoogerland M D, Baldwin K G H, Buckman S J 2005 Phys. Rev. Lett. 94 173201 Google Scholar
[54]	Łukomski M, MacAskill J A, Seccombe D P, McGrath C, Sutton S, Teeuwen J, Kedzierski W, Reddish T J, McConkey J W, van Wijngaarden W A 2005 J. Phys. B: At. Mol. Opt. Phys. 38 3535 Google Scholar
[55]	Byron L J, Dall R G, Truscott A G 2010 Phys. Rev. A 81 013405 Google Scholar
[56]	Daw A, Gardner L D, Janzen P H, Kohl J L 2006 Phys. Rev. A 73 032709 Google Scholar
[57]	Knehr E, Kuzmin A, Doerner S, Wuensch S, Ilin K, Schmidt H, Siegel M 2020 Appl. Phys. Lett. 117 132602 Google Scholar
[58]	Heddle D W O, Samuel M J 1970 J. Phys. B: Atom. Mol. Phys. 3 1593 Google Scholar
[59]	Stewart Jr M D, Chilton J E, Boffard J B, Lin C C 2002 Phys. Rev. A 65 032704 Google Scholar
[60]	McCarthy I E, Weigold E 1988 Rep. Prog. Phys. 51 299 Google Scholar
[61]	McCarthy I E, Weigold E 1991 Rep. Prog. Phys. 54 789 Google Scholar
[62]	Fursa D V, Bray I 1995 Phys. Rev. A 52 1279 Google Scholar
[63]	Bray I, Fursa D V 1996 Phys. Rev. Lett. 76 2674 Google Scholar
[64]	Bartschat K, Zatsarinny O 2015 Phys. Scr. 90 054006 Google Scholar
[65]	Zhao G P, Liu L, Chang Z, Wang J G, Janev R K 2018 J. Phys. B: At. Mol. Opt. Phys. 51 085201 Google Scholar
[66]	Liu Y D, Jia C C, Ma M X, Gao X, Liu L, Wu Y, Chen X J, Wang J G 2024 Chin. Phys. B 33 083401 Google Scholar
[67]	杨威, 蔡晓红, 于得洋 2005 54 2128 Google Scholar Yang W, Cai X H, Yu D Y 2005 Acta Phys. Sin. 54 2128 Google Scholar
[68]	Whiteford A D, Badnell N R, Ballance C P, O’Mullane M G, Summers H P, Thomas A L 2001 J. Phys. B: At. Mol. Opt. Phys. 34 3179 Google Scholar
[69]	Fan Q P, Wang W H, Hu F, Cao L F, Zhang Q Q, Liu Y W, Jiang G 2014 Chin. Phys. B 23 113401 Google Scholar
[70]	Chen Y Q, Jiang X W, Yao L F, Jiang W, Liu H N, Zhang Y 2023 Plasma Sources Sci. Technol. 32 045017 Google Scholar
[71]	Bar-Shalom A, Klapisch M, Oreg J 1988 Phys. Rev. A 38 1773 Google Scholar
[72]	Meng F C, Chen C Y, Wang Y S, Zou Y M 2007 Chinese Phys. Lett. 24 3404 Google Scholar
[73]	Gu M F 2008 Can. J. Phys. 86 675 Google Scholar
[74]	Podpaly Y, Clementson J, Beiersdorfer P, Williamson J, Brown G V, Gu M F 2009 Phys. Rev. A 80 052504 Google Scholar
[75]	Ma Y L, Liu L, Xie L Y, Wu Y, Zhang D H, Dong C Z, Qu Y Z, Wang J G 2022 Chin. Phys. B 31 043401 Google Scholar
[76]	Zhang C Y, Wu S J, Wang K, Si R, Yao K, Huang Z K, Wen W Q, Ma X W, Chen C Y, Badnell N R 2023 Phys. Rev. A 108 022801 Google Scholar
[77]	杜贵锋2011 硕士学位论文(兰州: 西北师范大学) Du G F 2011 M. S. Thesis (Lanzhou: Northwest Normal University
[78]	杨宁选2009 硕士学位论文(兰州: 西北师范大学) Yang N X 2009 M. S. Thesis (Lanzhou: Northwest Normal University
[79]	Macek J, Jaecks D H 1971 Phys. Rev. A 4 2288 Google Scholar
[80]	Bartschat K, Blum K, Hanne G F, Kessler J 1981 J. Phys. B: Atom. Mol. Phys. 14 3761 Google Scholar
[81]	Bartschat K, Scott N S, Blum K, Burke P G 1984 J. Phys. B: Atom. Mol. Phys. 17 269 Google Scholar
[82]	Khalid S M, Kleinpoppen H 1984 J. Phys. B: Atom. Mol. Phys. 17 243 Google Scholar
[83]	Raeker A, Blum K, Bartschat K 1993 J. Phys. B: Atom. Mol. Phys. 26 1491 Google Scholar
[84]	Kłosowski Ł, Piwiski M, Dziczek D, Wiśniewska K, Chwirot S 2007 Meas. Sci. Technol. 18 3801 Google Scholar
[85]	Kłosowski Ł, Piwiski M, Dziczek D, Pleskacz K, Chwirot S 2009 Phys. Rev. A 80 062709 Google Scholar
[86]	Hussey M, Murray A, MacGillivray W, King G C 2007 Phys. Rev. Lett. 99 133202 Google Scholar
[87]	Percival A K, Jhumka S, Hussey M, Murray A J 2011 J. Phys. B: At. Mol. Opt. Phys. 44 105203 Google Scholar
[88]	Polasik M 1989 Phys. Rev. A 39 616 Google Scholar
[89]	Wu Z W, Tian Z Q, Dong C Z, Surzhykov A, Fritzsche S 2023 New J. Phys. 25 093039 Google Scholar
[90]	Ding X B, Koike F, Murakami I, Kato D, Sakaue H A, Dong C Z, Nakamura N 2012 J. Phys. B: At. Mol. Opt. Phys. 45 035003 Google Scholar
[91]	Wang K, Li S, Jönsson P, Fu N, Dang W, Guo X L, Chen C Y, Yan J, Chen Z B, Si R 2017 J. Quant. Spectrosc. Radiat. Transf. 187 375 Google Scholar
[92]	颉录有2008 博士学位论文(兰州: 西北师范大学) Xie L Y 2008 Ph. D. Dissertation (Lanzhou: Northwest Normal University
[93]	武中文2012 硕士学位论文(兰州: 西北师范大学) Wu Z W 2012 M. S. Thesis 2012 (Lanzhou: Northwest Normal University
[94]	Parpia F A, Fischer C F, Grant I P 1996 Compt. Phys. Commun. 94 249 Google Scholar
[95]	Jönsson P, Gaigalas G, Bieroń J, Fischer C F, Grant I P 2013 Compt. Phys. Commun. 184 2197 Google Scholar
[96]	Fischer C F, Gaigalas G, Jönsson P, Bieroń J 2019 Compt. Phys. Commun. 237 184 Google Scholar
[97]	Fritzsche S, Fischer C F, Dong C Z 2000 Compt. Phys. Commun. 124 340 Google Scholar
[98]	Fritzsche S 2012 Compt. Phys. Commun. 183 1525 Google Scholar
[99]	Carse G D, Walker D W 1973 J. Phys. B: Atom. Mol. Phys. 6 2529 Google Scholar
[100]	Walker D W 1974 J. Phys. B: Atom. Mol. Phys. 7 97 Google Scholar
[101]	Dong C Z, Xie L Y, Zhou X X, Ma X W, Fritzsche S 2003 Hyperfine Interact. 146 161 Google Scholar
[102]	Li J G, Dong C Z, Yu Y J, Ding X B, Fritzsche S, Fricke B 2007 Sci. China Phys. Mech. 50 707 Google Scholar
[103]	Xie L Y, Wang J G, Janev R K, Qu Y Z, Dong C Z 2012 Eur. Phys. J. D 66 125 Google Scholar
[104]	Grant I P, McKenzie B J, Norrington P H, Mayers D F, Pyper N C 1980 Compt. Phys. Commun. 21 207 Google Scholar
[105]	Dyall K G, Grant I P, Johnson C T, Parpia F A, Plummer E P 1989 Compt. Phys. Commun. 55 425 Google Scholar
[106]	Jiang J, Dong C Z, Xie L Y, Wang J G, Yan J, Fritzsche S 2007 Chin. Phys. Lett. 24 691 Google Scholar
[107]	Li B W, Dong C Z, Jiang J, Wang J G 2010 Eur. Phys. J. D 59 201 Google Scholar
[108]	Jiang J, Dong C Z, Xie L Y, Wang J G 2008 Phys. Rev. A 78 022709 Google Scholar
[109]	马小云2013 硕士学位论文(兰州: 西北师范大学) Ma X Y 2013 M. S. Thesis (Lanzhou: Northwest Normal University
[110]	Grant I P 1970 Adv. Phys. 19 747 Google Scholar
[111]	Rodrigues G C, Ourdane M A, Bieroń J, Indelicato P, Lindroth E. 2000 Phys. Rev. A 63 012510 Google Scholar
[112]	Dong C Z, Fritzsche S 2005 Phys. Rev. A 72 012507 Google Scholar
[113]	Fischer C F, Godefroid M, Brage T, Jönsson P, Gaigalas G 2016 J. Phys. B: At. Mol. Opt. Phys. 49 182004 Google Scholar
[114]	Andersen N, Broad J T, Campbell E E B, Gallagher J W, Hertel I V 1997 Phys. Rep. 278 107 Google Scholar
[115]	Jung R O, Boffard J B, Anderson L W, Lin C C 2005 Phys. Rev. A 72 022723 Google Scholar
[116]	Jiang J, Dong C Z, Xie L Y, Zhou X X, Wang J G 2008 J. Phys. B: At. Mol. Opt. Phys. 41 245204 Google Scholar
[117]	Goeke J, Hanne G F, Kessler J 1989 J. Phys. B: Atom. Mol. Phys. 22 1075 Google Scholar
[118]	Beiersdorfer P, Osterheld A L, Chen M H, Henderson J R, Knapp D A, Levine M A, Marrs R E, Reed K J, Schneider M B, Vogel D A 1990 Phys. Rev. Lett. 65 1995 Google Scholar
[119]	Takács E, Meyer E S, Gillaspy J D, Roberts J R, Chantler C T, Hudson L T, Deslattes R D, Brown C M, Laming J M, Dubau J, Inal M K 1996 Phys. Rev. A 54 1342 Google Scholar
[120]	Dyl D, Dziczek D, Piwinski M, Gradziel M, Srivastava R, Dygdala R S, Chwirot S 1999 J. Phys. B: Atom. Mol. Phys. 32 837 Google Scholar
[121]	Srivastava R, Blumy K, McEachranz R P, Stauffer A D 1996 J. Phys. B: Atom. Mol. Phys. 29 3513 Google Scholar
[122]	Sohn M, Hanne G F 1992 J. Phys. B: Atom. Mol. Phys. 25 4627 Google Scholar
[123]	李博文, 蒋军, 董晨钟, 王建国, 丁晓彬 2009 58 5274 Google Scholar Li B W, Jiang J, Dong C Z, Wang J G, Ding X B 2009 Acta Phys. Sin. 58 5274 Google Scholar
[124]	Whitten B L, Lane N F, Weisheit J C 1984 Phys. Rev. A 29 945 Google Scholar
[125]	Murillo M S, Weisheit J C 1998 Phys. Rep. 302 1 Google Scholar
[126]	Hu F 2021 Radiat. Phys. Chem. 180 109293 Google Scholar
[127]	Pindzola M S, Loch S D, Colgan J, Fontes C J 2008 Phys. Rev. A 77 062707 Google Scholar
[128]	Jiang J, Dong C Z, Xie L Y 2014 Chin. Phys. Lett. 31 023401 Google Scholar

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