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Owing to the development of XUV and X ray of the free-electron lasers, the photoelectron angular distribution in the sequential two-photon double ionization has received increasing attention of theorists and experimentalists, because it provides the valuable information about the electronic structure of atom or molecule systems and allows the obtaining of additional information about mechanisms and pathways of the two-photon double ionization. In this paper, the expression of the sequential two-photon double ionization process of the photoelectron angular distributions, including the non-dipole effects, is obtained based on the multi-configuration Dirac-Fock method and the density matrix theory, and the corresponding calculation code is also developed. Based on the code, the sequential two-photon double ionization process of the 3p and 2p shells of Ar atom and K+ ion are studied, in which, the dipole and the non-dipole parameters of photoelectron angular distribution are investigated systematically. It is found that the angular distributions of the first- and second-step electrons in sequential two-photon double ionization are similar and the two photoionization processes affect each other. Near the ionization threshold, the photoionization cross-sections and anisotropy parameters for the 3p shell and the 2p shell show a large difference. While away from the threshold, the cross-section and angular anisotropy parameters of the 3p and 2p shells show similar behaviors. At the position of Cooper minimum of the photoionization cross section, the contribution of the electric dipole is suppressed, and the non-dipole effect is obvious. The non-dipole effect leads to a forward-backward asymmetric distribution of photoelectrons relative to the direction of incident light. The results of this paper will be helpful in studying the nonlinear processes of photon and matter interaction in the XUV range.
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Keywords:
- sequential two-photon double ionization /
- angular distribution of photoelectron /
- non-dipole effect
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图 1 Ar原子和K+离子np (n = 2, 3)壳层第一次和第二次光电离截面(1 b = 10–28 m2)
Figure 1. The first and second photoionization cross section of the np (n = 2, 3) shell in Ar atom and K+ ion.
图 2 Ar原子和K+离子np (n = 2, 3)壳层序列双光双电离中第1个光电子的电偶极角各向异性参数
$ \beta _2^{(1)} $ Figure 2. Asymmetry parameter of electric dipole
$ \beta _2^{(1)} $ for the first photoelectron angular distribution in 2PDI of the Ar and K+ np (n = 2, 3) shell as a function of the photon energy.
图 3 Ar原子和K+离子np (n = 2, 3)壳层序列双光双电离中第1个光电子的电偶极角各向异性参数
$ \beta _4^{(1)} $ Figure 3. Asymmetry parameter of electric dipole
$ \beta _4^{(1)} $ for the first photoelectron angular distribution in 2PDI of the Ar and K+ np (n = 2, 3) shell as a function of the photon energy.
图 4 Ar原子和K+离子np (n = 2, 3)壳层2PDI中第1个光电子的一级非偶极各向异性参数
$ {\delta ^{(1)}} $ Figure 4. Asymmetry parameter of non-dipole
$ {\delta ^{(1)}} $ for the first photoelectron angular distribution in 2PDI of the Ar and K+ np (n = 2, 3) shell as a function of the photon energy.
图 5 Ar原子和K+离子np (n = 2, 3)壳层2PDI中第1个光电子的一级非偶极各向异性参数
$ \gamma _2^{(1)} $ Figure 5. Asymmetry parameter of non-dipole
$ \gamma _2^{(1)} $ for the first photoelectron angular distribution in 2PDI of the Ar and K+ np (n = 2, 3) shell as a function of the photon energy.
图 6 Ar原子和K+离子np (n = 2, 3)壳层2PDI中第1个光电子的一级非偶极各向异性参数
$ \gamma _4^{(1)} $ Figure 6. Asymmetry parameter of non-dipole
$ \gamma _4^{(1)} $ for the first photoelectron angular distribution in 2PDI of the Ar and K+ np (n = 2, 3) shell as a function of the photon energy.
图 7 Ar原子3p3/2壳层2PDI过程第1个光电子角分布
Figure 7. The first photoelectron angular distribution in 2PDI of Ar atom 3p3/2 shell.
图 8 K+离子3p3/2壳层2PDI过程第1个光电子角分布
Figure 8. The first photoelectron angular distribution in 2PDI of the K+ ion 3p3/2 shell.
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[1] Böhme D K 2011 Phys. Chem. Chem. Phys. 13 18253
Google Scholar
[2] Thissen R, Witasse O, Dutuit O, et al. 2011 Phys. Chem. Chem. Phys. 13 18264
Google Scholar
[3] Gillaspy J D, Pomeroy J M, Perrella A C, et al. 2007 J. Phys. Conf. Ser. 58 451
Google Scholar
[4] Ott C, Kaldun A, Raith P, et al. 2013 Science 340 716
Google Scholar
[5] Braune M, Reinköster A, Viefhaus J, et al. 2007 XXV Int. Conf. on Photonic, Electronic and Atomic Collisions (ICPEAC) Freiburg, Germany, July 25–31, 2007 Fr034
[6] Moshammer R, Jiang Y H, Foucar L, et al. 2007 Phys. Rev. Lett. 98 203001
Google Scholar
[7] Rudenko A, Foucar L, Kurka M, et al. 2008 Phys. Rev. Lett. 101 073003
Google Scholar
[8] Kurka M, Rudenko A, Foucar L 2009 J. Phys. B 42 141002
Google Scholar
[9] Augustin S, Schulz M, Schmid G, et al. 2018 Phys. Rev. A 98 033408
Google Scholar
[10] Braune M, Hartmann G, Ilchen M, et al. 2015 J. Mod. Opt. 63 1047422
Google Scholar
[11] Fukuzawa H, Gryzlova E V, Motomura K, et al. 2010 J. Phys. B 43 111001
Google Scholar
[12] Gryzlova E V, Ma Ri, Fukuzawa H, et al. 2011 Phys. Rev. A 84 063405
Google Scholar
[13] Ilchen M G, Hartmann G, Gryzlova E V 2018 Nat. Commun. 9 4659
Google Scholar
[14] Carpeggiani P A, Gryzlova E V, Reduzzi M 2019 Nat. Phys. 15 170
Google Scholar
[15] Kheifets A S 2007 J. Phys. B 40 F313
Google Scholar
[16] Fritzsche S, Grum-Grzhimailo A N, Gryzlova E V, Kabachnik N M 2008 J. Phys. B 41 165601
Google Scholar
[17] Gryzlova E V, Grum-Grzhimailo A N, Fritzsche S, Kabachnik N M 2010 J. Phys. B 43 225602
Google Scholar
[18] Krӓssig B, Jung M, Gemmell D S, Kanter E P, LeBrun T, Southworth S H, Young L 1995 Phys. Rev. Lett. 75 4736
Google Scholar
[19] Jung M, Krӓssig B, Gemmell D S, Kanter E P, LeBrun T, Southworth S H, Young L 1996 Phys. Rev. A 54 2127
Google Scholar
[20] Hemmers O, Fisher G, Glans P, Hansen D L, Wang H, Whitfield S B, Wehlitz R, Levin J C, Sellin I A, Perera R C C, Dias E W B, Chakraborty H S, Deshmukh P C, Manson S T, Lindle D W 1997 J. Phys. B 30 L727
Google Scholar
[21] Holste K, Borovik A A, Buhr T, Ricz S, Kövér Á, Bernhardt D, Schippers S, Varga D, Müller A 2014 J. Phys. Confer. Ser. 488 022041
Google Scholar
[22] 马堃, 颉录有, 张登红, 蒋军, 董晨钟 2016 65 083201
Google Scholar
Ma K, Xie L Y, Zhang D H, Jiang J, Dong C Z 2016 Acta Phys. Sin. 65 083201
Google Scholar
[23] Gryzlova E V, Grum-Grzhimailo A N, Staroselskaya E I 2015 J. Electron. Spectrosc. Relat. Phenom. 15 277
Google Scholar
[24] Grum-Grzhimailo A N, Gryzlova E V, Fritzsche S 2016 J. Mod. Opt. 63 334
Google Scholar
[25] 马堃, 颉录有, 董晨钟 2020 69 053201
Google Scholar
Ma K, Xie L Y, Dong C Z 2020 Acta Phys. Sin. 69 053201
Google Scholar
[26] Wang M X, Chen S G, Liang H, Peng L Y 2020 Chin. Phys. B 29 013302
Google Scholar
[27] Kiselev M D, Carpeggiani P A, Gryzlova E V, et al. 2020 J. Phys. B 53 244006
Google Scholar
[28] Varvarezos L, Düsterer S, Kiselev M D, et al. 2021 Phys. Rev. A 103 022832
Google Scholar
[29] Fritzsche S 2012 Comput. Phys. Commun. 183 1525
Google Scholar
[30] Jönsson P, Gaigalas G, Bieroń J, et al. 2013 Comput. Phys. Commun. 184 2197
Google Scholar
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