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With the development of the intense light source, such as free electron lasers, the experiments on the nonlinear process in atomic photo absorption in the XUV and X-ray region became more and more feasible. As one of the simplest possible nonlinear processes, the sequential two-photon double ionization, in which the first photon produces an ion which is subsequently ionized by the second photon, attracts increasing attention of theorists and experimentalists. Study on the angular distributions and angular correlations of the photoelectrons in the sequential two-photon double ionization process are especially attractive, which provides valuable information about the electronic structure of atom or molecule systems and allows the obtaining of additional information about mechanism and pathway of the two-photon double ionization. In this paper, the expression for the photoelectron angular distribution in a sequential two-photon process is given based on the multi-configuration Dirac-Fock method and the density matrix theory. And then, the relativistic calculation program for photoelectron angular distribution is further developed with the help of the program packages GRASP2K and RATIP which are based on the multi-configuration Dirac-Fock method. By using this code, the sequential two-photon double ionization of the 3p shell in atomic argon is studied theoretically. The cross section, magnetic cross section, alignment of residual ions and the asymmetry parameter of the photoelectron angular distribution, each as a function of photon energy, for the first and the second step of sequential two-photon double ionization of argon are presented. The calculations predict that the alignment has a maximum value and the asymmetry parameter has a minimum value in the region of the cooper minimum. The angular distribution of the first step ionization for Ar atom and the second step ionization for Ar+ ion are given at 33.94 eV and 55.34 eV photon energy, respectively. In addition, the difference in property between the angular distributions of the first photoelectron in sequential two-photon double ionization and in conventional one-photon single ionization is discussed. The present calculated results are compared with other available results, showing that they are in good agreement with each other. The results of this paper will be helpful in studying nonlinear processes in the XUV range.
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Keywords:
- sequential two-photon double ionization /
- angular distribution of photoelectron /
- argon atom
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图 1 Ar原子序列双光双电离截面
Figure 1. The cross section of the sequential two-photon double ionization in argon atom.
图 2 Ar原子3p3/2光电离磁截面
Figure 2. The magnetic cross section of the 3p3/2 photoionization in argon atom.
图 3 Ar原子3p3/2光电离后剩余离子取向参数
Figure 3. The alignment of the residual ions of 3p3/2 photoioni-zation in argon atom.
图 4 Ar原子3p壳层序列双光双电离中第一个(a)和第二个(b)光电子的角各向异性参数
Figure 4. The asymmetry parameter of the first (a) and second (b) photoelectron angular distribution in sequential two-photon double ionization of the Ar 3p shell.
图 5 Ar原子3p壳层序列双光双电离第一个(a), (b)和第二个(c), (d)光电子角各向异性参数
Figure 5. The asymmetry parameter of the angular distribution of the first (a), (b) and second (c), (d) photoelectrons emitted in sequential two-photon double ionization of the Ar 3p shell.
图 6 Ar原子3p壳层序列双光双电离光电离角分布
Figure 6. Photoelectron angular distributions for the sequential two-photon double ionization of Ar 3p shell.
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[1] Bachau H, Lambropoulos P 1991 Phys. Rev. A 44 R9(R)
[2] Laulan S, Bachau H 2003 Phys. Rev. A 68 013409
Google Scholar
[3] Böhme D K 2011 Phys. Chem. Chem. Phys. 13 18253
Google Scholar
[4] Thissen R, Witasse O, Dutuit O, Wedlund C S, Gronoff G, Lilensten J 2011 Phys. Chem. Chem. Phys. 13 18264
Google Scholar
[5] Gillaspy J D, Pomeroy J M, Perrella A C, Grube H 2007 J. Phys. Conf. Ser. 58 451
Google Scholar
[6] McNeil B W J, Thompson N R 2010 Nat. Photon. 4 814
Google Scholar
[7] Wabnitz H, Bittner L, de Castro A R B, et al. 2002 Nature 420 482
Google Scholar
[8] Young L, Kanter E P, Krässig B, et al. 2010 Nature 466 56
Google Scholar
[9] 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 p34
[10] Kurka M, Rudenko A, Foucar, et al. 2009 J. Phys. B: At. Mol. Opt. Phys. 42 141002
Google Scholar
[11] Braune M, Hartmann G, Ilchen M, et al. 2016 J. Mod. Opt. 63 324
Google Scholar
[12] Augustin S, Schulz M, Schmid G, et al. 2018 Phys. Rev. A 98 033408
Google Scholar
[13] Ilchen M, Hartmann G, Gryzlova E V, et al. 2018 Nat. Commun. 9 4659
Google Scholar
[14] Carpeggiani P A, Gryzlova E V, Reduzzi M, et al. 2019 Nat. Phys. 15 170
Google Scholar
[15] Fritzsche S, Grum-Grzhimailo A N, Gryzlova E V, Kabachnik N M 2008 J. Phys. B: At. Mol. Opt. Phys. 41 165601
Google Scholar
[16] Gryzlova E V, Grum-GrzhimailoA N, Kuzmina E I, Strakhova S I 2014 J. Phys. B: At. Mol. Opt. Phys. 47 195601
Google Scholar
[17] Grum-Grzhimailo A N, Gryzlova E V 2014 Phys. Rev. A 89 043424
Google Scholar
[18] Grum-Grzhimailo A N, Gryzlova E V, Fritzsche S, Kabachnik N M 2016 J. Mod. Opt. 63 334
Google Scholar
[19] Gryzlova E V, Grum-Grzhimailo A N, Staroselskaya E I, Strakhova S I 2015 J. Electron Spectrosc. Relat. Phenom. 204 277
Google Scholar
[20] Ma K, Xie L Y, Zhang D H, Dong C Z 2015 Chin. Phys. B 24 073402
Google Scholar
[21] Ma K, Chen Z B, Xie L Y, Dong C Z 2018 J. Phys. B: At. Mol. Opt. Phys. 51 045203
Google Scholar
[22] Ma K, Chen Z B, Xie L Y, Dong C Z, Qu Y Z 2017 J. Phys. B: At. Mol. Opt. Phys. 50 225202
Google Scholar
[23] Ma K, Chen Z B, Xie L Y, Ding X B, Zhang D H, Dong C Z 2018 J. Electron Spectrosc. Relat. Phenom. 228 1
Google Scholar
[24] Blum K 1996 Density Matrix Theory and Applications (2nd Ed.) (New York: Plenum) pp35–60
[25] Balashov V V, Grum-Grzhimailo A N, Kabachnik N M 2000 Polarization and Correlation Phenomena in Atomic Collisions (New York: Kluwer Academic/Plenum) pp76–97
[26] Jönsson P, Gaigalas G, Bieroń J, Fischer C F, Grant I P 2013 Comput. Phys. Commun. 184 2197
Google Scholar
[27] Fritzsche S 2012 Comput. Phys. Commun. 183 1525
Google Scholar
[28] Langer B 1992 ZurEnergieabhängigkeit von Photoelektronen- satelliten (Studies of Vacuum Ultraviolet and X-ray Processes (Vol. 2) (New York: AMS Press) p145
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