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Angular distribution of the characteristic line \(1s2p\,^{3}P_{2} \rightarrow 1s^{2}\,^{1}S_{0}\) of thallium ions: hyperfine-induced multipole interference

  • Regular Article – Atomic and Molecular Collisions
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Abstract

Within the framework of the density matrix theory, the angular distribution of the characteristic magnetic-quadrupole line \(1s2p\,^{3}P_{2} \rightarrow 1s^{2}\,^{1}S_{0}\) following electron-impact excitation of heliumlike thallium ions with nuclear spin \(I \!=\! 1/2\) has been investigated by using the multiconfigurational Dirac–Hartree–Fock method and the relativistic distorted-wave theory. Special attention has been paid to exploring the question of how the angular distribution of the characteristic line is affected by the multipole interference between the dominant magnetic-quadrupole and hyperfine-induced electric-dipole decay channels of its hyperfine-structure-resolved component \(1s2p\,^{3}P_{2}, F\!=\!3/2 \rightarrow 1\,s^{2}\,^{1}S_{0}, F_{0}\!=\!1/2\). To this aim, detailed calculations are performed for spin-1/2 \(^{187}_{81}\)Tl\(^{79+}\) and \(^{207}_{81}\)Tl\(^{79+}\) ions with (relatively) large nuclear magnetic dipole moment. It is found that the hyperfine-induced multipole interference contributes to making the angular distribution of the magnetic-quadrupole line \(1s2p\,^{3}P_{2} \rightarrow 1s^{2}\,^{1}S_{0}\) less anisotropic for all the impact electron energies considered, although at any given impact energy its angular emission pattern remains always qualitatively consistent with each other for both the two cases without and with the interference contribution included. Moreover, for the case with the interference considered the angular distribution of the magnetic-quadrupole line is found to be sensitive to the nuclear magnetic dipole moment of the spin-1/2 ions, especially at low impact electron energies.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited [Authors’ comment: The authors confirm that all scientifically relevant data have been presented in the paper. Additional raw data are available from the corresponding author on reasonable request.].

References

  1. S. Fritzsche, A. Surzhykov, Th. Stöhlker, Dominance of the Breit interaction in the X-ray emission of highly charged ions following dielectronic recombination. Phys. Rev. Lett. 103, 113001 (2009)

    Article  ADS  Google Scholar 

  2. N. Nakamura, Breit interaction effect on dielectronic recombination of heavy ions. J. Phys. B At. Mol. Opt. Phys. 49, 212001 (2016)

    Article  ADS  Google Scholar 

  3. Z.W. Wu, M.M. Zhao, C. Ren, C.Z. Dong, J. Jiang, Effect of the Breit interaction on inner-shell electron-impact excitation and subsequent radiative decay of highly charged berylliumlike ions. Phys. Rev. A 101, 022701 (2020)

    Article  ADS  Google Scholar 

  4. M.H. Chen, J.H. Scofield, Relativistic effects on angular distribution and polarization of dielectronic satellite lines of hydrogenlike ions. Phys. Rev. A 52, 2057 (1995)

    Article  ADS  Google Scholar 

  5. A. Surzhykov, S. Fritzsche, T. Stöhlker, S. Tashenov, Application of radiative electron capture for the diagnostics of spin-polarized ion beams at storage rings. Phys. Rev. Lett. 94, 203202 (2005)

    Article  ADS  Google Scholar 

  6. S. Tashenov, D. Banaś, H. Beyer, C. Brandau, S. Fritzsche, A. Gumberidze, S. Hagmann, P.-M. Hillenbrand, H. Jörg, I. Kojouharov, C. Kozhuharov, M. Lestinsky, Y.A. Litvinov, A.V. Maiorova, H. Schaffner, V.M. Shabaev, U. Spillmann, T. Stöhlker, A. Surzhykov, S. Trotsenko, Observation of coherence in the time-reversed relativistic photoelectric effect. Phys. Rev. Lett. 113, 113001 (2014)

    Article  ADS  Google Scholar 

  7. Z.W. Wu, C.Z. Dong, J. Jiang, Degrees of polarization of the two strongest \(5f{\rightarrow }3d\) lines following electron-impact excitation and dielectronic recombination processes of Cu-like to Se-like gold ions. Phys. Rev. A 86, 022712 (2012)

    Article  ADS  Google Scholar 

  8. A. Surzhykov, S. Fritzsche, A. Gumberidze, T. Stöhlker, Lyman-\({{{\alpha }}}_{1}\) decay in hydrogenlike ions: interference between the \({E}1\) and \({M}2\) transition amplitudes. Phys. Rev. Lett. 88, 153001 (2002)

    Article  ADS  Google Scholar 

  9. Z.W. Wu, N.M. Kabachnik, A. Surzhykov, C.Z. Dong, S. Fritzsche, Determination of small level splittings in highly charged ions via angle-resolved measurements of characteristic X rays. Phys. Rev. A 90, 052515 (2014)

    Article  ADS  Google Scholar 

  10. Z.W. Wu, A.V. Volotka, A. Surzhykov, C.Z. Dong, S. Fritzsche, Level sequence and splitting identification of closely spaced energy levels by angle-resolved analysis of fluorescence light. Phys. Rev. A 93, 063413 (2016)

    Article  ADS  Google Scholar 

  11. Z.W. Wu, A.V. Volotka, A. Surzhykov, S. Fritzsche, Angle-resolved X-ray spectroscopic scheme to determine overlapping hyperfine splittings in highly charged heliumlike ions. Phys. Rev. A 96, 012503 (2017)

    Article  ADS  Google Scholar 

  12. J.R. Henderson, P. Beiersdorfer, C.L. Bennett, S. Chantrenne, D.A. Knapp, R.E. Marrs, M.B. Schneider, K.L. Wong, G.A. Doschek, J.F. Seely, C.M. Brown, R.E. LaVilla, J. Dubau, M.A. Levine, Polarization of X-ray emission lines from heliumlike scandium as a probe of the hyperfine interaction. Phys. Rev. Lett. 65, 705 (1990)

    Article  ADS  Google Scholar 

  13. M.K. Inal, D.H. Sampson, H.L. Zhang, J. Dubau, Effects of hyperfine interaction on the circular polarization of the Sc XX X-ray lines. Phys. Scr. 55, 170 (1997)

    Article  ADS  Google Scholar 

  14. R. Bensaid, M.K. Inal, J. Dubau, Polarization of line radiation due to mixed E1–M2 transitions. Application to hyperfine components of the heliumlike \(1s2p\,^{3}P_{2} \rightarrow 1s^{2}\,^{1}S_{0}\) line. J. Phys. B At. Mol. Opt. Phys. 39, 4131 (2006)

    Article  ADS  Google Scholar 

  15. R. Bensaid, A.K. Ferouani, M. Sahlaoui, Hyperfine-induced depolarization effect in the X-ray line emission \(1s2p\,^{3}P_{2} \rightarrow 1s^{2}\,^{1}S_{0}\) of He-like ions. Eur. Phys. J. D 75, 177 (2021)

    Article  ADS  Google Scholar 

  16. Z.W. Wu, A. Surzhykov, S. Fritzsche, Hyperfine-induced modifications to the angular distribution of the \(K\alpha _{1}\) X-ray emission. Phys. Rev. A 89, 022513 (2014)

    Article  ADS  Google Scholar 

  17. Z.W. Wu, Z.Q. Tian, J. Jiang, C.Z. Dong, S. Fritzsche, Hyperfine-induced effects on the \(K{{\alpha }}_{1}\) angular distribution following electron-impact excitation of heliumlike spin-\(1/2\)\({\rm Tl }^{79+}\) ions. Phys. Rev. A 104, 062814 (2021)

    Article  ADS  Google Scholar 

  18. A. Surzhykov, Yu. Litvinov, Th. Stöhlker, S. Fritzsche, Hyperfine-induced effects on the linear polarization of \(K\alpha _{1}\) emission from heliumlike ions. Phys. Rev. A 87, 052507 (2013)

    Article  ADS  Google Scholar 

  19. Z.W. Wu, Z.Q. Tian, J. Jiang, C.Z. Dong, S. Fritzsche, Hyperfine-induced effects on angular emission of the magnetic-quadrupole line \(1s2{p}_{3/2}\)\(^{3}P_{2}{\rightarrow }1{s}^{2}\)\(^{1}S_{0}\) following electron-impact excitation of \({\rm Tl }^{79+}\) ions. Phys. Rev. A 102, 042813 (2020)

    Article  ADS  Google Scholar 

  20. I.P. Grant, Relativistic Quantum Theory of Atoms and Molecules: Theory and Computation (Springer, New York, 2007)

    Book  Google Scholar 

  21. H.L. Zhang, D.H. Sampson, R.E.H. Clark, Relativistic cross sections for excitation of highly charged ions to specific magnetic sublevels by an electron beam. Phys. Rev. A 41, 198 (1990)

    Article  ADS  Google Scholar 

  22. K. Blum, Density Matrix Theory and Applications, 3rd edn. (Springer, Berlin, 2012)

    Book  MATH  Google Scholar 

  23. V.V. Balashov, A.N. Grum-Grzhimailo, N.M. Kabachnik, Polarization and Correlation Phenomena in Atomic Collisions (Kluwer Academic, New York, 2000)

    Book  Google Scholar 

  24. M.K. Inal, M. Benmouna, Comment on Hyperfine-induced modifications to the angular distribution of the \(K\alpha _{1}\) X-ray emission. Phys. Rev. A 91, 056501 (2015)

    Article  ADS  Google Scholar 

  25. A. Surzhykov, U.D. Jentschura, T. Stöhlker, S. Fritzsche, \(K\alpha _{1}\) radiation from heavy, heliumlike ions produced in relativistic collisions. Phys. Rev. A 74, 052710 (2006)

    Article  ADS  Google Scholar 

  26. F.A. Parpia, C.F. Fischer, I.P. Grant, GRASP92: a package for large-scale relativistic atomic structure calculations. Comput. Phys. Commun. 94, 249 (1996)

    Article  MATH  ADS  Google Scholar 

  27. J. Jiang, C.-Z. Dong, L.-Y. Xie, J.-G. Wang, J. Yan, S. Fritzsche, Relativistic distorted-wave calculations of electron impact excitation cross sections of Be-Like C\(^{2+}\) ions. Chin. Phys. Lett. 24, 691 (2007)

    Article  ADS  Google Scholar 

  28. S. Fritzsche, A fresh computational approach to atomic structures, processes and cascades. Comput. Phys. Commun. 240, 1 (2019)

    Article  MATH  ADS  Google Scholar 

  29. N.J. Stone, Table of nuclear magnetic dipole and electric quadrupole moments. At. Data Nucl. Data Tables 90, 75 (2005)

    Article  ADS  Google Scholar 

  30. B. Yang, D. Yu, C. Shao, X. Cai, Z. Wu, L. Xie, K.N. Lyashchenko, Y.S. Kozhedub, K. Ma, Y. Xue, W. Wang, M. Zhang, J. Liu, R. Lu, Z. Song, Y. Wu, F. Ruan, Y. Zhang, C. Dong, Z. Yang, State-selective nonradiative electron capture in collisions of 95–197\({{-}}{{\rm MeV/u}}{{\rm Xe}}^{54+}\) with Kr and Xe. Phys. Rev. A 104, 032815 (2021)

    Article  ADS  Google Scholar 

  31. S. Kraft-Bermuth, V. Andrianov, A. Bleile, A. Echler, P. Egelhof, P. Grabitz, S. Ilieva, O. Kiselev, C. Kilbourne, D. McCammon, J.P. Meier, P. Scholz, Precise determination of the 1s Lamb shift in hydrogen-like lead and gold using microcalorimeters. J. Phys. B At. Mol. Opt. Phys. 50, 055603 (2017)

    Article  ADS  Google Scholar 

  32. C. Pies, S. Schäfer, S. Heuser, S. Kempf, A. Pabinger, J.-P. Porst, P. Ranitsch, N. Foerster, D. Hengstler, A. Kampkötter, T. Wolf, L. Gastaldo, A. Fleischmann, C. Enss, maXs: Microcalorimeter arrays for high-resolution X-ray spectroscopy at GSI/FAIR. J. Low Temp. Phys. 167, 269 (2012)

    Article  ADS  Google Scholar 

  33. G. Weber, H. Bräuning, A. Surzhykov, C. Brandau, S. Fritzsche, S. Geyer, S. Hagmann, S. Hess, C. Kozhuharov, R. Märtin, N. Petridis, R. Reuschl, U. Spillmann, S. Trotsenko, D.F.A. Winters, Th. Stöhlker, Direct determination of the magnetic quadrupole contribution to the Lyman-\({{\alpha }}_{1}\) transition in a hydrogenlike ion. Phys. Rev. Lett. 105, 243002 (2010)

    Article  ADS  Google Scholar 

  34. Z. Hu, X. Han, Y. Li, D. Kato, X. Tong, N. Nakamura, Experimental demonstration of the Breit interaction which dominates the angular distribution of X-ray emission in dielectronic recombination. Phys. Rev. Lett. 108, 073002 (2012)

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported financially by the National Natural Science Foundation of China under Grants Nos. 12174315 and 11804280, the Chinese Scholarship Council under Grant No. 202008620004, the Key Program of the Research Ability Promotion Project for Young Scholars of the Northwest Normal University (China) under Grant No. NWNU-LKQN2019-5, the Longyuan Youth Innovation and Entrepreneurship Talent Project of Gansu Province under Grant No. 2021LQGR64, and the Youth Science and Technology Talent Promotion Project of Gansu Province under Grant No. GXH2020626-09.

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Authors and Affiliations

  1. Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province, College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Z. W. Wu & Z. Q. Tian

  2. Helmholtz-Institut Jena, Fröbelstieg 3, 07743, Jena, Germany

    Z. W. Wu & S. Fritzsche

  3. GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1, 64291, Darmstadt, Germany

    Z. W. Wu & S. Fritzsche

  4. Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743, Jena, Germany

    S. Fritzsche

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  1. Z. W. Wu
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Contributions

ZWW proposed the conceptualization of this work and finished writing the original draft of the manuscript. ZQT performed all the calculations involved. SF reviewed and revised the manuscript. All of the authors have read and agreed to the published version of the manuscript.

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Correspondence to Z. W. Wu.

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Atomic and Molecular Data and Their Applications: ICAMDATA 2022. Guest editors: Annarita Laricchiuta, Iouli E. Gordon, Christian Hill, Gianpiero Colonna, Sylwia Ptasinska.

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Wu, Z.W., Tian, Z.Q. & Fritzsche, S. Angular distribution of the characteristic line \(1s2p\,^{3}P_{2} \rightarrow 1s^{2}\,^{1}S_{0}\) of thallium ions: hyperfine-induced multipole interference. Eur. Phys. J. D 77, 95 (2023). https://doi.org/10.1140/epjd/s10053-023-00684-8

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