Advertisement

Construction of the energy matrix for complex atoms

Part V: Electrostatically correlated spin-orbit and electrostatically correlated hyperfine interactions
  • Magdalena ElantkowskaEmail author
  • Jarosław Ruczkowski
  • Jerzy Dembczyński
Open Access
Regular Article

Abstract.

The continuation of the previous series of papers related to the construction of the energy matrix for complex atoms is presented. The contributions from the second-order perturbation theory concerning electrostatically correlated spin-orbit interactions (CSO), as well as electrostatically correlated hyperfine interactions (CHFS) to the atomic structure of \( nl^{N}\), \( nl^{N}n_{1}l_{1}^{N_1}\) and \( nl^{N}n_{1}l_{1}^{N_1}n_{2}l_{2}^{N_2}\) configurations, are considered. This theory assumes that the electron excitation \( n_{0}l_{0}\rightarrow nl\) affects spin-orbit splitting and magnetic dipole and electric quadrupole hyperfine structure in the same way which will be discussed below. Part I of the series presented, in general terms, a method allowing the analysis of complex electronic systems. Parts II, III and IV provided a description of an electrostatic interaction up to second-order perturbation theory; they constitute the basis for the design of an efficient computer program package for large-scale calculations of accurate wave functions. Analyses presented in the entire series of our papers clearly demonstrate that obtaining the precise wave functions is impossible without considering the contribution from the second-order effects into fine and hyperfine atomic structure.

Keywords

Closed Shell Virtual State Open Shell Energy Matrix Empty Shell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    M. Elantkowska, J. Ruczkowski, J. Dembczyński, Eur. Phys. J. Plus 130, 14 (2015)CrossRefGoogle Scholar
  2. 2.
    L. Armstrong jr., Theory of the Hyperfine Structure of Free Atoms (Willey-Interscience, New York, 1971)Google Scholar
  3. 3.
    I. Lindgren, J. Morrison, Atomic Many-Body Theory (Springer-Verlag, Berlin, Heidelberg, New York, 1982)Google Scholar
  4. 4.
    L. Armstrong jr., S. Feneuille, Phys. Rev. 173, 58 (1968)CrossRefADSGoogle Scholar
  5. 5.
    L. Armstrong jr., S. Feneuille, Adv. At. Mol. Phys. 10, 1 (1974)CrossRefADSGoogle Scholar
  6. 6.
    J. Dembczyński, G. Szawioła, M. Elantkowska, E. Stachowska, J. Ruczkowski, Phys. Scr. 54, 444 (1996)CrossRefADSGoogle Scholar
  7. 7.
    M. Elantkowska, J. Ruczkowski, J. Dembczyński, Phys. Scr. 59, 49 (1999)CrossRefADSGoogle Scholar
  8. 8.
    M. Elantkowska, J. Ruczkowski, J. Dembczyński, Eur. Phys. J. Plus 130, 15 (2015)CrossRefGoogle Scholar
  9. 9.
    M. Elantkowska, J. Ruczkowski, J. Dembczyński, Eur. Phys. J. Plus 130, 83 (2015)CrossRefGoogle Scholar
  10. 10.
    M. Elantkowska, J. Ruczkowski, J. Dembczyński, Eur. Phys. J. Plus 130, 170 (2015)CrossRefGoogle Scholar
  11. 11.
    R.D. Cowan, The Theory of Atomic Structure and Spectra (Berkeley University of California Press, Berkeley, 1981)Google Scholar
  12. 12.
    B.R. Judd, H.M. Crosswhite, H. Crosswhite, Phys. Rev. 169, 1 (1968)CrossRefGoogle Scholar
  13. 13.
    K. Rajnak, B.G. Wybourne, Phys. Rev. 134, 596 (1964)CrossRefADSGoogle Scholar
  14. 14.
    A. Pasternak, Z.B. Goldschmidt, Phys. Rev. A 1, 55 (1972)CrossRefADSGoogle Scholar
  15. 15.
    Z.B. Goldschmidt, J.V. Mallow, Phys. Rev. A 29, 2401 (1984)CrossRefADSGoogle Scholar
  16. 16.
    P.G.H. Sandars, J. Beck, Proc. R. Soc. A 289, 97 (1965)CrossRefADSGoogle Scholar
  17. 17.
    B.R. Judd, Proc. R. Soc. 82, 874 (1963)CrossRefGoogle Scholar
  18. 18.
    B.R. Judd, La Structure Hyperfine Magnetigue des Atomes et des Molecules, edited by R. Lefebvre, C. Moser (C.N.R.S., Paris, 1967) p. 311Google Scholar
  19. 19.
    P.G.H. Sandars, Adv. Chem. Phys. 14, 365 (1969)Google Scholar
  20. 20.
    I. Lindgren, A. Rosen, Case Stud. At. Phys. 4, (1974)Google Scholar
  21. 21.
    S. Büttgenbach, Hyperfine Structure in 4d- and 5d-Shell Atoms (Springer, Berlin, 1982)Google Scholar
  22. 22.
    G. Olsson, A. Rosen, Phys. Scr. 26, 168 (1982)CrossRefADSGoogle Scholar
  23. 23.
    C. Bauche-Arnoult, Proc. R. Soc. A 322, 361 (1971)CrossRefADSGoogle Scholar
  24. 24.
    C. Bauche-Arnoult, J. Phys. 34, 301 (1973)CrossRefGoogle Scholar
  25. 25.
    J. Dembczyński, W. Ertmer, U. Johann, P. Unkel, Z. Phys. A 321, 1 (1985)CrossRefADSGoogle Scholar
  26. 26.
    J. Dembczyński, Physica C 141, 219 (1986)CrossRefGoogle Scholar
  27. 27.
    W. Ertmer, U. Johann, J. Dembczyński, Z. Michalski, Z. Phys. D 2, 67 (1986)CrossRefADSGoogle Scholar
  28. 28.
    R. Aydin et al., Z. Phys. D 15, 281 (1990)CrossRefADSGoogle Scholar
  29. 29.
    J. Dembczyński, G.H. Guthoehrlein, E. Stachowska, Phys. Rev. A 48, 2752 (1993)CrossRefADSGoogle Scholar
  30. 30.
    J. Dembczyński, M. Elantkowska, K. Bekk, H. Rebel, M. Wilson, Z. Phys. D 13, 181 (1989)CrossRefADSGoogle Scholar
  31. 31.
    J. Dembczyński, Phys. Scr. T65, 88 (1996)CrossRefADSGoogle Scholar
  32. 32.
    J. Dembczyński et al., Hyperfine Interact. 127, 49 (2000)CrossRefADSGoogle Scholar
  33. 33.
    J. Dembczyński, M. Elantkowska, B. Furmann, J. Ruczkowski, D. Stefańska, J. Phys. B: At. Mol. Opt. Phys. 43, 065001 (2010)CrossRefADSGoogle Scholar
  34. 34.
    G. Racah, Phys. Rev. 63, 367 (1943)CrossRefADSGoogle Scholar
  35. 35.
    G. Racah, Phys. Rev. 76, 1352 (1949)CrossRefADSzbMATHGoogle Scholar
  36. 36.
    V.L. Donlan, J. Chem. Phys. 52, 3431 (1970)CrossRefADSGoogle Scholar
  37. 37.
    H.A. Jahn, J. Hope, Phys. Rev. 93, 318 (1954)CrossRefADSzbMATHGoogle Scholar
  38. 38.
    R.J. Ord-Smith, Phys. Rev. 94, 1227 (1954)CrossRefADSzbMATHGoogle Scholar
  39. 39.
    A.P. Yutsis, I.B. Levinson, V.V. Vanagas, Mathematical Apparatus of the Angular Momentum Theory (Vilnius, 1960) (English translation: Israel Program for Scientific Translations, Jerusalem 1962 (Gordon and Breach, New York 1963))Google Scholar
  40. 40.
    B. Arcimowicz, J. Dembczyński, P. Głowacki, J. Ruczkowski, M. Elantkowska, G. Guthöhrlein, L. Windholz, Eur. Phys. J. ST 222, 2085 (2013)CrossRefGoogle Scholar
  41. 41.
    J. Ruczkowski, M. Elantkowska, J. Dembczyński, J. Quant. Spectrosc. Radiat. Transfer. 145, 20 (2014)CrossRefADSGoogle Scholar
  42. 42.
    J. Ruczkowski, M. Elantkowska, J. Dembczyński, J. Quant. Spectrosc. Radiat. Transfer. 149, 168 (2014)CrossRefADSGoogle Scholar
  43. 43.
    J. Dembczyński, M. Elantkowska, J. Ruczkowski, I.K. Öztürk, A. Er, F. Güzelçimen, Gö. Başar, S. Kröger, J. Phys. B: At. Mol. Opt. Phys. 48, 015006 (2015)CrossRefADSGoogle Scholar
  44. 44.
    J. Dembczyński, M. Elantkowska, J. Ruczkowski, Phys. Rev. A 92, 012519 (2015)CrossRefADSGoogle Scholar
  45. 45.
    J. Ruczkowski, M. Elantkowska, J. Dembczyński, J. Quant. Spectrosc. Radiat. Transfer. 170, 106 (2016)CrossRefADSGoogle Scholar

Copyright information

© The Author(s) 2016

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Magdalena Elantkowska
    • 1
    Email author
  • Jarosław Ruczkowski
    • 2
  • Jerzy Dembczyński
    • 2
  1. 1.Institute of Materials Research and Quantum EngineeringFaculty of Technical Physics, Poznan University of TechnologyPoznańPoland
  2. 2.Institute of Control and Information EngineeringFaculty of Electrical Engineering, Poznan University of TechnologyPoznańPoland

Personalised recommendations