Optics and Spectroscopy

, Volume 107, Issue 1, pp 9–15

Determination of the effective nuclear charge for free ions of transition metals from experimental spectra

  • R. Yu. Babkin
  • K. V. Lamonova
  • S. M. Orel
  • Yu. G. Pashkevich
Spectroscopy of Atoms and Molecules


The refined set of values of the effective nuclear charge (\( \bar Z_{ef} \)) and the set of one-electron spin-orbital constants (ξ3dteor) are obtained for ions of transition metals with the help of a semiempirical method of calculation of the spectrum of free ions with allowance for the spin-orbital interaction. The effective nuclear charge, which is a variable theoretical parameter, was determined from a comparison of theoretically calculated ion absorption spectra with experimental ones. The form of the potential for the calculation of the spin-orbital constant was chosen such that the calculated value ξ3dteor would coincide with the experimental one ξ3dexp. The calculated set of values \( \bar Z_{ef} \), ξ3dteor} can be used in semiempirical calculations of energy levels of 3d ions (ions with an incomplete 3d shell).

PACS numbers



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. J. P. Stewart, J. Comp. Aided Mol. Design 4, 1 (1990).CrossRefADSGoogle Scholar
  2. 2.
    J. Sugar and C. Corliss, Atomic Energy Levels of the Iron-Period Elements: Potassium through Nickel, J. Phys. Chem. Ref. Data 14,Suppl. 2 (1985).Google Scholar
  3. 3.
    E. S. Zhitlukhina, K. V. Lamonova, S. M. Orel, P. Lemmens, and Yu. G. Pashkevich, J. Phys. Cond. Matt. 119, 156216 (2007).Google Scholar
  4. 4.
    S. S. Batsanov and R. A. Zvyagina, Overlap Integrals and Effective Charges Problem (Nauka, Novosibirsk, 1966) [in Russian].Google Scholar
  5. 5.
    G. Breit, Proc. Nat. Acad. Sci. U.S.A. 14, 553 (1928).MATHCrossRefADSGoogle Scholar
  6. 6.
    H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Plenum, New York, 1977).Google Scholar
  7. 7.
    P. A. M. Dirac, The Principles of Quantum Mechanics (Oxford, London, 1978; Nauka, Moscow, 1979).Google Scholar
  8. 8.
    S. Sugano, Y. Tanabe, and H. Kamimura, Multiplets of Transition-Metal Ions in Crystals (Academic, New York, 1970).Google Scholar
  9. 9.
    I. I. Sobel’man, Introduction to the Theory of Atomic Spectra (Pergamon, New York, 1972).Google Scholar
  10. 10.
    M. E. El’yashevich, Atomic and Molecular Spectroscopy (Fizmatgiz, Moscow, 1962) [in Russian].Google Scholar
  11. 11.
    T. M. Dunn, Trans. Faraday Soc. 57, 1441 (1961).CrossRefGoogle Scholar
  12. 12.
    A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition ions (Oxford Univ. Press, Oxford, 1970).Google Scholar
  13. 13.
    M. Blume and R. E. Watson, Proc. R. Soc. (London) A 271, 565 (1963).CrossRefADSGoogle Scholar
  14. 14.
    E. Francisco and L. Pueyo, Phys. Rev. A 36, 5 (1987).CrossRefMathSciNetGoogle Scholar
  15. 15.
    A. Sommerfeld and G. Z. Wentzel, Phys. 7, 86 (1921).CrossRefGoogle Scholar
  16. 16.
    L. Pauling, Proc. R. Soc. (London) A 114, 181 (1927).CrossRefADSGoogle Scholar
  17. 17.
    W. Angus, Proc. R. Soc. (London) A 136, 569 (1932).CrossRefADSGoogle Scholar
  18. 18.
    K. W. F. Kohlrausch, Acta Phys. Austriaca 3, 452 (1949).Google Scholar
  19. 19.
    V. S. Urusov, Zh. Strukt. Khim. 3, 437 (1962).Google Scholar
  20. 20.
    S. S. Batsanov, L. N. Mazalov, and V. I. Chirkov, Izv. Sib. Otd. Akad. Nauk SSSR 2, 121 (1961).Google Scholar
  21. 21.
    J. C. Slater, Phys. Rev. 36, 57 (1930).CrossRefADSGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • R. Yu. Babkin
    • 1
  • K. V. Lamonova
    • 1
  • S. M. Orel
    • 1
  • Yu. G. Pashkevich
    • 1
  1. 1.Galkin Physicotechnical InstituteUkraine National Academy of SciencesDonetskUkraine

Personalised recommendations