Skip to main content
SpringerLink
Log in

Binding Energies in Electron Shells of Rare-Earth Atoms

  • ATOMS, MOLECULES, OPTICS
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

Experimental data on the orbital binding energies in each of electron subshells of rare-earth elements from lanthanum to lutetium including the first ionization potentials have been analyzed in detail using a semiclassical method to separate the dependences of binding energies on the atomic number and quantum numbers. The spread of experimental data for the N and O shells of lanthanides has been discussed. The analysis has confirmed the law of similarity of orbital binding energies in the atomic number in individual subshells that differs from Moseley’s law. Deviation from the common dependence usually indicates the inaccuracy of the corresponding measurement. The simplest interpolation of the found relations makes it possible to approximate experimental data with an accuracy of about 1%, to reconstruct missed data, and to correct inaccurate measurement results. The analysis of theoretical results also reveals such relations and their violation is attributed to the violation of the order of filling of 4f states.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.

Similar content being viewed by others

Notes

  1. We note that the energies of 4fj, 5s, and 5pj states for 69Tm and 70Yr are misprinted in [7].

REFERENCES

  1. N. E. Holden and T. Coplen, Chem. Int. 26, 8 (2004).

    Google Scholar 

  2. A. Tompson et al., X-Ray Data Booklet (Center for X‑ray Optics and Advanced Light Source, Lawrence Berkeley Natl. Labor., 2009). http://xdb.lbl.gov/.

  3. A. V. Naumkin, A. Kraut-Vass, S. W. Gaarenstroom, and C. J. Powell, NIST X-Ray Photoelectron Spectroscopy Database. https://srdata.nist.gov/xps/selEnergyType.aspx. Accessed 2012.

  4. NIST Atomic Spectra Database Ionization Energies Form. https://physics.nist.gov/PhysRefData/ASD/ ionEnergy.html. Accessed October 2019.

  5. D. Thomas, Binding Energies of Electrons in Atoms from H (Z = 1) to Lw (Z = 103). http://www.chembio uoguelph.ca/educmat/atomdata/bindener/elecbind.htm. Accessed 1997

  6. R. D. Deslattes, E. G. Kessler Jr., P. Indelicato, L. de Billy, E. Lindroth, and J. Anton, Rev. Mod. Phys. 75, 35 (2003).

    Article  ADS  Google Scholar 

  7. S. Kotochigova, Z. H. Levine, E. L. Shirley, M. D. Stiles, and Ch. W. Clark, Atomic Reference Data for Electronic Structure Calculations. http://www.nist.gov/pml/data/dftdata/index.cfm.

  8. J. A. Bearden and A. F. Burr, Rev. Mod. Phys. 39, 125 (1967).

    Article  ADS  Google Scholar 

  9. O. Mauron, J.-Cl. Dousse, S. Baechler, M. Berset, Y.‑P. Maillard, P.-A. Raboud, and J. Hoszowska, Phys. Rev. A 67, 032506 (2003).

    Article  ADS  Google Scholar 

  10. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Nauka, Moscow, 1989; Pergamon, New York, 1977).

  11. H. G. J. Moseley, Philos. Mag. 26, 1024 (1913).

    Article  Google Scholar 

  12. H. G. J. Moseley, Philos. Mag. 27, 703 (1914).

    Article  Google Scholar 

  13. G. V. Shpatakovskaya, JETP Lett. 108, 768 (2018).

    Article  ADS  Google Scholar 

  14. G. V. Shpatakovskaya, Phys. Usp. 62, 186 (2019).

    Article  ADS  Google Scholar 

  15. G. V. Shpatakovskaya and V. Ya. Karpov, J. Phys.: Conf. Ser. 774, 012002 (2016).

    Google Scholar 

  16. V. Ya. Karpov and G. V. Shpatakovskaya, J. Exp. Theor. Phys. 124, 369 (2017).

    Article  ADS  Google Scholar 

  17. G. V. Shpatakovskaya, KIAM Preprint No. 184 (Keldysh Inst. Appl. Math., Moscow, 2018). https://doi.org/10.20948/prepr-2018-184-e

  18. M. Cardona and L. Ley, Photoemission in Solids I: General Principles (Springer, Berlin, 1978).

    Book  Google Scholar 

  19. J. C. Fuggle and N. Martnsson, J. Electron Spectrosc. Relat. Phenom. 21, 275 (1980).

    Article  Google Scholar 

  20. W. C. Martin, R. Zalubas, and L. Hagan, Atomic Energy Levels: The Rare-Earth Elements, Natl. Stand. Ref. Data Ser., NSRDS-NBS 60 (Natl. Bur. Stand., U. S., 1978). https://doi.org/10.6028/NBS.NSRDS.60

  21. C. J. Powell, J. Electron Spectrosc. Relat. Phenom. 185, 1 (2012).

    Article  Google Scholar 

  22. S. Kotochigova, Z. H. Levine, E. L. Shirley, M. D. Stiles, and C. W. Clark, Phys. Rev. A 55, 191 (1997).

    Article  ADS  Google Scholar 

  23. J. P. Desclaux, Comput. Phys. Comm. 9, 31 (1975).

    Article  ADS  Google Scholar 

  24. J. P. Desclaux, in Methods and Techniques in Computational Chemistry, Vol. A: Small Systems of METTEC, Ed. by E. Clementi (STEF, Calgary, 1993), p. 253.

  25. P. Indelicato, S. Boucard, and E. Lindroth, Eur. Phys. J. D 3, 29 (1998).

    Article  ADS  Google Scholar 

  26. G. Malmsten, O. Nilsson, I. Thoren, and J.-E. Bergmark, Phys. Scr. 1, 37 (1970).

    Article  ADS  Google Scholar 

  27. D. Studer, S. Heinitz, R. Heinike, and P. Naubereit, Phys. Rev. A 99, 062513 (2019).

    Article  ADS  Google Scholar 

  28. D. D. Sarma and C. N. R. Rao, J. Electron Spectrosc. Relat. Phenom. 20, 25 (1980).

    Article  Google Scholar 

  29. D. F. Mullica, C. K. C. Lok, H. O. Perkins, G. A. Benesh, and V. Young, J. Electron Spectrosc. Relat. Phenom. 71, 1 (1995).

    Article  Google Scholar 

  30. E. F. Worden, R. W. Solarz, J. A. Paisner, and J. G. Conway, J. Opt. Soc. Am. 68, 52 (1978).

    Article  ADS  Google Scholar 

  31. Y. Uwamino, A. Tsuge, T. Ishizuka, and H. Yamatera, Bull. Chem. Soc. Jpn. 59, 2263 (1986).

    Article  Google Scholar 

  32. M. Aymar, A. Débarre, and O. Robaux, J. Phys. B 13, 1089 (1980).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    G. V. Shpatakovskaya

Authors
  1. G. V. Shpatakovskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. V. Shpatakovskaya.

Additional information

Translated by R. Tyapaev

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shpatakovskaya, G.V. Binding Energies in Electron Shells of Rare-Earth Atoms. J. Exp. Theor. Phys. 131, 385–393 (2020). https://doi.org/10.1134/S1063776120080063

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776120080063

Search

Navigation