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Relativistic Effects in Atomic Structure Calculations: An Introduction

  • J. P. Desclaux
Part of the NATO Advanced Study Institutes Series book series (SPEPO, volume 18)

Abstract

Let us first consider qualitatively how relativistic effects influence atomic structure calculations. Using atomic units (i.e. e = ħ = mo =1), the mean velocity of a 1s electron in a Coulomb field of charge Z is exactly equal to Z. In the same system of units the velocity of light is roughly 137; thus, for a rare earth atom the mean velocity of the 1s electron is already almost half the velocity of light, and its mass is about 1.15 that of the rest mass. We may get a feeling of the main changes induced by this variation in the mass by simply considering the Schrödinger equation for the apparent mass instead of the rest mass. As the energy is directly proportional to the mass (E = -Z2m/2n2) we conclude that the binding energy should increase while at the same time the charge density should contract towards the origin (the scaling factor is r/m). If we now consider electrons of higher quantum number n, we will conclude from the preceding argument that they will be essentially unaffected since their velocity is rather small compared to the light velocity. But as their wavefunctions have to be orthogonal to the inner electron ones, they experience an indirect relativistic effect which also results in a contraction of the charge density.

Keywords

Lamb Shift Relative Contraction Coulomb Field Relativistic Counterpart Open Shell System 
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.

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References

  1. 1.
    V.M. Burke and I.P. Grant, Proc. Phys. Soc. 90, 297 (1967)ADSCrossRefGoogle Scholar
  2. 2.
    P.M. Dirac, Proc. Roy. Soc. A117, 610 (1928)ADSGoogle Scholar
  3. 3.
    G. Breit, Phys. Rev. 34, 553 (1929)MathSciNetADSMATHCrossRefGoogle Scholar
  4. 3a.
    G. Breit, Phys. Rev. 36, 383 (1930)ADSMATHCrossRefGoogle Scholar
  5. 4.
    H. Bethe and E.E. Salpeter “Quantum Mechanics of One and Two-Electron Atoms” Springer-Verlag (Berlin 1957)MATHGoogle Scholar
  6. 5.
    I.P. Grant, Adv. Phys. 19, 747 (1970)ADSCrossRefGoogle Scholar
  7. 6.
    L.N. Labzovskii, Sov. Phys. JETP 32, 94 (1971)ADSGoogle Scholar
  8. 7.
    S. Feneuille and L. Armstrong, Phys. Rev. A8, 1173 (1973)ADSGoogle Scholar
  9. 8.
    J.P. Desclaux, Atom. Data Nucl. Data Tables 12, 312 (1973)ADSCrossRefGoogle Scholar
  10. 9.
    L. Chase, H.P. Kelly and H.S. Köhler, Phys. Rev. A3, 1550 (1971)ADSGoogle Scholar
  11. 10.
    B. Fricke, J.P. Desclaux and J.T. Waber, Phys. Rev. Lett. 28, 714 (1971)ADSCrossRefGoogle Scholar
  12. 11.
    A.J. Bearden and A.F. Burr, Rev. Mod. Phys. 39, 125 (1967)ADSCrossRefGoogle Scholar
  13. 12.
    C. Froese-Fischer, Atom. Data Nucl. Data Tables 12, 87 (1973)ADSCrossRefGoogle Scholar
  14. 13.
    K. Siegbahn Uppsala University Report UUIP 880–29–31 (1974)Google Scholar
  15. 14.
    E.U. Condon and G.H. Shortley “The Theory of Atomic Spectra” p. 294 (Cambridge U.P. 1935)Google Scholar
  16. 15.
    P.G.H. Sandars and J. Beck, Proc. Roy. Soc. A289, 97 (1966)ADSGoogle Scholar
  17. 16.
    L. Armstrong and S. Feneuille in Adv. in Atom. and Mol. Phys. 10, 1 (1974)Google Scholar
  18. 17. a).
    E. Luc-Koenig, J. Phys. B7, 1052 (1974)ADSGoogle Scholar
  19. 17. b).
    E. Luc-Koenig, C. Morrillon and J. Vergès, Physica 70, 175 (1973)ADSCrossRefGoogle Scholar
  20. 17. c).
    L. Holmgren and S. Garpman, Phys. Scripta 10, 215 (1974).ADSCrossRefGoogle Scholar
  21. 17. d).
    S. Garpman, L. Holmgren and A. Rosen, Phys. Scripta 10, 221 (1974)ADSCrossRefGoogle Scholar
  22. 17. e).
    E. Luc-Koenig, Thèse d’Etat Université de Paris 1975Google Scholar
  23. 18.
    I. Lindgren and A. Rosen, Case Studies in Atom. Phys. 4, 93 and 197 (1974)Google Scholar
  24. 19.
    D.F. Mayers, J. de Physique 31, C4–213 (1970).Google Scholar
  25. 20.
    J.P. Desclaux, C.M. Moser and G. Verhaegen, J. Phys. B4, 296 1971ADSGoogle Scholar
  26. 21.
    J.C. Slater in “Quantum Theory of Atomic Structure”, Vol. 2, Chap. 17 (McGraw Hill, N.Y. 1960)Google Scholar
  27. 22.
    J.P. Desclaux, Int. J. Quant. Chem. 6, 25 (1972)CrossRefGoogle Scholar
  28. 23.
    J. Andriessen and D. van Ormondt, J. Phys. B8, 1993 (1975)ADSGoogle Scholar
  29. 24.
    J.B. Mann and J.T. Waber, Atom. Data Tables 5, 201 (1973)ADSCrossRefGoogle Scholar
  30. 25.
    M.A. Coulthard, J. Phys. B6, 2224 (1973)ADSGoogle Scholar
  31. 26.
    J.P. Desclaux, Comp. Phys. Comm. 9, 31 (1975)ADSCrossRefGoogle Scholar
  32. 27.
    J. Berkowitz, J.L. Dehmer, Y.K. Kim and J.P. Desclaux, J. Chem. Phys. 61, 2556 (1974)ADSCrossRefGoogle Scholar
  33. 28.
    H. Hotop, private communicationGoogle Scholar
  34. 29.
    J.P. Desclaux and Y.K. Kim, J. Phys. B8, 1177 (1975)ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1976

Authors and Affiliations

  • J. P. Desclaux
    • 1
  1. 1.Institut Max von Laue - Paul LangevinGrenoble CedexFrance

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