Advertisement

Perturbation Theory for QED Calculations of High-Z Few-electron Atoms

  • V.M. Shabaev
Chapter
  • 665 Downloads
Part of the Lecture Notes in Physics book series (LNP, volume 695)

Abstract

Experimental investigations of heavy few-electron ions (see, e.g., [1]) have triggered a great interest to accurate quantum electrodynamic (QED) calculations of these systems. At present, such calculations are feasible only by perturbation theory in two small parameters α and 1/Z, where α ≈ 1/137 is the fine structure constant and Z is the nuclear charge number. For heavy few-electron ions, the parameters α and 1/Z characterize the QED and interelectronic-interaction corrections, respectively. To derive formal expressions for these corrections in a systematic way one needs to employ special methods.

Keywords

Perturbation Theory Green Function Energy Shift Photon Mass Heisenberg Representation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H.F. Beyer, H.-J. Kluge, V.P. Shevelko: X-ray Radiation of Highly Charged Ions (Springer, Berlin 1997)Google Scholar
  2. 2.
    M. Gell-Mann, F. Low: Phys. Rev. 84, 350 (1951)zbMATHMathSciNetCrossRefADSGoogle Scholar
  3. 3.
    J. Sucher: Phys. Rev. 107, 1448 (1957)MathSciNetCrossRefADSGoogle Scholar
  4. 4.
    L.N. Labzowsky: Zh. Eksp. Teor. Fiz. 59, 168 (1970) [Sov. Phys. JETP 32, 94 (1970)]Google Scholar
  5. 5.
    M.A. Braun, A.D. Gurchumelia: Teor. Mat. Fiz. 45, 199 (1980) [Theor. Math. Phys. 45, N2 (1980)]Google Scholar
  6. 6.
    M.A. Braun, A.D. Gurchumelia, U.I. Safronova: Relativistic Atom Theory (Nauka, Moscow 1984Google Scholar
  7. 7.
    L. Labzowsky, G. Klimchitskaya, Yu. Dmitriev: Relativistic Effects in Spectra of Atomic Systems (IOP Publishing, Bristol 1993Google Scholar
  8. 8.
    P.J. Mohr, G. Plunien, G. Soff: Phys. Rep. 293, 227 (1998)CrossRefADSGoogle Scholar
  9. 9.
    J. Sapirstein: Rev. Mod. Phys. 70, 55 (1998)CrossRefADSGoogle Scholar
  10. 10.
    J. Hubbard: Proc. Roy. Soc. A 240, 539 (1957)zbMATHMathSciNetADSGoogle Scholar
  11. 11.
    S.S. Schweber: An Introduction to Relativistic Quantum Field Theory (Harper & Row, New York 1961zbMATHGoogle Scholar
  12. 12.
    A.N. Vasil'ev, A.L. Kitanin: Teor. Mat. Fiz. 24, 219 (1975) [Theor. Math. Phys. 24, N2 (1975)]zbMATHMathSciNetGoogle Scholar
  13. 13.
    S.A. Zapryagaev, N.L. Manakov, V.G. Pal'chikov: Theory of One- and Two- Electron Multicharged Ions (Energoatomizdat, Moscow 1985)Google Scholar
  14. 14.
    J. Sapirstein: Phys. Scr. 36, 801 (1987)ADSCrossRefGoogle Scholar
  15. 15.
    Yu.Yu. Dmitriev, T.A. Fedorova: Phys. Lett. A 245, 555 (1998)CrossRefADSGoogle Scholar
  16. 16.
    I. Lindgren, S. Salomonson, B. Åsén: Phys. Rep. 389, 161 (2004)CrossRefADSGoogle Scholar
  17. 17.
    V.M. Shabaev: The quantum-electrodynamical perturbation theory in the Raylegh-Schrödinger form for the calculation of the energy levels of atomic systems. In: Many-particles Effects in Atoms, ed by U.I. Safronova (AN SSSR, Nauchnyi Sovet po Spektroskopii, Moscow 1988) pp 15–23Google Scholar
  18. 18.
    V.M. Shabaev: The quantum-electrodynamical perturbation theory in the Raylegh-Schrödinger form for the calculation of the transition probabilities and the cross-sections of various processes. In: Many-particles Effects in Atoms, ed by U.I. Safronova (AN SSSR, Nauchnyi Sovet po Spektroskopii, Moscow 1988) pp 24–33Google Scholar
  19. 19.
    V.M. Shabaev: Izv. Vuz. Fiz. 33, 43 (1990) [Sov. Phys. Journ. 33, 660 (1990)]Google Scholar
  20. 20.
    V.M. Shabaev: Teor. Mat. Fiz. 82, 83 (1990) [Theor. Math. Phys. 82, 57 (1990)]Google Scholar
  21. 21.
    V.M. Shabaev: J. Phys. A 24, 5665 (1991)MathSciNetCrossRefADSGoogle Scholar
  22. 22.
    V.M. Shabaev: Phys. Rep. 356, 119 (2002)zbMATHCrossRefADSGoogle Scholar
  23. 23.
    V.M. Shabaev, I.G. Fokeeva: Phys. Rev. A 49, 4489 (1994)CrossRefADSGoogle Scholar
  24. 24.
    V.M. Shabaev: Phys. Rev. A 50, 4521 (1994)CrossRefADSGoogle Scholar
  25. 25.
    V.A. Yerokhin, A.N. Artemyev, T. Beier et al: Phys. Rev. A 60, 3522 (1999)CrossRefADSGoogle Scholar
  26. 26.
    A.N. Artemyev, T. Beier, G. Plunien et al: Phys. Rev. A 62, 022116 (2000)CrossRefADSGoogle Scholar
  27. 27.
    V.M. Shabaev, V.A. Yerokhin, T. Beier et al: Phys. Rev. A 61, 052112 (2000)CrossRefADSGoogle Scholar
  28. 28.
    E.-O. Le Bigot, P. Indelicato, V.M. Shabaev: Phys. Rev. A 63, 040501(R) (2001)Google Scholar
  29. 29.
    V.M. Shabaev: Phys. Rev. A 64, 052104 (2001)CrossRefADSGoogle Scholar
  30. 30.
    P. Indelicato, V.M. Shabaev, A.V. Volotka: Phys. Rev. A 69, 062506 (2004)CrossRefADSGoogle Scholar
  31. 31.
    M.A. Braun: Teor. Mat. Fiz. 72, 394 (1987) [Theor. Math. Phys. 72, 958 (1987)]MathSciNetGoogle Scholar
  32. 32.
    V.M. Shabaev: Teor. Mat. Fiz. 63, 394 (1985) [Theor. Math. Phys. 63, 588 (1985)]Google Scholar
  33. 33.
    C. Itzykson, J.-B. Zuber: Quantum Field Theory (McGraw-Hill, New York 1980Google Scholar
  34. 34.
    J.D. Bjorken, D. Drell: Relativistic Quantum Fields (McGraw-Hill, New York 1965zbMATHGoogle Scholar
  35. 35.
    V.L. Bonch-Bruevich, S.V. Tyablikov: The Green Function Method in Statistical Mechanics (North-Holland Publishing Company, Amsterdam 1962zbMATHGoogle Scholar
  36. 36.
    A.B. Migdal: Theory of Finite Fermi Systems and Properties of Atomic Nuclei (Nauka, Moscow 1983)Google Scholar
  37. 37.
    A.A. Logunov, A.N. Tavkhelidze: Nuovo Cim. 29, 380 (1963)MathSciNetCrossRefGoogle Scholar
  38. 38.
    R.N. Faustov: Teor. Mat. Fiz. 3, 240 (1970) [Theor. Math. Phys. 3, N2 (1970)]Google Scholar
  39. 39.
    B. Sz-Nagy: Comm. Math. Helv. 19, 347 (1946/47)CrossRefGoogle Scholar
  40. 40.
    T. Kato: Progr. Theor. Phys. 4, 514 (1949)CrossRefADSGoogle Scholar
  41. 41.
    T. Kato: Perturbation Theory for Linear Operators (Springer, Berlin 1966)zbMATHGoogle Scholar
  42. 42.
    M. Reed, B. Simon: Methods of Modern Mathematical Physics, vol. 4 (Academic Press, New York 1978)zbMATHGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • V.M. Shabaev
    • 1
  1. 1.Department of PhysicsSt. Petersburg State UniversitySt. PetersburgRussia

Personalised recommendations