Nuclear recoil and vacuum-polarization effects on the binding energies of supercritical H-like ions

  • Ivan A. Aleksandrov
  • Günter Plunien
  • Vladimir M. Shabaev
Regular Article

Abstract

The Dirac Hamiltonian including nuclear recoil and vacuum-polarization operators is considered in a supercritical regime Z> 137. It is found that the nuclear recoil operator derived within the Breit approximation “regularizes” the Hamiltonian for the point-nucleus model and allows the ground state level to go continuously down and reach the negative energy continuum at a critical value Z cr ≈ 145. If the Hamiltonian contains both the recoil operator and the Uehling potential, the 1s level reaches the negative energy continuum at Z cr ≈ 144. The corresponding calculations for the excited states have been also performed. This study shows that, in contrast to previous investigations, a point-like nucleus can have effectively the charge Z> 137.

Graphical abstract

Keywords

Atomic Physics 

References

  1. 1.
    S.S. Gershtein, Y.B. Zeldovich, Zh. Eksp. Teor. Fiz. 57, 654 (1969) [Sov. Phys. J. Exp. Theor. Phys. 30, 358 (1970)]Google Scholar
  2. 2.
    W. Pieper, W. Greiner, Z. Phys. 218, 327 (1969)CrossRefADSGoogle Scholar
  3. 3.
    Y.B. Zeldovich, V.S. Popov, Sov. Phys. Usp. 14, 673 (1972)CrossRefADSGoogle Scholar
  4. 4.
    W. Greiner, B. Müller, J. Rafelski, Quantum Electrodynamics of Strong Fields (Springer-Verlag, Berlin, 1985)Google Scholar
  5. 5.
    P. Gärtner, U. Heinz, B. Müller, W. Greiner, Z. Physik A 300, 143 (1981)CrossRefADSGoogle Scholar
  6. 6.
    K. Case, Phys. Rev. 80, 797 (1950)CrossRefADSMathSciNetMATHGoogle Scholar
  7. 7.
    C. Burnap, H. Brysk, P. Zweifel, Nuovo Cimento 64 407 (1981)CrossRefMathSciNetGoogle Scholar
  8. 8.
    J. Xia, Trans. Am. Math. Soc. 351, 1989 (1999)CrossRefMATHGoogle Scholar
  9. 9.
    H. Hogreve, J. Phys. A 46, 025301 (2013)CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    D. Gitman, A. Levin, I. Tyutin, B. Voronov, Phys. Scr. 87, 038104 (2013)CrossRefADSGoogle Scholar
  11. 11.
    V.B. Berestetsky, E.M. Lifshitz, L.P. Pitaevsky, Quantum Electrodynamics (Pergamon Press, Oxford, 1982)Google Scholar
  12. 12.
    V.M. Shabaev, Teor. Mat. Fiz. 63, 394 (1985) [Theor. Math. Phys. 63, 588 (1985)]CrossRefGoogle Scholar
  13. 13.
    K. Pachucki, H. Grotch, Phys. Rev. A 51, 1854 (1995)CrossRefADSGoogle Scholar
  14. 14.
    V.M. Shabaev, Phys. Rev. A 57, 59 (1998)CrossRefADSGoogle Scholar
  15. 15.
    G.S. Adkins, S. Morrison, J. Sapirstein, Phys. Rev. A 76, 042508 (2007)CrossRefADSGoogle Scholar
  16. 16.
    B. Voronov, D. Gitman, I. Tyutin, Russ. Phys. J. 50, 1 (2007)CrossRefADSMathSciNetMATHGoogle Scholar
  17. 17.
    B. Voronov, D. Gitman, I. Tyutin, Russ. Phys. J. 50, 853 (2007)CrossRefMathSciNetMATHGoogle Scholar
  18. 18.
    B. Voronov, D. Gitman, I. Tyutin, Russ. Phys. J. 51, 115 (2008)CrossRefMathSciNetMATHGoogle Scholar
  19. 19.
    C. Fulton, H. Langer, A. Luger, Math. Nachr. 285, 1791 (2012)CrossRefMathSciNetMATHGoogle Scholar
  20. 20.
    M.Yu. Kuchiev, V.V. Flambaum, Phys. Rev. D 73, 093009 (2006)CrossRefADSGoogle Scholar
  21. 21.
    M.Yu. Kuchiev, V.V. Flambaum, Mod. Phys. Lett. A 21, 781 (2006)CrossRefADSMATHGoogle Scholar
  22. 22.
    V.V. Flambaum, M.Yu. Kuchiev, Phys. Rev. Lett. A 98, 181805 (2007)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Ivan A. Aleksandrov
    • 1
    • 2
  • Günter Plunien
    • 3
  • Vladimir M. Shabaev
    • 1
  1. 1.Department of PhysicsSt. Petersburg State UniversitySaint PetersburgRussia
  2. 2.ITMO UniversitySaint PetersburgRussia
  3. 3.Institut für Theoretische PhysikDresdenGermany

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