Skip to main content
SpringerLink
Log in

High Z effects in accounting for radiative component of the electron magnetic moment in hydrogen-like atoms

  • Physics of Elementary Particles and Atomic Nuclei. Theory
  • Published:
Physics of Particles and Nuclei Letters Aims and scope Submit manuscript

Abstract

The behavior of electron energy levels in hydrogen-like atoms is studied while taking into account the nonperturbative interaction between the radiative component of the magnetic moment of a free electron Δg free and the Coulomb field of an atomic nucleus with charge Z, including those with Z > 137. It is shown that for Zα ≪ 1 the energy-level shift is rather effectively determined through the matrix elements of the corresponding Dirac-Pauli operator with relativistic Coulomb wave functions. At the same time, for superheavy nuclei with Z ∼ 170, this shift, generated by Δg free, is genuinely nonperturbative, behaves like ∼Z 5 near the threshold of negative continuum, exceeds all the estimates of radiative corrections coming from vacuum polarization and electron self-energy known so far, and turns out to be at least of the same order as the effects of nuclear charge screening by filled electron shells.

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

Similar content being viewed by others

References

  1. J. Mondejar, J. H. Piclum, and A. Czarnecki, Phys. Rev. A 81, 062511 (2010).

    Article  ADS  Google Scholar 

  2. M. Vogel et al., Eur. Phys. J.: Special Topics 163, 113 (2008).

    Article  ADS  Google Scholar 

  3. D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev. Lett. 100, 120801 (2008).

    Article  ADS  Google Scholar 

  4. R. Ruffini, G. Vereshchagin, and S.-S. Xue, Phys. Rep. 487, 1–140 (2010) (Preprint arXiv: 0910.0974v3).

    Article  ADS  Google Scholar 

  5. W. Greiner and S. Schramm, Am. J. Phys 76, 509 (2008).

    Article  ADS  Google Scholar 

  6. A. Czarnecki et al., arXiv:1007.1176v1[hep-ph].

  7. S. G. Karshenboim, Phys. Lett. A 266, 380 (2000).

    Article  ADS  Google Scholar 

  8. T. Beier et al., Phys. Rev. A 62, 032510 (2001).

    Article  ADS  Google Scholar 

  9. V. M. Shabaev and V. A. Yerokhin, Phys. Rev. Lett. 88, 091801 (2002).

    Article  ADS  Google Scholar 

  10. B. Odom et al., Phys. Rev. Lett. 97, 030801 (2006).

    Article  ADS  Google Scholar 

  11. T. Kinoshita, “Lepton g — 2 from 1947 to Present. Lepton Dipole Moments,” Adv. Ser. Dir. HEP 20, 69, Ed. by B. L. Roberts and W. J. Marciano (World Sci., Singapoure, 2010).

    Google Scholar 

  12. S. Laporta and E. Remiddi, “Analytic QED Calculations of the Anomalous Magnetic Moment of the Electron. Lepton Dipole Moments,” Adv. Ser. Dir. HEP 20, 119, Ed. by B. L. Roberts and W. J. Marciano (World Sci., Singapoure, 2010).

    Google Scholar 

  13. D. Hanneke, S. Fogwell Hoogerheide, and G. Gabrielse, arXiv:1009.4831v1[physics.atom-ph].

  14. T. Kinoshita and M. Nio, Phys. Rev. D 73, 013003 (2006).

    Article  ADS  Google Scholar 

  15. T. Beier, Phys. Rep. 339, 79 (2000).

    Article  ADS  Google Scholar 

  16. P. J. Mohr and B. N. Taylor, Rev. Mod. Phys. 72, 351 (2000), Rev. Mod. Phys. 77, 1 (2005).

    Article  ADS  MATH  Google Scholar 

  17. K. Pachuki et al., Phys. Rev. A 72, 022108 (2005).

    Article  ADS  Google Scholar 

  18. G. Breit, Nature 122, 649 (1928).

    Article  ADS  Google Scholar 

  19. R. N. Faustov, Phys. Lett. B, 422 (1970), Nuovo Cim. A 69, 37 (1970).

    Google Scholar 

  20. H. Grotch, Phys. Rev. A 2, 1605 (1970).

    Article  ADS  Google Scholar 

  21. V. M. Shabaev, Phys. Rev. A 64, 052104 (2001).

    Article  ADS  Google Scholar 

  22. A. P. Martynenko and R. N. Faustov, Zh. Eksp. Teor. Fiz. 93, 471 (2001).

    Google Scholar 

  23. H. Grotch, Phys. Rev. Lett. 24, 39 (1970).

    Article  ADS  Google Scholar 

  24. A. Czarnecki, K. Melnikov, and A. Yelkhovsky, Phys. Rev. A 63, 012509 (2001).

    Article  ADS  Google Scholar 

  25. R. N. Lee et al., Phys. Rev. A 71, 052501 (2005).

    Article  ADS  Google Scholar 

  26. U. D. Jentschura et al., arXiv:0510.049v2[physics.atom-ph].

  27. U. D. Jentschura, Phys. Rev. A 79, 044501 (2009).

    Article  ADS  Google Scholar 

  28. S. G. Karshenboim, V. G. Ivanov, and V. M. Shabaev, Zh. Eksp. Teor. Fiz. 120, 546 (2001) [in Russian].

    Google Scholar 

  29. V. M. Shabaev et al., arXiv:0510.083v1[physics.atomph].

  30. J. Schwinger, Phys. Rev. 73, 416 (1948).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. J. D. Bjorken and S. L. Drell, Relyativistskaya Kvantovaya Teoriya (Nauka, Moscow, 1978) [in Russian].

    Google Scholar 

  32. V. B. Berestetskii, E. M. Lifshits, and L. P. Pitaevskii, Kvantovaya Electrodinamika (Nauka, Moscow, 1989) [in Russian].

    Google Scholar 

  33. A. O. Barut and J. Kraus, Phys. Lett. B 59, 175 (1975), J. Math. Phys. 17, 506 (1976).

    Article  ADS  Google Scholar 

  34. B. L. Voronov, D. T. Gitman, and I. V. Tyutin, Teor. Mat. Fiz. 150, 41 (2007).

    Article  MathSciNet  Google Scholar 

  35. K. Sveshnikov and D. Khomovskii, Vestn. MGU: Fizika, Astronomiya, (5), 22–28 (2012).

    Google Scholar 

  36. S. S. Gershtein and Ya. B. Zel’dovich, Zh. Eksp. Teor. Fiz. 57, 654 (1969).

    Google Scholar 

  37. W. Pieper and W. Greiner, Z. Phys. 218, 327 (1969).

    Article  ADS  Google Scholar 

  38. Ya. B. Zel’dovich and V. S. Popov, Usp. Fiz. Nauk 105, 403 (1971).

    Google Scholar 

  39. A. A. Grib, S. G. Mamaev, and V. M. Mostepanenko, Vakuumnye Kvantovye Effekty v Sil’nykh Polyakh (Energoatomizdat, Moscow, 1988) [in Russian].

    Google Scholar 

  40. W. Greiner, B. Mueller, and J. Rafelski, Quantum Electrodynamics of Strong Fields (Springer, Berlin, 1985).

    Book  Google Scholar 

  41. J. Reinhardt and W. Greiner, Quantum Electrodynamics (Springer, Berlin, 2003).

    MATH  Google Scholar 

  42. W. Greiner and J. Reinhardt, Quantum Aspects of Beam Physics, 438–463 (World Sci., Singapoure, 1999).

    Google Scholar 

  43. P. Krekora et al., Phys. Rev. Lett. 95(7), 070403 (2005).

    Article  ADS  Google Scholar 

  44. V. I. Zagrebaev and W. Greiner, J. Phys. G (NP) 34, 1 (2007).

    Article  ADS  Google Scholar 

  45. G. Soff et al., Phys. Rev. Lett. 48, 1465 (1982).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Physics and Institute for Theoretical Problems of Microphysics, Moscow State University, Moscow, 119899, Russia

    K. A. Sveshnikov & D. I. Khomovskii

Authors
  1. K. A. Sveshnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. I. Khomovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. A. Sveshnikov.

Additional information

Original Russian Text © K.A. Sveshnikov, D.I. Khomovskii, 2013, published in Pis’ma v Zhurnal Fizika Elementarnykh Chastits i Atomnogo Yadra, 2013, No. 2(179), pp. 187–206.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sveshnikov, K.A., Khomovskii, D.I. High Z effects in accounting for radiative component of the electron magnetic moment in hydrogen-like atoms. Phys. Part. Nuclei Lett. 10, 119–131 (2013). https://doi.org/10.1134/S1547477113020155

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1547477113020155

Keywords

Search

Navigation