Skip to main content
Log in

Semi-analytic approach to higher-order corrections in simple muonic bound systems: Vacuum polarization, self-energy and radiative-recoil

  • Regular Article
  • Atomic Physics
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

The current discrepancy of theory and experiment observed recently in muonic hydrogen necessitates a reinvestigation of all corrections to contribute to the Lamb shift in muonic hydrogen (μH), muonic deuterium (μD), the muonic \hbox{${}^3{\rm He}$} 3 He ion (denoted here as μ 3He+), as well as in the muonic \hbox{${}^4{\rm He}$} 4 He ion (μ 4He+). Here, we choose a semi-analytic approach and evaluate a number of higher-order corrections to vacuum polarization (VP) semi-analytically, while remaining integrals over the spectral density of VP are performed numerically. We obtain semi-analytic results for the second-order correction, and for the relativistic correction to VP. The self-energy correction to VP is calculated, including the perturbations of the Bethe logarithms by vacuum polarization. Subleading logarithmic terms in the radiative-recoil correction to the 2S–2P Lamb shift of order α()5 μ 3ln() / (m μ m N ) are also obtained. All calculations are nonperturbative in the mass ratio of orbiting particle and nucleus.

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

Access this article

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. P.J. Mohr, B.N. Taylor, D.B. Newell, Rev. Mod. Phys. 80, 633 (2008)

    Article  ADS  Google Scholar 

  2. J. Malenfant, Phys. Rev. D 36, 863 (1987)

    Article  ADS  Google Scholar 

  3. S.G. Karshenboim, U.D. Jentschura, V.G. Ivanov, G. Soff, Phys. Lett. B 424, 397 (1998)

    Article  ADS  Google Scholar 

  4. S.J. Brodsky, R.F. Lebed, Phys. Rev. Lett. 102, 213401 (2009)

    Article  ADS  Google Scholar 

  5. V.B. Berestetskii, E.M. Lifshitz, L.P. Pitaevskii, Quantum Electrodynamics, 2nd edn. (Pergamon Press, Oxford, UK, 1982)

  6. R. Pohl et al., Nature 466, 213 (2010)

    Article  ADS  Google Scholar 

  7. S.J. Brodsky, P.J. Mohr, in Structure and Collisions of Ions and Atoms, edited by I.A. Sellin (Springer, Berlin, 1978), pp. 3–67

  8. E. Borie, G.A. Rinker, Rev. Mod. Phys. 54, 67 (1982)

    Article  ADS  Google Scholar 

  9. U.D. Jentschura, Phys. Rev. A 64, 013403 (2001)

    Article  ADS  Google Scholar 

  10. U.D. Jentschura, Phys. Rev. A 84, 012505 (2011)

    Article  ADS  Google Scholar 

  11. K. Pachucki, Phys. Rev. A 53, 2092 (1996)

    Article  ADS  Google Scholar 

  12. A.P. Martynenko, Phys. Rev. A 76, 012505 (2007)

    Article  ADS  Google Scholar 

  13. U.D. Jentschura, Ann. Phys. (N.Y.) 326, 500 (2011)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. K. Pachucki, Ann. Phys. (N.Y.) 226, 1 (1993)

    Article  ADS  Google Scholar 

  15. K. Pachucki, J. Phys. B 31, 5123 (1998)

    Article  ADS  Google Scholar 

  16. E.E. Salpeter, Phys. Rev. 87, 328 (1952)

    Article  MATH  ADS  Google Scholar 

  17. G.W. Erickson, J. Phys. Chem. Ref. Data 6, 831 (1977)

    Article  ADS  Google Scholar 

  18. E. Borie, e-print arXiv:1103.1772 (physics.atom-ph)

  19. J. Zatorski, Ph.D. thesis, University of Warsaw, Warsaw, 2009 (unpublished)

  20. G. Pustovalov, Zh. Éksp. Teor. Fiz. 32, 1519 (1957), [JETP 5, 1234 (1957)]

    Google Scholar 

  21. S.G. Karshenboim, Can. J. Phys. 76, 169 (1998)

    ADS  Google Scholar 

  22. K. Pachucki, S.G. Karshenboim, J. Phys. B 28, L221 (1995)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to U. D. Jentschura.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jentschura, U.D., Wundt, B.J. Semi-analytic approach to higher-order corrections in simple muonic bound systems: Vacuum polarization, self-energy and radiative-recoil. Eur. Phys. J. D 65, 357–366 (2011). https://doi.org/10.1140/epjd/e2011-20338-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjd/e2011-20338-2

Keywords

Navigation