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The two-loop self-energy: diagrams in the coordinate-momentum representation

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Abstract

The paper reports a technique of evaluation of Feynman diagrams in the mixed coordinate-momentum representation. The technique is employed for a recalculation of the two-loop self-energy correction for the ground state of hydrogen-like ions with the nuclear charge numbers Z=10-30. The numerical accuracy is considerably improved as compared to the previous calculations. The higher-order (in Zα) remainder function is inferred from the numerical results and extrapolated towards Z=0 and 1. The extrapolated value for hydrogen is consistent (but still not in perfect agreement) with the analytical result obtained within the perturbative approach.

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References

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

    Article  ADS  Google Scholar 

  2. K. Pachucki, Phys. Rev. A 63, 042503 (2001)

    Article  ADS  Google Scholar 

  3. K. Pachucki, U.D. Jentschura, Phys. Rev. Lett. 91, 113005 (2003)

    Article  ADS  Google Scholar 

  4. A. Czarnecki, U.D. Jentschura, K. Pachucki, Phys. Rev. Lett. 95, 180404 (2005)

    Article  ADS  Google Scholar 

  5. U.D. Jentschura, A. Czarnecki, K. Pachucki, Phys. Rev. A 72, 062102 (2005)

    Article  ADS  Google Scholar 

  6. M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004)

    Article  ADS  Google Scholar 

  7. I. Draganić, J.R. Crespo López-Urrutia, R. DuBois, S. Fritzsche, V.M. Shabaev, R.S. Orts, I.I. Tupitsyn, Y. Zou, J. Ullrich, Phys. Rev. Lett. 91, 183001 (2003)

    Article  ADS  Google Scholar 

  8. C. Brandau et al., Phys. Rev. Lett. 91, 073202 (2003)

    Article  ADS  Google Scholar 

  9. P. Beiersdorfer, H. Chen, D.B. Thorn, E. Träbert, Phys. Rev. Lett. 95, 233003 (2005)

    Article  ADS  Google Scholar 

  10. S.W. Epp et al., Phys. Rev. Lett. 98, 183001 (2007)

    Article  ADS  Google Scholar 

  11. E.H. Wichmann, N.M. Kroll, Phys. Rev. A 101, 843 (1956)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. P.J. Mohr, Ann. Phys. (NY) 88, 26 (1974)

    Article  ADS  Google Scholar 

  13. P.J. Mohr, Ann. Phys. (NY) 88, 52 (1974)

    Article  ADS  Google Scholar 

  14. A.M. Desiderio, W.R. Johnson, Phys. Rev. A 3, 1267 (1971)

    Article  ADS  Google Scholar 

  15. S. Mallampalli, J. Sapirstein, Phys. Rev. A 57, 1548 (1998)

    Article  ADS  Google Scholar 

  16. V.A. Yerokhin, V.M. Shabaev, Phys. Rev. A 64, 062507 (2001)

    Article  ADS  Google Scholar 

  17. V.A. Yerokhin, P. Indelicato, V.M. Shabaev, Phys. Rev. Lett. 91, 073001 (2003)

    Article  ADS  Google Scholar 

  18. V.A. Yerokhin, P. Indelicato, V.M. Shabaev, Eur. Phys. J. D 25, 203 (2003)

    Article  ADS  Google Scholar 

  19. V.A. Yerokhin, P. Indelicato, V.M. Shabaev, Phys. Rev. A 71, R040101 (2005)

    Article  ADS  Google Scholar 

  20. V.A. Yerokhin, P. Indelicato, V.M. Shabaev, Phys. Rev. Lett. 97, 253004 (2006)

    Article  ADS  Google Scholar 

  21. V.A. Yerokhin, Phys. Rev. A 80, 040501(R) (2009)

    Article  ADS  Google Scholar 

  22. V.A. Yerokhin, P. Indelicato, V.M. Shabaev, Phys. Rev. A 77, 062510 (2008)

    Article  ADS  Google Scholar 

  23. V.A. Yerokhin, V.M. Shabaev, Phys. Rev. A 60, 800 (1999)

    Article  ADS  Google Scholar 

  24. M.E. Rose, Relativistic Electron Theory (John Wiley & Sons, New York, 1961)

    MATH  Google Scholar 

  25. W.R. Johnson, S.A. Blundell, J. Sapirstein, Phys. Rev. A 37, 2764 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  26. D.A. Varshalovich, A.N. Moskalev, V.K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapure, 1988)

    Google Scholar 

  27. V.A. Yerokhin, A.N. Artemyev, T. Beier, G. Plunien, V.M. Shabaev, G. Soff, Phys. Rev. A 60, 3522 (1999)

    Article  ADS  Google Scholar 

  28. T. Appelquist, S.J. Brodsky, Phys. Rev. A 2, 2293 (1970)

    Article  ADS  Google Scholar 

  29. K. Pachucki, Phys. Rev. Lett. 72, 3154 (1994)

    Article  ADS  Google Scholar 

  30. M.I. Eides, V.A. Shelyuto, Phys. Rev. A 52, 954 (1995)

    Article  ADS  Google Scholar 

  31. S.G. Karshenboim, Zh. Eksp. Teor. Fiz. 103, 1105 (1993) [JETP 76, 541 (1993)]

    Google Scholar 

  32. V.A. Yerokhin, Phys. Rev. Lett. 86, 1990 (2001)

    Article  ADS  Google Scholar 

  33. P.J. Mohr, Phys. Rev. Lett. 34, 1050 (1975)

    Article  ADS  Google Scholar 

  34. C. Schwob, L. Jozefowski, B. de Beauvoir, L. Hilico, F. Nez, L. Julien, F. Biraben, O. Acef, J.J. Zondy, A. Clairon, Phys. Rev. Lett. 82, 4960 (1999)

    Article  ADS  Google Scholar 

  35. P.J. Mohr, G. Plunien, G. Soff, Phys. Rep. 293, 227 (1998)

    Article  Google Scholar 

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Authors and Affiliations

  1. Center for Advanced Studies, St. Petersburg State Polytechnical University, Polytekhnicheskaya 29, St. Petersburg, 195251, Russia

    V. A. Yerokhin

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  1. V. A. Yerokhin
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Correspondence to V. A. Yerokhin.

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Yerokhin, V. The two-loop self-energy: diagrams in the coordinate-momentum representation. Eur. Phys. J. D 58, 57–68 (2010). https://doi.org/10.1140/epjd/e2010-00089-4

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  • DOI: https://doi.org/10.1140/epjd/e2010-00089-4

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