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Two-body corrections to the g factors of the bound muon and nucleus in light muonic atoms

Abstract

A nonrelativistic (NR) theory of recoil corrections to the magnetic moments of bound particles is revisited. A number of contributions can be described within an NR theory with the help of various potentials. We study those potential-type contributions for two-body atomic systems. We have developed an approach, that allows us to find the g factor for an electron or muon in a two-body bound system for an arbitrary electrostatic interaction together with the m/M recoil corrections, as well as the binding corrections to the g factor of the nucleus. We focus our attention on light muonic two-body atoms, where the recoil effects are enhanced. Both mentioned kinds of contributions have been previously known only for the pure Coulomb effects. We have applied the here-obtained master equations to a few particular cases of perturbations of the Coulomb potential. In particular, the results on the recoil corrections to the finite-nuclear-size (FNS) and Uehling-potential contributions to the g factor of the bound muon are obtained. The Uehling-potential and FNS contributions to the g factor of the bound nucleus have been found as well together with the related recoil corrections. We have generalized the results for the case of the g factor of a bound muon in a three-body atomic system consisting of an electron, a muon, and a spinless nucleus.

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References

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

    Google Scholar 

  2. T.N. Mamedov, K.I. Gritsay, A.V. Stoykov, Phys. Rev. A 75, 054501 (2007)

    ADS  Google Scholar 

  3. T.N. Mamedov, A.S. Baturin, D. Herlach, O.D. Maslov, A.V. Stokov, U. Zimmermann, JETP Lett. 76, 693 (2002)

    ADS  Google Scholar 

  4. T.N. Mamedov, D. Herlach, K.I. Gritsaj, O. Korman, J. Major, A.V. Stoikov, U. Zimmermann, JETP 93, 941 (2001)

    ADS  Google Scholar 

  5. J.H. Brewer, Hyperfine Interact. 17–19, 873 (1984)

    ADS  Google Scholar 

  6. T. Yamazaki, S. Nagamiya, O. Hashimoto, K. Nagamine, K. Nakai, K. Sugimoto, K.M. Crowe, Phys. Lett. B 53, 117 (1974)

    ADS  Google Scholar 

  7. D.P. Hutchinson, J. Menes, G. Shapiro, A.M. Patlach, Phys. Rev. 131, 1362 (1963)

    ADS  Google Scholar 

  8. K.-N. Huang, V.W. Hughes, Phys. Rev. A 20, 706 (1979)

    ADS  Google Scholar 

  9. E. Borie, Z. Phys. A 291, 107 (1979)

    ADS  Google Scholar 

  10. S.D. Lakdawala, P.J. Mohr, Phys. Rev. A 22, 1572 (1980)

    ADS  Google Scholar 

  11. M.Ya. Amusia, M.Ju. Kuchiev, V.L. Yakhontov, J. Phys. B: At., Mol. Phys. 16, L71 (1983)

    ADS  Google Scholar 

  12. V.L. Yakhontov, M.Ya. Amusia, J. Phys. B: At., Mol. Opt. Phys. 27, 3743 (1994)

    ADS  Google Scholar 

  13. S.G. Karshenboim, V.G. Ivanov, M. Amusia, Phys. Rev. A 91, 032510 (2015)

    ADS  Google Scholar 

  14. S.G. Karshenboim, V.G. Ivanov, V.I. Korobov, Phys. Rev. A 97, 022504 (2018)

    ADS  Google Scholar 

  15. S.G. Karshenboim, R.N. Lee, A.I. Milstein, Phys. Rev. A 72, 042101 (2005)

    ADS  Google Scholar 

  16. S.G. Karshenboim, V.G. Ivanov, Phys. Rev. A 97, 022506 (2018)

    ADS  Google Scholar 

  17. H. Grotch, R.A. Hegstrom, Phys. Rev. A 4, 59 (1970)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  19. R.N. Faustov, Phys. Lett. B 33, 422 (1970)

    ADS  Google Scholar 

  20. F.E. Close, H. Osborn, Phys. Lett. B 34, 400 (1971)

    ADS  Google Scholar 

  21. M.I. Eides, H. Grotch, Ann. Phys. 260, 191 (1997)

    ADS  Google Scholar 

  22. K. Pachucki, Phys. Rev. 78, 012504 (2008)

    ADS  Google Scholar 

  23. M.I. Eides, T.J.S. Martin, Phys. Rev. Lett. 105, 100402 (2010)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  25. S.G. Karshenboim, V.G. Ivanov, V.M. Shabaev, Can. J. Phys. 79, 81 (2001)

    ADS  Google Scholar 

  26. S.G. Karshenboim, V.G. Ivanov, V.M. Shabaev, JETP 93, 477 (2001)

    ADS  Google Scholar 

  27. K. Pachucki, A. Czarnecki, U.D. Jentschura, V.A. Yerokhin, Phys. Rev. A 72, 022108 (2005)

    ADS  Google Scholar 

  28. S.G. Karshenboim, V.G. Ivanov, Phys. Lett. B 786, 485 (2018)

    ADS  Google Scholar 

  29. A.B. Mickelwait, H.C. Corben, Phys. Rev. 96, 1145 (1954)

    ADS  Google Scholar 

  30. G.E. Pustovalov, Sov. Phys. JETP 5, 1234 (1957)

    Google Scholar 

  31. D. Eiras, J. Soto, Phys. Lett. B 491, 101 (2000)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  33. S.G. Karshenboim, JETP 89, 850 (1999)

    ADS  Google Scholar 

  34. S.G. Karshenboim, V.G. Ivanov, E.Yu. Korzinin, Eur. Phys. J. D 39, 351 (2006)

    ADS  Google Scholar 

  35. EYu Korzinin, V.G. Ivanov, S.G. Karshenboim, Eur. Phys. J. D 41, 1 (2007)

    ADS  Google Scholar 

  36. A.P. Martynenko, Phys. Lett. B 602, 73 (2004)

    ADS  Google Scholar 

  37. P.A. Souder, D.E. Casperson, T.W. Crane, V.W. Hughes, D.C. Lu, H. Orth, H.W. Reist, M.H. Yam, G. Zu Putlitz, Phys. Rev. Lett. 34, 1417 (1975)

    ADS  Google Scholar 

  38. C.J. Gardner, A. Badertscher, W. Beer, P.R. Bolton, P.O. Egan, M. Gladisch, M. Greene, V.W. Hughes, D.C. Lu, F.G. Mariam, P.A. Souder, Phys. Rev. Lett. 48, 1168 (1982)

    ADS  Google Scholar 

  39. S.G. Karshenboim, V.G. Ivanov, Phys. Rev. A 94, 062515 (2016)

    ADS  Google Scholar 

  40. N.C. Pyper, Z.C. Zhang, Mol. Phys. 97, 391 (1997)

    ADS  Google Scholar 

  41. E.A. Moore, Mol. Phys. 97, 375 (1997)

    ADS  Google Scholar 

  42. S.G. Karshenboim, V.G. Ivanov, Can. J. Phys. 80, 1305 (2002)

    ADS  Google Scholar 

  43. V.G. Ivanov, S.G. Karshenboim, R.N. Lee, Phys. Rev. 79, 012512 (2009)

    ADS  Google Scholar 

  44. A. Yelkhovsky, https://arXiv:hep-ph/0108091

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

    ADS  Google Scholar 

  46. V.M. Shabaev, J. Phys. B 26, 1103 (1993)

    ADS  Google Scholar 

  47. S.G. Karshenboim, E.Y. Korzinin, V.A. Shelyuto, V.G. Ivanov, J. Phys. Chem. Ref. Data 44, 031202 (2015)

    ADS  Google Scholar 

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Correspondence to Savely G. Karshenboim.

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Karshenboim, S.G., Ivanov, V.G. Two-body corrections to the g factors of the bound muon and nucleus in light muonic atoms. Eur. Phys. J. D 73, 210 (2019). https://doi.org/10.1140/epjd/e2019-100072-7

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Keywords

  • Atomic Physics