Skip to main content
SpringerLink
Log in

Energy Interval 1S–2S in Muonic Hydrogen and Helium

  • NUCLEI, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

The interval of a large structure of energy spectrum (1S–2S) in muonic helium and hydrogen is calculated using a quasi-potential method in quantum electrodynamics. Corrections of the order α4, α5, and α6 determined by relativistic effects, vacuum polarization effects, nuclear structure and recoil, as well as by combined corrections including those listed above, are taken into account. The nuclear structure effects are expressed in terms of the charge radius of nuclei in the case of the one-photon interaction and electromagnetic form factors of nuclei in the case of the two-photon interaction. Numerical values obtained for the (1S–2S) interval can be used for comparison with future experimental data and for more accurate determination of the charge radii of nuclei.

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

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.
Fig. 14.

Similar content being viewed by others

REFERENCES

  1. A. Antognini et al., Science (Washington, DC, U. S.) 339, 417 (2013).

    Article  ADS  Google Scholar 

  2. A. Antognini, F. Kottmann, F. Biraben, et al., Ann. Phys. 331, 127 (2013).

    Article  ADS  Google Scholar 

  3. R. Pohl et al., Science (Washington, DC, U. S.) 353, 669 (2016).

    Article  ADS  Google Scholar 

  4. M. Diepold, B. Franke, J. J. Krauth, et al., Ann. Phys. 396, 220 (2018).

    Article  ADS  Google Scholar 

  5. R. Pohl, J. Phys. Soc. Jpn. 85, 091003 (2016).

    Article  ADS  Google Scholar 

  6. A. E. Dorokhov et al., Europhys. J. Web Conf. 191, 04001 (2018).

    Article  Google Scholar 

  7. S. G. Karshenboim et al., J. Phys. Chem. Ref. Data 44, 031202 (2015).

    Article  ADS  Google Scholar 

  8. C. J. Parthey et al., Phys. Rev. Lett. 107, 203001 (2011).

    Article  ADS  Google Scholar 

  9. C. J. Parthey et al., Phys. Rev. Lett. 104, 233001 (2010).

    Article  ADS  Google Scholar 

  10. I. Fan et al., Phys. Rev. A 89, 032513 (2014).

    Article  ADS  Google Scholar 

  11. M. I. Eides, H. Grotch, and V. A. Shelyuto, Phys. Rep. 342, 62 (2001);

    Article  Google Scholar 

  12. M. I. Eides, H. Grotch, and V. A. Shelyuto, Theory of Light Hydrogenic Bound States (Springer, Berlin, Heidelberg, New York, 2007).

    MATH  Google Scholar 

  13. P. Crivelli, Hyperfine Interact. 239, 49 (2018).

    Article  ADS  Google Scholar 

  14. M. Herrmann et al., Phys. Rev. A 79, 052505 (2009).

    Article  ADS  Google Scholar 

  15. R. K. Altmann et al., Phys. Rev. Lett. 117, 173201 (2016).

    Article  ADS  Google Scholar 

  16. S. Tomas et al., Ann. Phys. 531, 1800363 (2019).

    Article  Google Scholar 

  17. P. J. Mohr, D. B. Newell, and B. N. Taylor, Rev. Mod. Phys. 88, 035009 (2016).

    Article  ADS  Google Scholar 

  18. A. P. Martynenko, J. Exp. Theor. Phys. 101, 1021 (2005).

    Article  ADS  Google Scholar 

  19. A. A. Krutov, A. P. Martynenko, G. A. Martynenko, and R. N. Faustov, J. Exp. Theor. Phys. 120, 73 (2015).

    Article  ADS  Google Scholar 

  20. K. Pachucki, Phys. Rev. A 54, 1994 (1996).

    Article  ADS  Google Scholar 

  21. E. Borie, Ann. Phys. 327, 733 (2012).

    Article  ADS  Google Scholar 

  22. J. L. Friar and G. L. Payne, Phys. Rev. C 72, 014002 (2005).

    Article  ADS  Google Scholar 

  23. C. E. Carlson, M. Gorchtein, and M. Vanderhaeghen, Phys. Rev. A 89, 022504 (2014).

    Article  ADS  Google Scholar 

  24. C. Peset and A. Pineda, J. High Energy Phys. 1704, 060 (2017).

  25. R. N. Faustov et al., Phys. Rev. A 90, 012520 (2014).

    Article  ADS  Google Scholar 

  26. R. N. Faustov et al., Phys. Lett. B 733, 354 (2014).

    Article  ADS  Google Scholar 

  27. A. A. Krutov and A. P. Martynenko, Phys. Rev. A 84, 052514 (2011).

    Article  ADS  Google Scholar 

  28. E. Yu. Korzinin et al., Phys. Rev. A 97, 012514 (2018).

    Article  ADS  Google Scholar 

  29. S. G. Karshenboim et al., Phys. Rev. A 81, 060501 (2010).

    Article  ADS  Google Scholar 

  30. A. E. Dorokhov et al., Phys. Rev. A 98, 042501 (2018).

    Article  ADS  Google Scholar 

  31. C. Ji, S. Bacca, N. Barnea, et al., J. Phys. G 45, 093002 (2018).

    Article  ADS  Google Scholar 

  32. B. Franke et al., Eur. Phys. J. D 71, 341 (2017).

    Article  ADS  Google Scholar 

  33. O. Tomalak, Eur. Phys. J. C 77, 858 (2017).

    Article  ADS  Google Scholar 

  34. R. N. Faustov et al., Europhys. J. Web Conf. 204, 05005 (2019).

    Article  Google Scholar 

  35. K. Pachucki and S. G. Karshenboim, J. Phys. B: At. Mol. Opt. Phys. 28, L22 (1995).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  37. G. Källen and A. Sabry, Mat. Fys. Medd. Dan. Vid. Selesk. 29 (17), 1 (1955); in Portrait of Gunnar Källen, Ed. by C. Jarlskog (Springer, Switzerland, 2014), p. 555.

    Google Scholar 

  38. T. Kinoshita and M. Nio, Phys. Rev. Lett. 82, 3240 (1999).

    Article  ADS  Google Scholar 

  39. T. Kinoshita and M. Nio, Phys. Rev. D 60, 053008 (1999).

    Article  ADS  Google Scholar 

  40. T. Kinoshita and W. B. Lindquist, Phys. Rev. D 27, 853 (1983).

    Article  ADS  Google Scholar 

  41. P. A. Baikov and D. J. Broadhurst, in New Computing Techniques in Physics Research IV, Ed. by B. Denby and D. Perrei-Gallix (World Scientific, Singapore, 1995), p. 167.

    Google Scholar 

  42. R. N. Faustov, A. L. Kataev, S. A. Larin, and V. V. Starshenko, Phys. Lett. B 254, 241 (1991).

    Article  ADS  Google Scholar 

  43. D. J. Broadhurst, A. L. Kataev, and O. V. Tarasov, Phys. Lett. B 298, 445 (1993).

    Article  ADS  Google Scholar 

  44. A. H. Hoang, J. H. Kühn, and T. Teubner, Nucl. Phys. B 452, 173 (1995).

    Article  ADS  Google Scholar 

  45. K. G. Chetyrkin et al., Phys. Lett. B 384, 233 (1996).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  47. H. F. Hameka, J. Chem. Phys. 47, 2728 (1967).

    Article  ADS  Google Scholar 

  48. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Fizmatlit, Moscow, 2008; Pergamon, New York, 1977, 3rd ed.).

  49. I. Angeli and K. P. Marinova, At. Data Nucl. Data Tabl. 99, 69 (2013).

    Article  ADS  Google Scholar 

  50. R. N. Faustov and A. P. Martynenko, Phys. Rev. A 67, 052506 (2003).

    Article  ADS  Google Scholar 

  51. J. J. Kelly, Phys. Rev. C 70, 068202 (2004).

    Article  ADS  Google Scholar 

  52. D. Abbott, A. Ahmidouch, H. Anklin, et al., Eur. Phys. J. A 7, 421 (2000).

    Article  ADS  Google Scholar 

  53. R. N. Faustov, A. P. Martynenko, F. A. Martynenko, and V. V. Sorokin, Phys. Lett. B 775, 79 (2017).

    Article  ADS  Google Scholar 

  54. J. R. Sapirstein and D. R. Yennie, in Quantum Electrodynamics, Ed. by T. Kinoshita (World Scientific, Singapore, 1990), p. 560.

    Google Scholar 

  55. M. I. Eides and H. Grotch, Phys. Rev. A 55, 3351 (1997).

    Article  ADS  Google Scholar 

  56. K. Pachucki and H. Grotch, Phys. Rev. A 51, 1854 (1995).

    Article  ADS  Google Scholar 

  57. V. M. Shabaev, Sov. J. Theor. Math. Phys. 63, 588 (1985).

    Article  Google Scholar 

  58. A. S. Elkhovskii, J. Exp. Theor. Phys. 83, 230 (1996).

    ADS  Google Scholar 

  59. V. A. Yerokhin and V. M. Shabaev, Phys. Rev. Lett. 115, 233002 (2015).

    Article  ADS  Google Scholar 

  60. V. A. Yerokhin and V. M. Shabaev, J. Phys. Chem. Ref. Data 44, 033103 (2015).

    Article  ADS  Google Scholar 

  61. J. L. Friar, Ann. Phys. 122, 151 (1979).

    Article  ADS  Google Scholar 

  62. R. Barbieri, M. Caffo, and E. Remiddi, Nuovo Cim. Lett. 7, 60 (1973).

    Article  Google Scholar 

  63. E. Borie, Z. Phys. A 302, 187 (1981).

    Article  ADS  Google Scholar 

  64. J. L. Friar, J. Martorell, and D. W. L. Sprung, Phys. Rev. A 59, 4061 (1999).

    Article  ADS  Google Scholar 

  65. A. P. Martynenko and R. N. Faustov, Phys. At. Nucl. 64, 1282 (2001).

    Article  Google Scholar 

  66. E. Yu. Korzinin et al., Phys. Rev. A 98, 062519 (2018).

    Article  ADS  Google Scholar 

  67. S. G. Karshenboim, E. Yu. Korzinin, V. G. Ivanov, and V. A. Shelyuto, JETP Lett. 92, 8 (2010).

    Article  ADS  Google Scholar 

  68. A. E. Dorokhov, A. P. Martynenko, F. A. Martynenko, and A. E. Radzhabov, Europhys. J. Web Conf. 204, 05008 (2019).

    Article  Google Scholar 

  69. K. Pachucki, Phys. Rev. Lett. 106, 193007 (2011).

    Article  ADS  Google Scholar 

  70. J. L. Friar, Phys. Rev. C 88, 034003 (2013).

    Article  ADS  Google Scholar 

  71. P. Cancio Pastor et al., Phys. Rev. Lett. 108, 143001 (2012).

    Article  ADS  Google Scholar 

  72. R. van Rooij et al., Science (Washington, DC, U. S.) 333, 196 (2011).

    Article  ADS  Google Scholar 

Download references

Funding

This work was supported by the Russian Science Foundation (project no. 18-12-00128) and the Russian Foundation for basic research (project no. 18-32-00023) (F.A.M.).

Author information

Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Moscow oblast, Russia

    A. E. Dorokhov

  2. Samara National Research University, 443011, Samara, Russia

    A. P. Martynenko, F. A. Martynenko & O. S. Sukhorukova

  3. Institute of Educational Informatics, Federal Research Center “Informatics and Management,” Russian Academy of Sciences, 119333, Moscow, Russia

    R. N. Faustov

Authors
  1. A. E. Dorokhov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. P. Martynenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. A. Martynenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. O. S. Sukhorukova
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. R. N. Faustov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. E. Dorokhov, A. P. Martynenko, F. A. Martynenko or R. N. Faustov.

Additional information

Translated by N. Wadhwa

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dorokhov, A.E., Martynenko, A.P., Martynenko, F.A. et al. Energy Interval 1S–2S in Muonic Hydrogen and Helium. J. Exp. Theor. Phys. 129, 956–972 (2019). https://doi.org/10.1134/S1063776119110098

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776119110098

Search

Navigation