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  • Letter
  • Open Access

Self-energy correction to the energy levels of heavy muonic atoms

Natalia S. Oreshkina*

  • Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany

  • *Natalia.Oreshkina@mpi-hd.mpg.de
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Phys. Rev. Research 4, L042040 – Published 30 November, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L042040

Abstract

The fully relativistic, rigorous QED calculations of the self-energy correction to the fine-structure levels of heavy muonic atoms are reported, including rigorous predictions for excited states. We discuss nuclear model and parameter dependence for this contribution as well as numerical convergence issues. The presented results mostly agree with previously reported estimations, with some exceptions, including ones used for the determination of the nuclear root-mean-square radii, and underline the importance of rigorous QED calculations for the theoretical prediction of the spectra of muonic atoms.

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References (36)

  1. J. A. Wheeler, Some consequences of the electromagnetic interaction between μ−-mesons and nuclei, Rev. Mod. Phys. 21, 133 (1949).
  2. E. Borie and G. A. Rinker, The energy levels of muonic atoms, Rev. Mod. Phys. 54, 67 (1982).
  3. S. Devons and I. Duerdoth, Muonic atoms, in Advances in Nuclear Physics: Volume 2, edited by M. Baranger and E. Vogt (Springer US, Boston, MA, 1995), pp. 295–423.
  4. R. Pohl et al., The size of the proton, Nature (London) 466, 213 (2010).
  5. C. Piller, C. Gugler, R. Jacot-Guillarmod, L. A. Schaller, L. Schellenberg, H. Schneuwly, G. Fricke, T. Hennemann, and J. Herberz, Nuclear charge radii of the tin isotopes from muonic atoms, Phys. Rev. C 42, 182 (1990).
  6. L. Schaller, L. Schellenberg, A. Ruetschi, and H. Schneuwly, Nuclear charge radii from muonic x-ray transitions in beryllium, boron, carbon and nitrogen, Nucl. Phys. A 343, 333 (1980).
  7. T. Y. Saito, M. Niikura, T. Matsuzaki, H. Sakurai, M. Igashira, H. Imao, K. Ishida, T. Katabuchi, Y. Kawashima, M. K. Kubo, Y. Miyake, Y. Mori, K. Ninomiya, A. Sato, K. Shimomura, P. Strasser, A. Taniguchi, D. Tomono, and Y. Watanabe, Muonic x-ray measurement for the nuclear charge distribution: the case of stable palladium isotopes, arXiv:2204.03233.
  8. A. Antognini, N. Berger, T. E. Cocolios, R. Dressler, R. Eichler, A. Eggenberger, P. Indelicato, K. Jungmann, C. H. Keitel, K. Kirch, A. Knecht, N. Michel, J. Nuber, N. S. Oreshkina, A. Ouf, A. Papa, R. Pohl, M. Pospelov, E. Rapisarda, N. Ritjoho et al., Measurement of the quadrupole moment of Re185 and Re187 from the hyperfine structure of muonic X rays, Phys. Rev. C 101, 054313 (2020).
  9. W. Dey, P. Ebersold, H. Leisi, F. Scheck, H. Walter, and A. Zehnder, Nuclear spectroscopic ground-state quadrupole moments from muonic atoms: The quadrupole moment of Lu175, Nucl. Phys. A 326, 418 (1979).
  10. A. Rüetschi, L. Schellenberg, T. Phan, G. Piller, L. Schaller, and H. Schneuwly, Magnetic hyperfine structure in muonic Bi209, Nucl. Phys. A 422, 461 (1984).
  11. Y. Tanaka, R. M. Steffen, E. B. Shera, W. Reuter, M. V. Hoehn, and J. D. Zumbro, Precision Muonic-Atom Measurements of Nuclear Quadrupole Moments and the Sternheimer Effect in Rare-Earth Atoms, Phys. Rev. Lett. 51, 1633 (1983).
  12. P. Bergem, G. Piller, A. Rueetschi, L. A. Schaller, L. Schellenberg, and H. Schneuwly, Nuclear polarization and charge moments of Pb208 from muonic x rays, Phys. Rev. C 37, 2821 (1988).
  13. C. S. Wu and L. Wilets, Muonic atoms and nuclear structure, Annu. Rev. Nucl. Sci. 19, 527 (1969).
  14. N. Michel, N. S. Oreshkina, and C. H. Keitel, Theoretical prediction of the fine and hyperfine structure of heavy muonic atoms, Phys. Rev. A 96, 032510 (2017).
  15. A. S. M. Patoary and N. S. Oreshkina, Finite nuclear size effect to the fine structure of heavy muonic atoms, Eur. Phys. J. D 72, 54 (2018).
  16. N. Michel and N. S. Oreshkina, Higher-order corrections to the dynamic hyperfine structure of muonic atoms, Phys. Rev. A 99, 042501 (2019).
  17. N. Paul, G. Bian, T. Azuma, S. Okada, and P. Indelicato, Testing Quantum Electrodynamics with Exotic Atoms, Phys. Rev. Lett. 126, 173001 (2021).
  18. T. Okumura, T. Azuma, D. A. Bennett, P. Caradonna, I. Chiu, W. B. Doriese, M. S. Durkin, J. W. Fowler, J. D. Gard, T. Hashimoto, R. Hayakawa, G. C. Hilton, Y. Ichinohe, P. Indelicato, T. Isobe, S. Kanda, D. Kato, M. Katsuragawa, N. Kawamura, Y. Kino et al., Deexcitation Dynamics of Muonic Atoms Revealed by High-Precision Spectroscopy of Electronic K X Rays, Phys. Rev. Lett. 127, 053001 (2021).
  19. T. Beier, The gj factor of a bound electron and the hyperfine structure splitting in hydrogenlike ions, Phys. Rep. 339, 79 (2000).
  20. R. Barrett, Radiative corrections in muonic atoms, Phys. Lett. B 28, 93 (1968).
  21. A. Haga, Y. Horikawa, and H. Toki, Reanalysis of muonic Zr90 and Pb208 atoms, Phys. Rev. C 75, 044315 (2007).
  22. K. T. Cheng, W.-D. Sepp, W. R. Johnson, and B. Fricke, Self-energy corrections in heavy muonic atoms, Phys. Rev. A 17, 489 (1978).
  23. T. Q. Phan, P. Bergem, A. Rüetschi, L. A. Schaller, and L. Schellenberg, Nuclear polarization in muonic Zr90, Phys. Rev. C 32, 609 (1985).
  24. Y. Yamazaki, H. D. Wohlfahrt, E. B. Shera, M. V. Hoehn, and R. M. Steffen, Discrepancy between Theory and Experiment in Nuclear Polarization Corrections of Muonic Pb208, Phys. Rev. Lett. 42, 1470 (1979).
  25. I. A. Valuev, G. Colò, X. Roca-Maza, C. H. Keitel, and N. S. Oreshkina, Evidence Against Nuclear Polarization as Source of Fine-Structure Anomalies in Muonic Atoms, Phys. Rev. Lett. 128, 203001 (2022).
  26. G. E. Brown, J. S. Langer, and G. W. Schaefer, Lamb shift of a tightly bound electron I. Method, Proc. R. Soc. A 251, 92 (1959).
  27. A. M. Desiderio and W. R. Johnson, Lamb shift and binding energies of K electrons in heavy atoms, Phys. Rev. A 3, 1267 (1971).
  28. P. J. Mohr, Self-energy of the n=2 states in a strong Coulomb field, Phys. Rev. A 26, 2338 (1982).
  29. P. Indelicato and P. J. Mohr, Coordinate-space approach to the bound-electron self-energy, Phys. Rev. A 46, 172 (1992).
  30. V. A. Yerokhin and V. M. Shabaev, First-order self-energy correction in hydrogenlike systems, Phys. Rev. A 60, 800 (1999).
  31. N. S. Oreshkina, H. Cakir, B. Sikora, V. A. Yerokhin, V. Debierre, Z. Harman, and C. H. Keitel, Self-energy-corrected Dirac wave functions for advanced QED calculations in highly charged ions, Phys. Rev. A 101, 032511 (2020).
  32. N. J. Snyderman, Electron radiative self-energy of highly stripped heavy atoms, Ann. Phys. (NY) 211, 43 (1991).
  33. F. A. Parpia and A. K. Mohanty, Relativistic basis-set calculations for atoms with Fermi nuclei, Phys. Rev. A 46, 3735 (1992).
  34. V. M. Shabaev, I. I. Tupitsyn, V. A. Yerokhin, G. Plunien, and G. Soff, Dual Kinetic Balance Approach to Basis-Set Expansions for the Dirac Equation, Phys. Rev. Lett. 93, 130405 (2004).
  35. QUADPACK, http://www.netlib.org/quadpack/.
  36. The absolute value of the anomaly, i.e., the difference between the experiment and theory, is estimated to be about 20(8) eV for muonic zirconium [23], 150(20) eV for muonic tin [5], and 324(27) eV for muonic lead [12].

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Phys. Rev. Research 4, L042040– Published 30 November, 2022
  • Received 3 June 2022
  • Revised 5 August 2022
  • Accepted 28 September 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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