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Relativistic nuclear recoil effects in hyperfine splitting of hydrogenic systems

Jakub Hevler, Andrzej Maroń, Krzysztof Pachucki

Abstract

The finite nuclear mass $(Z\,α)^2\,m/M\,E_F$ correction to the hyperfine splitting in hydrogenic systems is calculated using a combined relativistic heavy particle and nonrelativistic quantum electrodynamics. The obtained results are in disagreement with previous calculations by Bodwin and Yennie [Phys. Rev. D {\bf 37}, 498 (1988)]. The comparison of improved theoretical predictions with the corresponding measurements in hydrogen reveals $5σ$ discrepancy, which indicates problems with the proton structure corrections.

Relativistic nuclear recoil effects in hyperfine splitting of hydrogenic systems

Abstract

The finite nuclear mass correction to the hyperfine splitting in hydrogenic systems is calculated using a combined relativistic heavy particle and nonrelativistic quantum electrodynamics. The obtained results are in disagreement with previous calculations by Bodwin and Yennie [Phys. Rev. D {\bf 37}, 498 (1988)]. The comparison of improved theoretical predictions with the corresponding measurements in hydrogen reveals discrepancy, which indicates problems with the proton structure corrections.
Paper Structure (14 sections, 125 equations, 2 tables)

This paper contains 14 sections, 125 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Leading order HFS
  3. Leading recoil correction to HFS
  4. Formulas for relativistic recoil correction to HFS
  5. High-energy part: HPQED
  6. Low-energy part: NRQED
  7. Results for relativistic recoil HFS
  8. Improved theory of hyperfine splitting in hydrogenic systems
  9. Specific difference $D_{21}$
  10. Summary and conclusions
  11. Spin algebra in $d$-dimensions
  12. Bound-state matrix elements in $d$-dimensions
  13. Integration of the high-energy part
  14. Atomic units in $d$-dimensions