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Theory Framework for Medium-Mass Muonic Atoms

S. Rathi, I. A. Valuev, Z. Sun, M. Heines, P. Indelicato, B. Ohayon, N. S. Oreshkina

Abstract

We present a state-of-the-art theoretical approach for computing bound-state energies in muonic atoms, incorporating improved quantum electrodynamics effects and nuclear polarization corrections with a systematic assessment of theoretical uncertainties. Our approach is based on a combination of the $Zα$-expansion and the all-order formalism (Furry picture) optimized for the medium-mass range $(3 \leq Z \lesssim 30)$ and guided by the accuracy requirements of modern muonic spectroscopy experiments. These calculations are directly relevant to ongoing and forthcoming measurements aimed at extracting nuclear structure parameters, particularly nuclear charge radii, with unprecedented precision.

Theory Framework for Medium-Mass Muonic Atoms

Abstract

We present a state-of-the-art theoretical approach for computing bound-state energies in muonic atoms, incorporating improved quantum electrodynamics effects and nuclear polarization corrections with a systematic assessment of theoretical uncertainties. Our approach is based on a combination of the -expansion and the all-order formalism (Furry picture) optimized for the medium-mass range and guided by the accuracy requirements of modern muonic spectroscopy experiments. These calculations are directly relevant to ongoing and forthcoming measurements aimed at extracting nuclear structure parameters, particularly nuclear charge radii, with unprecedented precision.
Paper Structure (13 sections, 15 equations, 4 figures, 5 tables)

This paper contains 13 sections, 15 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. All order approach
  3. QED corrections
  4. Relativistic recoil
  5. Electron screening
  6. Nuclear polarization
  7. New QED corrections specific to Medium-$Z$
  8. Recoil Correction to VP
  9. Corrections calculated in the nonrelativistic approximation
  10. Second-order recoil
  11. Recoil Correction to SE
  12. SE-eVP
  13. Conclusion

Figures (4)

  • Figure 1: Comparison of Bohr-model of the $1s$ orbital radius (squares) and nuclear charge radii (circles) from angeli2013table for nuclei across the periodic table.
  • Figure 2: Corrections currently unknown in the NRQED and all-order approaches that are relevant to the $1s$ binding energies of muonic atoms, shown relative to the finite nuclear size contribution and compared with current experimental accuracy goals.
  • Figure 3: Feynman diagram representation of the QED contributions considered in this work. (a) One-loop Uehling VP (VP$_{11}$), (b) Hadronic VP (hVP$_{11}$), (c) Källén-Sabry VP (eVP$_{11}^2$), (d) Wichmann-Kroll VP (VP$_{13}$), (e) Self-Energy (SE), (f) Interlinked SE-VP (SE-eVP). For illustrative purposes, only a single representative diagram is shown for each contribution class.
  • Figure 4: Leading-order NP as effective self-energy. The shaded circle represents the NP insertion.