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arXiv · 2502.09455

Recoil corrections with finite nuclear size in hydrogenic systems

Krzysztof Pachucki·Vojtěch Patkóš·Vladimir A. Yerokhin
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Abstract

Formulas for the combined nuclear-recoil and finite-nuclear-size effects of order $(Z\,α)^5$ and $(Z\,α)^6$ are derived without any expansion in the nuclear charge radius $r_C$, making them applicable to both electronic and muonic atoms. The obtained results are particularly relevant for high-precision determinations of root-mean-square charge radii from muonic atom spectroscopy. We demonstrate that calculations of the atomic isotope shift based on the widely used Breit approximation give rise to an unphysical nuclear-size contribution that is linear in the nuclear charge radius $r_C$ at order $(Z\,α)^5$. This spurious term vanishes in a full QED treatment, leaving the correct contribution quadratic in $r_C$. For electronic atoms, this quadratic term is significantly smaller than the spurious linear contribution.

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Krzysztof Pachucki, Vojtěch Patkóš, Vladimir A. Yerokhin. 2025-03-28. Recoil corrections with finite nuclear size in hydrogenic systems. https://arxiv.org/abs/2502.09455

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