Wichmann-Kroll Correction in Muonic Atoms and Hydrogen-Like Electronic Ions: a Comparative Study of Two Methods

Abstract:

Wichmann-Kroll corrections are calculated in both hydrogen-like electronic ions and muonic systems ( — ) using two independent methods. The Gaussian finite basis set approach, enhanced with dual basis construction, analytical large-distance corrections, and  -spline representations, provides computational efficiency. The Green function method, based on semi-analytical construction from Dirac solutions with Fermi nuclear charge distributions, offers higher systematic accuracy and freedom from basis-dependent artifacts. Results are consistent with the literature values, providing reliable reference data for precision spectroscopy of exotic atoms.

Z. A. Mandrykina, Z. Sun, N. S. Oreshkina, „Wichmann-Kroll Correction in Muonic Atoms
and Hydrogen-Like Electronic Ions: a Comparative Study of Two Methods“, 30. Jan. 2026,
arXiv:2601.22979 (2026).

https://arxiv.org/abs/2601.22979

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