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Abstract

In this thesis, several aspects of nuclear structure effects and corrections from quantum electrodynamics
(QED) in the spectra of hydrogen-like systems are investigated. The first part is
concerned with the structure of bound states between a muon and an atomic nucleus, so-called
muonic atoms. Here, precise calculations for transition energies and probabilities are presented,
using state-of-the-art numerical methods. QED corrections, hyperfine interactions, and the interaction
with atomic electrons were evaluated and finite nuclear size effects were incorporated
non-perturbatively. Furthermore, new methods for the calculation of higher-order corrections for
the hyperfine structure are presented, including a complete calculation of the second-order hyperfine
structure and leading-order vacuum polarization corrections for extended electric quadrupole
distributions inside the nucleus. In connection with recent x-ray spectroscopic measurements on
muonic atoms, the nuclear quadrupole moment of 185/75Re and 187/75Re is extracted. The second part
of this thesis is about the g factor of a bound electron and its dependence on the shape of the
nuclear charge distribution. A numerical, non-perturbative approach for the calculation of the
corresponding nuclear shape correction is presented and implications for the uncertainties of theoretical predictions are discussed. In particular, the model-uncertainty of the finite-nuclear-size
correction to the g factor can be reduced due to the more realistic model of the nuclear charge
distribution. Finally, calculations of finite-size and vacuum-polarization corrections to the g factor
of a muon bound to a 4/2He nucleus significantly contribute to the theoretical prediction on the
10⁻⁹ uncertainty level. As shown in an earlier work, an experimental value of the same accuracy could give access to an improved value of the muon’s mass or magnetic moment anomaly.