Vorschau

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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 Re-185 and Re-187 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 He-4 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.