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#### Relativistic theory of nuclear structure effects in heavy atomic systems

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##### Citation

Michel, N. (2019). Relativistic theory of nuclear structure effects in heavy atomic systems. PhD Thesis, Ruprecht-Karls-Universität, Heidelberg.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002B-A5A0-1

##### 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

(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.