Investigation of atomic nuclei via electronic processes

In atomic physics, nuclei are often described as a point-like charges with an infinite mass that binds the electrons. With more and more precise experimental techniques, however, this approximation is no longer sufficient and it is necessary to develop a better theoretical understanding of the ways atomic nuclei interact with the electron shell. We do observe for example small shifts in the lines of spectra of different isotopes of the same atomic species. In this thesis, we present calculations for these isotope shifts and use them to derive the difference between the nuclear charge radii of two thorium isotopes, ${}^{232}$Th and ${}^{229}$Th as well as ${}^{229}$Th and the isomeric state ${}^{229m}$Th. These results are of particular interest for the development of a future nuclear clock and coherent high-energy light sources. Moreover, we discuss precise isotope shift calculations for singly charged barium and compare them with a recent experiment. We motivate the relevance of such studies for the search for physics beyond the Standard Model. Spectral lines, however, do not only shift but also split due to the non-point-like nature of atomic nuclei. From the spectroscopy of this hyperfine splitting, it is possible to extract the multipole moments of the nuclear electromagnetic field. As a part of this thesis, we present the first value of the nuclear magnetic dipole moment of the ${}^{229m}$Th nuclear isomer that does not rely on previous calculations or measurements. Having extracted several important properties of the ${}^{229}$Th nucleus and the isomer ${}^{229m}$Th using atomic theory we invert our view in the second part of this thesis. Namely, we want to use processes in the electron shell to populate the ${}^{229m}$Th isomeric state. Preparatory to our calculations for the actual excitation of the isomer, we discuss the atomic structure of thorium. Of particular experimental interest is the level structure of singly charged thorium. In a recent study, we show the results of atomic structure calculations that help to interpret measured thorium spectra and can be used to estimate the probability of a nuclear excitation via the electron shell in this system. A deeper and more accurate discussion is performed for the comparably simple triply charged thorium ion. This study helps to test the various approximations necessary to discuss systems with a more complicated electronic structure. Bringing everything together the final publication presented in this thesis proposes an experimental setup to excite the ${}^{229}$Th nucleus in a controlled way depending on the yet to be found energy of the nuclear isomeric state. This method is currently applied in an experiment at the German National Metrology Institute.