First high-precision mass measurements at PENTATRAP on highly charged Xe and Re ions

The high-precision Penning-trap mass spectrometer Pentatrap was designed to perform mass-ratio measurements of highly charged ions with relative uncertainties of 10${}^{-11}$. The unique features of the Pentatrap experiment are the external ion sources providing highly charged ions, the detection systems with single-ion sensitivity and especially the stack of five Penning traps, which allows simultaneous measurements of single ions in the traps. In the scope of this thesis, the first high-precision mass measurements with a relative precision partially below $\delta$m/m $\approx$ 10${}^{-11}$ were performed. As a first benchmark test, the mass differences of five xenon isotope pairs were determined. Comparison to the literature values led to an improvement of the uncertainty of the mass differences of a factor between 4 and 1700, in agreement with literature. In order to demonstrate the accuracy of Pentatrap, the binding energy of the 37${}^{th}$ electron in ${}^{132}$Xe was determined as a proof-of-principle measurement by determining the mass difference of ${}^{132}$Xe${}^{17+}$ and ${}^{132}$Xe${}^{18+}$. The agreement of the result with theory allows performing stringent tests of quantum electrodynamics using binding energies in ions with an even higher charge state in the future. Lastly, the discovery of metastable electronic states in highly charged rhenium and osmium ions by mass difference measurements, confirmed by theory, extends the applicability of Penning-trap mass spectrometry to tests of atomic structure theories and to the identification of long-lived excited states for a possible new generation of clocks using highly charged ions.