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Abstract

During this work, microwave spectroscopy of the Zeeman and hyperfine structure of 9Be3+ was performed to measure its magnetic moments and zero-field splitting. To this end, the experimental Penning-trap setup, previously used for spectroscopy on 3He+, was upgraded, and the measurement techniques were improved. Most significantly, the implementation of phase-sensitive methods served a twofold improvement. Firstly, the statistical measurement uncertainty was reduced by a factor of 20. Secondly, they enabled the development of robust methods to characterize the fields and motion inside the trap, resulting in relative systematic uncertainties due to field imperfections well below 10−11. By measurement of nuclear-spin transitions in 9Be3+, its nuclear magnetic moment and zero-field splitting were determined with relative uncertainties of 0.6x10−9 and 4x10−12, respectively. Compared to previous determinations, the uncertainty of the nuclear magnetic moment of 9Be was improved by a factor 30 with only the magnetic moment of the proton being more precise. Further, a comparison with established measurements on 9Be+ enabled a crucial test of diamagnetic shielding parameters essential for transferring nuclear magnetic moments across different charge states. Additionally, electron-spin transitions were measured using the phase-sensitive measurement technique. The resonance centers could be determined with relative statistical uncertainties of 2x10−11 improving on state-of-the-art bound-electron �-factor measurements. These measurements pave the way towards a determination of the electron mass in atomic mass units with relative uncertainties below 10−11.