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Abstract

The ground-state hyperfine splitting of 3He+ in a strong external magnetic field is investigated in a Penning-trap setup that was newly constructed in the context of this thesis. The nuclear g-factor of 3He+ g'_I = −4.255 099 606 9(30)stat(17)sys was measured for the first time directly. This result is one order of magnitude more precise than previous indirect determinations and provides a calibration for 3He NMR probes via the accurately calculated diamagnetic shielding parameters of 3He+ and atomic 3He. The experimental result for the bound electron g-factor of 3He+ g_e = −2.002 177 415 79(34)stat(30)sys is consistent with the state-of-the-art theoretical value. Furthermore, the zero-field hyperfine splitting E_HFS= −8 665 649 865.77(26)stat(1)sys Hz was extracted from the measurement and allows to calculate the Zemach radius r_Z = 2.608(24) fm, which characterizes the electric and magnetic form factors of the nucleus.