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Abstract

Within this thesis the g-factor of the valence electron bound in lithiumlike silicon ²⁸Si¹¹⁺ has been measured with a relative precision of δg/g = 1.1 • 10⁻⁹. The determination of the g-factor is based on a measurement of the free cyclotron and the Larmor frequency of a single ion stored in a triple Penning trap setup. The free cyclotron frequency is determined from the non-destructive measurement of the eigenfrequencies of the trapped ion. To determine the Larmor frequency the continuous Stern-Gerlach effect is employed, which couples the spin orientation to the axial mode. Thus, a spin flip manifests as a tiny frequency jump of the axial frequency. The implementation of dedicated stabilization systems for temperature and magnetic field minimized environmental influences on the ion. The presented result g_exp= 2.000 889 889 9(21) constitutes the most precise g-factor measurement of a three-electron system to date. It is in excellent agreement with the theoretical prediction g_theo = 2.000 889 909(51) and confirms the relativistic many electron calculations at the level of 10⁻⁴. Since the sensitivity of this test is limited by the theoretical value, which is more than order of magnitude less precise than the experimental result, any further improvement of the theoretical uncertainty will directly improve the test of the relativistic many-electron calculations.