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Abstract

In the context of this thesis the electron mass has been determined in atomic mass units with a relative uncertainty of 2.8・10⁻¹¹, which represents a 13-fold improvement of the 2010 CODATA value. The underlying measurement principle combines a highprecision measurement of the Larmor-to-cyclotron frequency ratio on a single hydrogenlike carbon ion ¹²C⁵⁺ with a very accurate g-factor calculation. Furthermore, this thesis contains the first isotope shift measurement of bound-electron g-factors of highly charged ions. Here, the g-factors of the valence electrons of the lithiumlike calcium isotopes ⁴⁰Ca¹⁷⁺ and ⁴⁸Ca¹⁷⁺ have been measured with relative uncertainties of a few 10⁻¹⁰, constituting a so-far unrivaled level of precision for lithiumlike ions. These calcium isotopes provide a unique system across the entire nuclear chart to test the pure relativistic nuclear recoil effect. The corresponding and successfully tested theoretical prediction is based on bound-state quantum electrodynamics but goes beyond the standard formalism, the so-called Furry picture, where the nucleus is considered as a classical source of the Coulomb field. The three Larmor-to-cyclotron frequency ratios of ¹²C⁵⁺, ⁴⁰Ca¹⁷⁺ and ⁴⁸Ca¹⁷⁺ have been determined in sequence in a non-destructive manner on single trapped ions stored in a triple Penning trap setup. The cyclotron frequency is measured by a dedicated phase-sensitive detection technique while simultaneously probing the Larmor frequency. The spin-state of the bound valence electron is determined by the continuous Stern-Gerlach effect. In the very last part of this thesis, a new design of a highly compensated cylindrical Penning trap has been developed, which will be used in next generation’s high-precision Penning trap experiments.