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Abstract

The Alphatrap experiment is a cryogenic Penning-trap setup with the
main objective to determine the g factor of the electron bound to heavy nuclei. Within
this thesis, the results of several such measurements are presented. Among these, the
measurement of the g factor of ²⁰Ne⁹¸ exhibits a 3σ discrepancy between theory and
experimental value, which has been attributed to the required input parameter of the
atomic mass of ²⁰Ne. An independent measurement has recently confirmed the deviation
of the mass, fully resolving the discrepancy. Furthermore, a measurement of ²²Ne⁹¸ can
be used to improve the precision of the atomic mass of ²²Ne by a factor 8 compared to the
literature value, when using the theoretically predicted g factor as an input. However,
the main focus of this thesis is the development of a novel technique, which, based upon
the coupling of two ions as an ion crystal, enables the most precise determination of
a g-factor difference to date. This difference, determined for the isotopes 20Ne9¸ and
22Ne9¸ with a relative precision of 5.6 x 10^-13 with respect to the g factor, improves the
precision for isotopic shifts of g factors by about two orders of magnitude. Based upon
the agreement with theory, the quantum electrodynamic contribution to the nuclear
recoil can be confirmed. Alternatively, the result can be applied to improve the precision
of the charge radius difference of the isotopes by about one order of magnitude or to
constrain new physics by limiting a potential fifth-force of the Higgs-portal mechanism.