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Abstract

In this thesis, the first high-precision measurement of the ground-state g-factor of a
boronlike ion, ⁴⁰Ar¹³⁺, with a fractional uncertainty of 1.4 × 10⁻⁹, is presented. The
measurement has been performed on a single boronlike argon ion with the double
Penning-trap setup of the newly developed ALPHATRAP experiment. Within this work,
the trap tower of the experiment has been developed, assembled and tested prior
to commissioning it together with the rest of the ALPHATRAP setup. The resulting
measurement presented here corresponds to the most precise g-factor determination
of a five-electron system to date. Not only does it allow testing the currently
available theoretical predictions for the many-electron, QED and nuclear-recoil
contributions, but also distinguishes between calculations that are in disagreement.
The g-factor obtained here is in agreement with the most recent and most precise
theoretical prediction, which has a relative uncertainty of 9 × 10⁻⁷. This level
of agreement constitutes one of the most accurate tests of many-electron QED
contributions in strong fields. The sensitivity of this test will improve in the future
with anticipated improvements on the theoretical g-factor, which includes higherorder
QED contributions. Furthermore, this measurement paves the way towards the
independent determination of the fine-structure constant with heavier highly charged
ions in ALPHATRAP, where a specific difference of the boron- and hydrogenlike ions’
g-factors will be used to cancel nuclear structure effects.