Towards electronic g-factor measurements in medium-heavy hydrogen-like and lithium-like ions

Measurements of the anomalous magnetic moment of the electron bound in hydrogen-like ions with spinless nuclei have proven to be highly sensitive tests of corresponding calculations based on bound-state quantum electrodynamics. Measurements performed on H-like carbon 12C5+ and oxygen 16O7+ together with bound-state QED calculations on the same level of accuracy have achieved sensitivities around 0.25% of the QED bound state contributions to the calculated electronic g-factors of these ions. Currently, a similar experiment on hydrogen-like calcium 40Ca19+, lithium-like calcium 40Ca17+ and other medium-heavy ions is being prepared, which is capable of increasing this sensitivity on the experimental side by more than one order of magnitude. To that end, several novel experimental techniques have been developed. In the following, we will give a motivation for such a measurement, present the experimental requirements and technique and discuss the possible benefits.