The magnetic moment μ of a bound electron, generally expressed by the g-factor μ=−g μB s ħ−1 with μB the Bohr magneton and s the electron's spin, can be calculated by bound-state quantum electrodynamics (BS-QED) to very high precision. The recent ultra-precise experiment on hydrogen-like silicon determined this value to eleven significant digits, and thus allowed to rigorously probe the validity of BS-QED. Yet, the investigation of one of the most interesting contribution to the g-factor, the relativistic interaction between electron and nucleus, is limited by our knowledge of BS-QED effects. By comparing the g-factors of two isotopes, it is possible to cancel most of these contributions and sensitively probe nuclear effects. Here, we present calculations and experiments on the isotope dependence of the Zeeman effect in lithium-like calcium ions. The good agreement between the theoretical predicted recoil contribution and the high-precision g-factor measurements paves the way for a new generation of BS-QED tests.

The atomic mass difference of (163)Ho and (163)Dy has been directly measured with the Penning-trap mass spectrometer SHIPTRAP applying the novel phase-imaging ion-cyclotron-resonance technique. Our measurement has solved the long-standing problem of large discrepancies in the Q value of the electron capture in (163)Ho determined by different techniques. Our measured mass difference shifts the current Q value of 2555(16) eV evaluated in the Atomic Mass Evaluation 2012 [G. Audi et al., Chin. Phys. C 36, 1157 (2012)] by more than 7σ to 2833(30(stat))(15(sys)) eV/c(2). With the new mass difference it will be possible, e.g., to reach in the first phase of the ECHo experiment a statistical sensitivity to the neutrino mass below 10 eV, which will reduce its present upper limit by more than an order of magnitude.

For the first time a direct determination of the atomic mass difference of 187 Re and 187 Os has been performed with the Penning-trap mass spectrometer SHIPTRAP applying the novel phaseimaging ion-cyclotron-resonance technique. The obtained value of 2492(30stat)(15sys) eV is in excellent agreement with the Q-values determined indirectly with microcalorimetry and thus resolves a long-standing discrepancy with older proportional counter measurements. This is essential for the determination of the neutrino mass from the β − -decay of 187 Re as planned in the future microcalorimetric measurements. In addition, an accurate mass difference of 187 Re and 187 Os is also important for the assessment of 187 Re for cosmochronology.