Precision measurements of the magnetic properties of the electron have played an important role in the development of quantum electrodynamics (QED). In 1947, for example, a value had been measured which was slightly higher than the value that had been predicted by the Dirac theory. It was only by means of QED that this discrepancy between the measured value and the predicted value could be resolved. The magnetic moment μ and the spin s of the electron fulfil the equation μ = g ∙ μB∙s/ħ, whereby μB is the Bohr magneton. For the dimensionless electron g-factor, the measurements carried out since that time resulted in increasingly accurate values which were in agreement with the results of ever more comprehensive QED calculations.
As known from QED, the interaction of the electron with the vacuum already has an influence on the g-factor. If, however, the electron is bound to an atomic nucleus, the strong electric field of the nucleus leads to the numerical value of the g-factor changing distinctly. Sven Sturm, Anke Wagner and Prof. Klaus Blaum of the Max Planck Institute for Nuclear Physics (MPIK) in Heidelberg measured the electron g-factor in such a hydrogen-like and highly charged ion with high precision. In 2012, they were awarded the Helmholtz Prize for their work.
The experiments carried out by Anke Wagner and Sven Sturm within the scope of their dissertations were based on a procedure developed by Heinz-Jürgen Kluge and Günter Werth in Mainz. For this purpose, a cryogenically cooled, 13-fold-charged silicon-28 ion, which had only one electron left, was kept in a Penning trap with electric and magnetic fields in a very good vacuum.
Whereas the ion, which had the mass M and the charge q, carried out a cyclotron movement with the frequency fC = q ∙ B/(2πM) in the magnetic field B, the magnetic moment of the electron precessed in the B field with the Larmor frequency fL = g ∙ µB ∙ B/h. By measuring the cyclotron frequency and the Larmor frequency, the researchers could determine the g-factor from their quotient: g = (2fL/ fc) ∙ q ∙ m/ (e ∙ M). The cyclotron frequency was measured with the aid of image currents caused by the circling ion in the electrodes of the Penning trap. In order to determine the Larmor frequency, the researchers irradiated the ion with microwaves whose frequency they changed.
In doing so, they observed at which frequency a resonance occurred and the electron spin reversed. If such a spin flip had taken place, this could be seen from the fact that the longitudinal oscillations which the ion carried out in the Penning trap parallel to the magnetic field lines changed their frequency slightly. The resonance frequency determined in this way agrees with the Larmor frequency. The three scientists received the result g = 1.995 348 958 for the g-factor (with an uncertainty of a few 10–10) which agreed perfectly with the result of the QED calculations. The measurements were thus so sensitive that they could detect the influence of the nucleus size on the magnetic moment of the electron. As a result, the QED has also successfully passed this most stringent test so far.