_{Fig. 1: The drawing of one of the two Bragg crystal spectrometers mounted at the gas-jet target of the ESR for measurement of the intra-shell transition in He-like uranium (left panel).An illustration of helium-like uranium, with the strong-field QED effects represented by Feynman diagrams with the background showing an x-ray image of the measured transition (right panel).}

Quantum electrodynamics (QED) describes interactions between light and matter, and is an important corner stone of the Standard Model. Testing it with high precision, especially in the regime of extremely strong electromagnetic fields, is therefore of high importance for fundamental research, as well as for applications, such as new frequency standards.

At present, most stringent tests of QED are based on extremely precise studies performed in the domain of relatively low electromagnetic field strengths and light atoms and ions, where perturbation methods can be efficiently implemented in the QED calculations. In the regime of extreme fields of heavy ions, the QED calculations enter a qualitatively different non-perturbative regime (with respect to the nuclear charge), making accurate theoretical predictions challenging. Experiments in this domain are equally challenging and thus QED tests in strong fields currently lack the high precision reached for light atoms. New tests are required, in particular in the regime of extreme fields of heavy ions, where QED effects are greatly enhanced due to the extremely strong electromagnetic field of the heavy nucleus, reaching several orders of magnitude higher than the most intense laser fields available nowadays.

GSI/FAIR is at present the unique place worldwide where the heaviest ions in any desired charge-state can be produced with subsequent acceleration and stripping, followed by cooling and storage in the dedicated storage ring ESR.

Recently, an international research team has carried out a high-precision x-ray spectroscopy measurement on helium-like uranium, the simplest and heaviest multi-electron atomic system. Dedicated Bragg crystal spectrometers were constructed and mounted at the gas-jet interaction chamber of the ESR (see Fig. 1). A new calibration method and other improvements resulted in a 37-parts-per-million transition energy accuracy, almost one order of magnitude better than in previous efforts. This enables the first test of higher-order QED effects in
a high-Z helium-like ion, providing a new important benchmark of theory for the regime of extreme fields.

_{Fig. 2: Comparison of our experimental result for the intra-shell transition in He-like uranium with the previous measurement and with predictions of different theoretical models (left panel). Different contributions including two-loop and two-electron QED effects to the total energy of the intra-shell transitions in He-like uranium in comparison with our experimental accuracy (right panel).}

R. Loetzsch et al., Nature 625, 673-678 (2024)

M. Trassinelli, Atoms 11, 64 (2023), https://doi.org/10.3390/atoms11040064