Nonperturbative calculation of the two-loop lamb shift in Li-like ions

Testing quantum electrodynamics in extreme fields using helium-like uranium

Quantum electrodynamics (QED), the quantum field theory that describes the interaction between light and matter, is commonly regarded as the best-tested quantum theory in modern physics. However, this claim is mostly based on extremely precise studies performed in the domain of relatively low field strengths and light atoms and ions1-6. In the realm of very strong electromagnetic fields such as in the heaviest highly charged ions (with nuclear charge Z ≫ 1), QED calculations enter a qualitatively different, non-perturbative regime. Yet, the corresponding experimental studies are very challenging, and theoretical predictions are only partially tested. Here we present an experiment sensitive to higher-order QED effects and electron-electron interactions in the high-Z regime. This is achieved by using a multi-reference method based on Doppler-tuned X-ray emission from stored relativistic uranium ions with different charge states. The energy of the 1s1/22p3/2 J = 2 → 1s1/22s1/2 J = 1 intrashell transition in the heaviest two-electron ion (U90+) is obtained with an accuracy of 37 ppm. Furthermore, a comparison of uranium ions with different numbers of bound electrons enables us to disentangle and to test separately the one-electron higher-order QED effects and the bound electron-electron interaction terms without the uncertainty related to the nuclear radius. Moreover, our experimental result can discriminate between several state-of-the-art theoretical approaches and provides an important benchmark for calculations in the strong-field domain.

X-ray Spectroscopy Based on Micro-Calorimeters at Internal Targets of Storage Rings

With metallic-magnetic calorimeters (MMCs), promising detectors for high-precision X-ray spectrometry in atomic and fundamental physics experiments are available. In this work, we present a pilot experiment based on a maXs-30 type MMC-spectrometer for recording X-rays emitted in collisions of lithium-like uranium ions with a molecular nitrogen gas jet in the internal target of the ESR storage ring of the GSI. Sample spectra have been measured, and a multitude of X-ray transitions have been unambiguously identified. As a first test and for comparison with data recorded at an EBIT, the 2s Lamb shift in lithium-like uranium was estimated.

Ab initio Calculations of Energy Levels in Be-Like Xenon: Strong Interference between Electron-Correlation and QED Effects

The strong mixing of close levels with two valence electrons in Be-like xenon greatly complicates ab initio QED calculations beyond the first-order approximation. Because of a strong interplay between the electron-electron correlation and QED effects, the standard single-level perturbative QED approach may fail, even if it takes into account the second-order screened QED diagrams. In the present Letter, the corresponding obstacles are overcome by working out the QED perturbation theory for quasidegenerate states. The contributions of all the Feynman diagrams up to the second order are taken into account. The many-electron QED effects are rigorously evaluated in the framework of the extended Furry picture to all orders in the nuclear-strength parameter αZ. The higher-order electron-correlation effects are considered within the Breit approximation. The nuclear recoil effect is accounted for as well. The developed approach is applied to high-precision QED calculations of the ground and singly excited energy levels in Be-like xenon. The most accurate theoretical predictions for the binding and excitation energies are obtained. These results deviate from the most precise experimental value by 3σ but perfectly agree with a more recent measurement.

Quantum Electrodynamical Shifts in Multivalent Heavy Ions

The quantum electrodynamics (QED) corrections are directly incorporated into the most accurate treatment of the correlation corrections for ions with complex electronic structure of interest to metrology and tests of fundamental physics. We compared the performance of four different QED potentials for various systems to access the accuracy of QED calculations and to make a prediction of highly charged ion properties urgently needed for planning future experiments. We find that all four potentials give consistent and reliable results for ions of interest. For the strongly bound electrons, the nonlocal potentials are more accurate than the local potential.

Dominance of the Breit interaction in the x-ray emission of highly charged ions following dielectronic recombination

The Breit interaction typically appears as a-more or less small-correction to the Coulomb repulsion acting among the electrons. We here propose two x-ray measurements on the angular distribution and linear polarization of the 1s2s(2)2p(1/2) J=1-->1s(2)2s(2) J=0 electric-dipole radiation of high-Z, beryllium-like ions, following the resonant electron capture into initially lithium-like ions, for which the Breit interaction strongly dominates the Coulomb repulsion and leads to a qualitative change in the expected x-ray emission pattern. The proposed measurements are feasible with present-day x-ray detectors and may serve a stringent test on relativistic corrections to the electron-electron interaction in the presence of strong fields.

Screened radiative corrections from hyperfine-split dielectronic resonances in lithiumlike scandium

Term energies for dielectronic-recombination Rydberg resonances below 0.07 eV are determined for Sc18+ with absolute accuracies below 0.0002 eV by electron collision spectroscopy in an ion storage ring, using the twin-electron-beam technique and a cryogenic photocathode. The lithiumlike 2s_{1/2}-2p_{3/2} transition energy for Z=21 is determined to 4.6 ppm, less than 1% of the few-body effects on radiative corrections. Features from the hyperfine structure of the 2s state could be resolved in the dielectronic-recombination spectrum.

Soft x-ray laser spectroscopy on trapped highly charged ions at FLASH

In a proof-of-principle experiment, we demonstrate high-resolution resonant laser excitation in the soft x-ray region at 48.6 eV of the 2 (2)S(1/2) to 2 (2)P(1/2) transition of Li-like Fe23+ ions trapped in an electron beam ion trap by using ultrabrilliant light from Free Electron Laser in Hamburg (FLASH). High precision spectroscopic studies of highly charged ions at this and upcoming x-ray lasers with an expected accuracy gain up to a factor of a thousand, become possible with our technique, thus potentially yielding fundamental insights, e.g., into basic aspects of QED.