The physics of strong fields with the associated relativistic and quantum electrodynamic (QED) effects can be uniquely studied with ions with only one or a few electrons and the highest atomic numbers. The phenomena are accessible via accurate spectroscopy of X-rays emitted during or after recombination or capture processes. The processes take place in the interaction of heavy ions with a superimposed electron beam or gas-jet target. These can be investigated experimentally in the ESR and CRYRING@ESR storage rings at GSI. The X-ray energy regime to be covered spans from few keV to several tens of keV, corresponding to the Balmer and Lyman series as well as to intra-shell transitions in heavy highly-charged ions.  

Crystal spectrometers offer superb energy resolution for x-ray spectroscopy, exceeding those of conventional semiconductor detectors by at least one order of magnitude. Therefore, they represent very powerful tools for precision x-ray spectroscopy.

The challenges with high-resolution crystal spectrometers lie mainly in the relatively low intensity of the X-rays emitted by the stored ions in combination with low detection efficiency of such devices. Furthermore, Doppler shifts and broadening are a serious problem for precision spectroscopy, as well as the geometric constraints that are given by the electron cooler and the gas jet of the storage ring. However, these challenges can be overcome with the necessary technical effort. By mounting two identical X-ray spectrometers symmetrically at the gas jet of the ESR the Doppler effect can be partially compensated and/or determined.

In order to measure with high resolution x-rays in the few keV energy range corresponding to e.g. intra-shell transitions in the L-shell of He-, Li-, and Be-like uranium ions, dedicated Bragg crystal spectrometers have been constructed. The two spectrometers are mounted in the Johann geometry with 50 × 25 mm 2 cylindrically bent germanium (220) crystals and a radius of curvature of R = 2,000 mm. The cylindrically bent crystals for this construction are prepared and characterized at the Friedrich Schiller University of Jena in collaboration with the Helmholtz Institute Jena. The two spectrometers are equipped with two X-ray CCD cameras: Andor iKon-L SO in the outer spectrometer and Great Eyes 2048 2048 BI in the inner spectrometer. Both cameras have 2,048 × 2,048 pixels with a size of 13.5 × 13.5 μm². Both spectrometers are under vacuum (10⁻⁵ −10⁻⁴ mbar) to reduce the X-ray absorption. For both moving and stationary X-ray sources, the corresponding Bragg angle of the crystal spectrometers is fixed to Θ = 45.85°. The resulting detectable energy range is about 80 eV for the first-order reflection. For each arm, the distance D between the CCD and the crystal is fixed by the focusing conditions of the Johann geometry, namely, D = R sinΘ = 1,435 mm. The distance between the gas-jet target and the crystal is reduced to 885 mm to increase the spectrometer efficiency and make the spectrometer not sensitive to spatial inhomogeneities of the source. The energy calibration is performed using a zinc Kα₁ line, produced by irradiating at 45° a movable 10-μm thick target with an X-ray tube equipped with a Mo cathode. The thickness and the angle of the target are chosen to have X-rays emitted in both directions of the alignment axis of the common spectrometers, passing through the ESR gas-target chamber for the inner spectrometer.

_{Figure 1: The drawing (left panel) and the photo (right panel) of one of the two Bragg crystal spectrometers mounted at the gas-jet target of the ESR for measurement of the intra-shell transitions in He-, Li-, and Be-like uranium ions.}

The recent measurement using these Bragg crystal spectrometers at the gas-jet target of the ESR (see Fig. 1) has allowed for a gain in accuracy of almost one order of magnitude on the absolute energy of the 2p-2s intra-shell transition in He-like uranium [Lo24]. For the first time, the prediction of non-perturbative two-loop QED contributions has been tested. Moreover, by comparing of transition energies from different ions with the same nucleus i.e., different charge states, a gain in accuracy of more than 20 could be achieved and one-electron and many-electron QED contributions could be clearly disentangled for the first time in such a high-field regime. See also: "Testing quantum electrodynamics in extreme fields with the heaviest two-electron ion".

With adapted X-ray crystal optics, it is possible to measure X-ray lines of fast ions in high resolution with very little Doppler broadening. The feasibility of such systems was already demonstrated in experiments at the ESR. For the hard X-ray regime, the FOCAL (Focusing Compensated Asymmetric Laue) X-ray optics was developed in transmission mode [Be04, Be09], which is operated in the asymmetric Laue case. Figure 2 shows a schematic representation of this configuration with two transmission crystal spectrometers arranged symmetrically with respect to the ion beam.

This ensures that systematic line shifts caused by the Doppler effect can be compensated. The suitability of this crystal optics for precision wavelength measurements in the hard X-ray range was demonstrated in a pilot experiment at the ESR. As a result, Figure 3 shows the measured Lyman-α doublet of hydrogen-like Pb⁸¹⁺. The inclination of the spectral lines in the two-dimensional intensity distribution as a result of the Doppler effect is in quantitative agreement with the expectations.

In a production run conducted in 2012 over a period of three weeks at the gas jet of the ESR storage ring, the 2p_1/2,3/2→1s_1/2 Lyman--α transitions of hydrogen-like Au⁷⁸⁺ were measured in high resolution via spectroscopy of the corresponding x-rays located near 63 keV (see Fig. 4). The aim of the experiment was to access the QED contributions to the 1s binding energy experimentally in order to provide an accurate comparison with the most advanced calculations [Ga18].

The experiment was made possible by the FOCAL x-ray crystal optics which overcomes both the limiting spectral resolving power of previously used germanium solid-state detectors and the prohibitively low detection efficiency of conventional crystal spectrometers [Be15]. Still the event rate observed is very low amounting to only few events per hour in the Lyman-α₁ line in each of the two spectrometers. The amazingly low background revealed in the measured spectra is due to a number of measures including active shielding, optimized 2D position-sensitive germanium strip detectors allowing energy gating and fast timing necessary for measuring the x rays in coincidence with particles undergoing electron capture and detected in a high-performance gaseous particle detector downstream the gas jet. Two identical crystal spectrometers were set up at the gas-jet target for a Doppler self-compensation leading to a cancellation of significant part of angular uncertainties. Last but not least, the present measurement has become feasible due to the dramatic increase of the stored ion number in the ESR over the years since its inauguration.

[Lo24] R. Loetzsch et al., Nature 625, 673-678 (2024).

[Be04] H. F. Beyer et al., Spectrochim. Acta Part B 59 1535 (2004).

[Be09] H. F. Beyer et al., Spectrochimica Acta Part B 64 736 (2009).

[Ga18] T. Gassner et al., New journal of physics 20, 073033 (2018).

[Be15] H. F. Beyer et al., J. Phys. B: At. Mol. Opt. Phys. 48 144010 (2015).