The rigorous two-center approach based on the dual-kinetically balanced finite-basis-set expansion is applied to one-electron, heteronuclear diatomic Bi-Au, U-Pb, and Cf-U quasimolecules. The obtained 1σ ground-state energies are compared with previous calculations, when possible. Upon analysis of three different placements of the coordinate system’s origin in the monopole approximation of the two-center potential: (1) in the middle, between the nuclei, (2) in the center of the heavy nucleus, and (3) in the center of the light nucleus, a substantial difference between the results is found. The leading contributions of one-electron quantum electrodynamics (self-energy and vacuum polarization) are evaluated within the monopole approximation as well.

/pdf/finite-basis-set-approach-to-the-two-center-heteronuclear-2k2a4uv7.pdf

Finite-Basis-Set Approach to the Two-Center Heteronuclear Dirac Problem

The low-energy heavy ion storage ring CRYRING was transported from Stockholm to Darmstadt, modernized and reconfigured, and recommissioned as CRYRING@ESR. The machine is now in operation with all installations in service and is available as a user facility for experiments proposed through the SPARC collaboration. During the 2020–2022 period, we brought a number of experimental installations into service and used them to measure first data: the ultra-cold electron cooler for merged-beam electron–ion collisions, the gas jet target for atomic collisions, a next-generation microcalorimeter-based X-ray spectroscopy setup, and others. Ions can be injected either in low charge states from a local ion source through a 300 keV/u RFQ linac, or in high charge states from the GSI accelerator chain through ESR. This allows for very broad access to ions across the entire periodic table. CRYRING@ESR is able to de- or accelerate ions and cool and store beams of isotopically pure species in a desired charge state. While the analysis is still largely ongoing, the first experimental data already show that the machine reached its expected performance level, and our high expectations regarding achievable resolution in spectroscopy experiments have been fulfilled. With access to new classes of ions available through ESR injection and a new generation of experimental instrumentation, CRYRING@ESR is a unique facility for experiments with heavy, highly charged ions. Here, we will review our present setup and machine performance, discuss the data from our first commissioning experiments and briefly preview the upcoming new installations for the coming years.

/pdf/first-experiments-with-cryring-esr-1fqtel0b.pdf

First Experiments with CRYRING@ESR

X-ray emission as a result of radiative recombination (RR) at threshold energies in the electron cooler of CRYRING@ESR was investigated for decelerated bare lead ions at a beam energy of 10 MeV/u. The recorded spectra are dominated by characteristic transitions in Pb81+, namely, the Lyman, Balmer and Paschen series, as a result of decay cascades from high-n states that are preferentially populated by the RR processes. In addition, a rigorous theoretical model is applied for the interpretation of measured X-ray spectra, and shows good agreement.

https://www.mdpi.com/2218-2004/11/1/2/pdf?version=1672392405

Radiative Recombination Studies for Bare Lead Ions Interacting with Low-Energy Electrons

We report on a new experimental approach for the Doppler correction of X-rays emitted by heavy ions, using novel metallic magnetic calorimeter detectors which uniquely combine a high spectral resolution with a broad bandwidth acceptance. The measurement was carried out at the electron cooler of CRYRING@ESR at GSI, Darmstadt, Germany. The X-ray emission associated with the radiative recombination of cooler electrons and stored hydrogen-like uranium ions was investigated using two novel microcalorimeter detectors positioned under 0∘ and 180∘ with respect to the ion beam axis. This new experimental setup allowed the investigation of the region of the N, M → L transitions in helium-like uranium with a spectral resolution unmatched by previous studies using conventional semiconductor X-ray detectors. When assuming that the rest-frame energy of at least a few of the recorded transitions is well-known from theory or experiments, a precise measurement of the Doppler shifted line positions in the laboratory system can be used to determine the ion beam velocity using only spectral information. The spectral resolution achievable with microcalorimeter detectors should, for the first time, allow intrinsic Doppler correction to be performed for the precision X-ray spectroscopy of stored heavy ions. A comparison with data from a previous experiment at the ESR electron cooler, as well as the conventional method of conducting Doppler correction using electron cooler parameters, will be discussed.

/pdf/towards-an-intrinsic-doppler-correction-for-x-ray-7zb50vqm.pdf

Towards an Intrinsic Doppler Correction for X-ray Spectroscopy of Stored Ions at CRYRING@ESR

Systematic QED calculations of ionization energies of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>2</a:mn><a:mi>s</a:mi></a:mrow></a:math>, <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mn>2</b:mn><b:msub><b:mi>p</b:mi><b:mrow><b:mn>1</b:mn><b:mo>/</b:mo><b:mn>2</b:mn></b:mrow></b:msub></b:mrow></b:math>, and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>2</c:mn><c:msub><c:mi>p</c:mi><c:mrow><c:mn>3</c:mn><c:mo>/</c:mo><c:mn>2</c:mn></c:mrow></c:msub></c:mrow></c:math> states as well as the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>2</d:mn><d:msub><d:mi>p</d:mi><d:mrow><d:mn>1</d:mn><d:mo>/</d:mo><d:mn>2</d:mn></d:mrow></d:msub><d:mtext>–</d:mtext><d:mn>2</d:mn><d:mi>s</d:mi></d:mrow></d:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mn>2</e:mn><e:msub><e:mi>p</e:mi><e:mrow><e:mn>3</e:mn><e:mo>/</e:mo><e:mn>2</e:mn></e:mrow></e:msub><e:mtext>–</e:mtext><e:mn>2</e:mn><e:mi>s</e:mi></e:mrow></e:math> transition energies are performed for Li-like ions with the nuclear charge numbers <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi>Z</f:mi><f:mo>=</f:mo><f:mn>10</f:mn><f:mo>–</f:mo><f:mn>100</f:mn></f:mrow></f:math>. The convergence of QED perturbative expansion is improved by using the extended Furry picture, which starts from the Dirac equation with a local screening potential. An treatment is accomplished for one- and two-photon electron-structure QED effects and the one-photon screening of the self-energy and vacuum-polarization corrections. This is complemented with an approximate treatment of the two-photon QED screening and higher-order (three or more photon) electron-structure effects. As a result, the obtained theoretical predictions improve upon the accuracy achieved in previous calculations. Comparison with available experimental data shows a good agreement between theory and experiment. In most cases, the theoretical values surpass the experimental results in precision with only a few exceptions. In the case of uranium and bismuth, the comparison provides one of the most stringent tests of bound-state QED in the strong-field regime. Alternatively, the obtained results can be employed for high-precision determinations of nuclear charge radii. 

QED calculations of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>2</mml:mn><mml:mi>p</mml:mi><mml:mo>–</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mi>s</mml:mi></mml:mrow></mml:math> transition energies in Li-like ions

B. Zhu, 2, 3, 4, ∗ A. Gumberidze, T. Over, G. Weber, 2 Z. Andelkovic, A. Bräuning-Demian, R. Chen, 5 D. Dmytriiev, O. Forstner, 2, 3 C. Hahn, 2, 3 F. Herfurth, M. O. Herdrich, 2, 3 P. -M. Hillenbrand, 6 A. Kalinin, F. M. Kröger, 2, 3 M. Lestinsky, Y. A. Litvinov, E. B. Menz, 2, 3 W. Middents, 2, 3 T. Morgenroth, 2, 3 N. Petridis, Ph. Pfäfflein, 2, 3 M. S. Sanjari, 7 R. S. Sidhu, U. Spillmann, R. Schuch, S. Schippers, S. Trotsenko, 2 L. Varga, G. Vorobyev, and Th. Stöhlker 2, 3, † Helmholtz Institute Jena, D-07743 Jena, Germany GSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt, Germany Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität Jena, D-07743 Jena, Germany School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China I. Physikalisches Institut, Justus-Liebig-Universität Gießen, D-35392 Giessen, Germany Aachen University of Applied Sciences, D-52005 Aachen, Germany Physics Department, Stockholm University, S-106 91 Stockholm, Sweden (Dated: January 19, 2022)

X-ray emission associated with radiative recombination for Pb$^{82+}$ ions at threshold energies

pdf/quantum-electrodynamics-in-strong-electromagnetic-fields-cheilwwdowfh.pdf

Quantum Electrodynamics in Strong Electromagnetic Fields: Substate Resolved 
Kα
 Transition Energies in Heliumlike Uranium

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X-ray emission associated with radiative recombination for Pb$^{82+}$ ions at threshold energies

Quantum Electrodynamics in Strong Electromagnetic Fields: Substate Resolved Kα Transition Energies in Heliumlike Uranium