Sailer, T. et al. Measurement of the bound-electron g-factor difference in coupled ions. Nature 606, 479–483 (2022).
Google Scholar
Hanneke, D., Fogwell, S. & Gabrielse, G. New measurement of the electron magnetic moment and the fine structure constant. Phys. Rev. Lett. 100, 120801 (2008).
Google Scholar
Aoyama, T., Hayakawa, M., Kinoshita, T. & Nio, M. Tenth-order QED contribution to the electron g − 2 and an improved value of the fine structure constant. Phys. Rev. Lett. 109, 111807 (2012).
Google Scholar
Morel, L., Yao, Z., Cladé, P. & Guellati-Khélifa, S. Determination of the fine-structure constant with an accuracy of 81 parts per trillion. Nature 588, 61–65 (2020).
Google Scholar
Biesheuvel, J. et al. Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD+. Nat. Commun. 7, 10385 (2016).
Google Scholar
Rengelink, R. J. et al. Precision spectroscopy of helium in a magic wavelength optical dipole trap. Nat. Phys. 14, 1132–1137 (2018).
Google Scholar
Yerokhin, V. A., Pachucki, K. & Patkóš, V. Theory of the Lamb shift in hydrogen and light hydrogen-like ions. Ann. Phys. 531, 1800324 (2019).
Yerokhin, V. A., Patkóš, V. & Pachucki, K. Atomic structure calculations of helium with correlated exponential functions. Symmetry 13, 1246 (2021).
Google Scholar
Shabaev, V. M. Two-time Green’s function method in quantum electrodynamics of high-Z few-electron atoms. Phys. Rep. 356, 119–228 (2002).
Google Scholar
Indelicato, P. & Mohr, P.J. in Handbook of Relativistic Quantum Chemistry (ed. Liu, W.) 131–242 (Springer, 2016).
Yerokhin, V. A. & Shabaev, V. M. Lamb shift of n = 1 and n = 2 states of hydrogenlike atoms, 1 ≤ Z ≤ 110. J. Phys. Chem. Ref. Data 44, 033103 (2015).
Google Scholar
Malyshev, A. V., Kozhedub, Y. S. & Shabaev, V. M. Ab initio calculations of the 2p3/2 → 2s transition in He-, Li-, and Be-like uranium. Phys. Rev. A 107, 042806 (2023).
Google Scholar
Kozlov, M. G., Safronova, M. S., López-Urrutia, J. R. C. & Schmidt, P. O. Highly charged ions: optical clocks and applications in fundamental physics. Rev. Mod. Phys 90, 045005 (2018).
Google Scholar
King, S. A. et al. An optical atomic clock based on a highly charged ion. Nature 611, 43–47 (2022).
Google Scholar
Safronova, M. S. et al. Search for new physics with atoms and molecules. Rev. Mod. Phys 90, 025008 (2019).
Google Scholar
Abi, B. et al. Measurement of the positive muon anomalous magnetic moment to 0.46 ppm. Phys. Rev. Lett. 126, 141801 (2021).
Google Scholar
Gurung, L., Babij, T. J., Hogan, S. D. & Cassidy, D. B. Precision microwave spectroscopy of the positronium n = 2 fine structure. Phys. Rev. Lett. 125, 073002 (2020).
Google Scholar
Volotka, A. V. et al. Test of many-electron QED effects in the hyperfine splitting of heavy high-Z ions. Phys. Rev. Lett. 108, 073001 (2012).
Google Scholar
Ullmann, J. et al. High precision hyperfine measurements in bismuth challenge bound-state strong-field QED. Nat. Commun. 8, 15484 (2017).
Google Scholar
Skripnikov, L. V. et al. New nuclear magnetic moment of 209Bi: resolving the bismuth hyperfine puzzle. Phys. Rev. Lett. 120, 093001 (2018).
Google Scholar
Sturm, S. et al. g factor of hydrogenlike 28Si13+. Phys. Rev. Lett. 107, 023002 (2011).
Google Scholar
Glazov, D. A. et al. g factor of lithiumlike silicon: new challenge to bound-state QED. Phys. Rev. Lett. 123, 173001 (2019).
Google Scholar
Kosheleva, V. P., Volotka, A. V., Glazov, D. A., Zinenko, D. V. & Fritzsche, S. g factor of lithiumlike silicon and calcium: resolving the disagreement between theory and experiment. Phys. Rev. Lett. 128, 103001 (2022).
Google Scholar
Morgner, J. et al. Stringent test of QED with hydrogen-like tin. Nature 622, 53–57 (2023).
Google Scholar
Shabaev, V. M. et al. Stringent tests of QED using highly charged ions. Hyperfine Interact. 239, 60 (2018).
Google Scholar
Indelicato, P. QED tests with highly charged ions. J. Phys. B 52, 232001 (2019).
Google Scholar
Gumberidze, A. et al. Quantum electrodynamics in strong electric fields: the ground-state Lamb shift in hydrogenlike uranium. Phys. Rev. Lett. 94, 223001 (2005).
Google Scholar
Gumberidze, A. et al. Electron-electron interaction in strong electromagnetic fields: the two-electron contribution to the ground-state energy in He-like uranium. Phys. Rev. Lett. 92, 203004–4 (2004).
Google Scholar
Thorn, D. B. et al. Precision measurement of the K-shell spectrum from highly charged xenon with an array of x-ray calorimeters. Phys. Rev. Lett. 103, 163001 (2009).
Google Scholar
Trassinelli, M. et al. Observation of the 2p3/2 → 2s1/2 intra-shell transition in He-like uranium. Europhys. Lett. 87, 63001 (2009).
Google Scholar
Steck, M. & Litvinov, Y. A. Heavy-ion storage rings and their use in precision experiments with highly charged ions. Prog. Part. Nucl. Phys. 115, 103811 (2020).
Google Scholar
Beiersdorfer, P., Chen, H., Thorn, D. B. & Trabert, E. Measurement of the two-loop Lamb shift in lithiumlike U89+. Phys. Rev. Lett. 95, 233003 (2005).
Google Scholar
Hengstler, D. et al. Towards FAIR: first measurements of metallic magnetic calorimeters for high-resolution x-ray spectroscopy at GSI. Phys. Scripta T166, 014054 (2015).
Google Scholar
Kraft-Bermuth, S. et al. Precise determination of the 1s Lamb shift in hydrogen-like lead and gold using microcalorimeters. J. Phys. B 50, 055603 (2017).
Google Scholar
Gassner, T. et al. Wavelength-dispersive spectroscopy in the hard x-ray regime of a heavy highly-charged ion: the 1s Lamb shift in hydrogen-like gold. New J. Phys. 20, 073033 (2018).
Google Scholar
Beiersdorfer, P., Knapp, D., Marrs, R. E., Elliott, S. R. & Chen, M. H. Structure and Lamb shift of 2s1/−2p3/2 levels in lithiumlike U89+ through neonlike U82+. Phys. Rev. Lett. 71, 3939 (1993).
Google Scholar
Beiersdorfer, P. Spectral measurements of few-electron uranium ions produced and trapped in a high-energy electron beam ion trap. Nucl. Instrum. Methods Phys. Res. B 99, 114–116 (1995).
Google Scholar
Deslattes, R. D. et al. X-ray transition energies: new approach to a comprehensive evaluation. Rev. Mod. Phys. 75, 35–99 (2003).
Google Scholar
Trassinelli, M. et al. Doppler-tuned Bragg spectroscopy of excited levels in He-like uranium: a discussion of the uncertainty contributions. J. Phys. Conf. Ser. 163, 012026 (2009).
Artemyev, A. N., Shabaev, V. M., Yerokhin, V. A., Plunien, G. & Soff, G. QED calculation of the n = 1 and n = 2 energy levels in He-like ions. Phys. Rev. A 71, 062104 (2005).
Google Scholar
Kozhedub, Y. S., Malyshev, A. V., Glazov, D. A., Shabaev, V. M. & Tupitsyn, I. I. QED calculation of electron-electron correlation effects in heliumlike ions. Phys. Rev. A 100, 062506 (2019).
Google Scholar
Drake, G. W. F. Theoretical energies for the n = 1 and 2 states of the helium isoelectronic sequence up to Z = 100. Can. J. Phys. 66, 586 (1988).
Google Scholar
Chen, M. H., Cheng, K. T. & Johnson, W. R. Relativistic configuration-interaction calculations of n = 2 triplet states of heliumlike ions. Phys. Rev. A 47, 3692 (1993).
Google Scholar
Plante, D. R., Johnson, W. R. & Sapirstein, J. Relativistic all-order many-body calculations of the n = 1 and n = 2 states of heliumlike ions. Phys. Rev. A 49, 3519–3530 (1994).
Google Scholar
Cheng, K. T., Chen, M. H. & Sapirstein, J. Quantum electrodynamic corrections in high-Z Li-like and Be-like ions. Phys. Rev. A 62, 054501 (2000).
Google Scholar
Stöhlker, T. et al. Charge-exchange cross sections and beam lifetimes for stored and decelerated bare uranium ions. Phys. Rev. A 58, 2043–2050 (1998).
Google Scholar
Franzke, B. The heavy ion storage and cooler ring project ESR at GSI. Nucl. Instrum. Methods Phys. Res. B 24-25, 18–25 (1987).
Google Scholar
Kühnel, M. et al. Low-Z internal target from a cryogenically cooled liquid microjet source. Nucl. Instrum. Methods Phys. Res. A 602, 311–314 (2009).
Google Scholar
Fourment, C. et al. Broadband, high dynamics and high resolution charge coupled device-based spectrometer in dynamic mode for multi-keV repetitive x-ray sources. Rev. Sci. Instrum. 80, 083505 (2009).
Google Scholar
Zamponi, F., Kämpfer, T., Morak, A., Uschmann, I. & Förster, E. Characterization of a deep depletion, back-illuminated charge-coupled device in the x-ray range. Rev. Sci. Instrum. 76, 116101 (2005).
Google Scholar
Trassinelli, M. Bayesian data analysis tools for atomic physics. Nucl. Instrum. Methods Phys. Res. B 408, 301–312 (2017).
Google Scholar
Trassinelli, M. The Nested_fit data analysis program. Proceedings 33, 14 (2019).
Trassinelli, M. & Ciccodicola, P. Mean shift cluster recognition method implementation in the nested sampling algorithm. Entropy 22, 185 (2020).
Google Scholar
Trassinelli, M. Shape and satellite studies of highly charged ions x-ray spectra using bayesian methods. Atoms 11, 64 (2023).
Google Scholar
Weber, G. et al. Total projectile electron loss cross sections of U28+ ions in collisions with gaseous targets ranging from hydrogen to krypton. Phys. Rev. ST Accel. Beams 18, 034403 (2015).
Google Scholar
Gassner, T. & Beyer, H. F. Spatial characterization of the internal gas target at the ESR for the FOCAL experiment. Phys. Scripta 2015, 014052 (2015).
Schmelling, M. Averaging correlated data. Phys. Scr. 51, 676 (1995).
Google Scholar
Bevington, P. R. & Robinson, D. K. Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 2003).
Gregory, P. Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with Mathematica Support (Cambridge Univ. Press, 2005).
Froese Fischer, C. The Hartree-Fock Method for Atoms (Wiley, 1977).
Gorceix, O., Indelicato, P. & Desclaux, J. P. Multiconfiguration Dirac-Fock studies of two-electron ions. I. Electron-electron interaction. J. Phys. B 20, 639 (1987).
Google Scholar
Gorceix, O. & Indelicato, P. Effect of the complete Breit interaction on two-electron ion energy levels. Phys. Rev. A 37, 1087–1094 (1988).
Google Scholar
Indelicato, P. & Desclaux, J. P. Multiconfiguration Dirac-Fock calculations of transition energies with QED corrections in three-electron ions. Phys. Rev. A 42, 5139–5149 (1990).
Google Scholar
Shabaev, V. M. QED theory of the nuclear recoil effect in atoms. Phys. Rev. A 57, 59–67 (1998).
Google Scholar
Shabaev, V. M. & Artemyev, A. N. Relativistic nuclear recoil corrections to the energy levels of multicharged ions. J. Phys. B 27, 1307 (1994).
Google Scholar
Li, J. et al. Mass- and field-shift isotope parameters for the 2s−2p resonance doublet of lithiumlike ions. Phys. Rev. A 86, 022518 (2012).
Google Scholar
Mohr, P. J. & Soff, G. Nuclear size correction to the electron self-energy. Phys. Rev. Lett. 70, 158–161 (1993).
Google Scholar
Beier, T., Mohr, P. J., Persson, H. & Soff, G. Influence of nuclear size on QED corrections in hydrogenlike heavy ions. Phys. Rev. A 58, 954 (1998).
Google Scholar
Indelicato, P. Nonperturbative evaluation of some QED contributions to the muonic hydrogen n=2 Lamb shift and hyperfine structure. Phys. Rev. A 87, 022501 (2013).
Google Scholar
Shabaev, V. M., Tupitsyn, I. I. & Yerokhin, V. A. Model operator approach to the Lamb shift calculations in relativistic many-electron atoms. Phys. Rev. A 88, 012513 (2013).
Google Scholar
Shabaev, V. M., Tupitsyn, I. I. & Yerokhin, V. A. QEDMOD: Fortran program for calculating the model Lamb-shift operator. Comp. Phys. Commun. 189, 175–181 (2015).
Yerokhin, V. A. Two-loop self-energy in the Lamb shift of the ground and excited states of hydrogenlike ions. Phys. Rev. A 97, 052509 (2018).
Google Scholar
Yerokhin, V. A., Indelicato, P. & Shabaev, V. M. Nonperturbative calculation of the two-loop Lamb shift in Li-like ions. Phys. Rev. Lett. 97, 253004 (2006).
Google Scholar
Yerokhin, V. A., Indelicato, P. & Shabaev, V. M. Two-loop QED corrections in few-electron ions. Can. J. Phys. 85, 521–529 (2007).
Google Scholar
Yerokhin, V. A., Indelicato, P. & Shabaev, V. M. Two-loop QED corrections with closed fermion loops. Phys. Rev. A 77, 062510 (2008).
Google Scholar
Angeli, I. & Marinova, K. P. Table of experimental nuclear ground state charge radii: an update. At. Data Nucl. Data Tables 99, 69–95 (2013).
Google Scholar
Plunien, G., Müller, B., Greiner, W. & Soff, G. Nuclear polarization contribution to the Lamb shift in heavy atoms. Phys. Rev. A 39, 5428–5431 (1989).
Google Scholar
Plunien, G. & Soff, G. Nuclear-polarization contribution to the Lamb shift in actinide nuclei. Phys. Rev. A 51, 1119–1131 (1995).
Google Scholar
Plunien, G. & Soff, G. Erratum: nuclear-polarization contribution to the Lamb shift in actinide nuclei. Phys. Rev. A 53, 4614–4615 (1996).
Google Scholar