QED theory
Precision experiments only test QED when the theory is just as precise. The team develops the relativistic atomic-structure and QED calculations needed to interpret our measurements on highly charged ions and exotic atoms, and those of many groups worldwide.
The team’s theory work is carried out by Jonas Sommerfeldt and Paul Indelicato (CNRS).
MCDFGME
Multiconfiguration Dirac-Fock for exotic atoms
Our multiconfiguration Dirac-Fock code, developed by Paul Indelicato and the late Jean-Paul Desclaux, handles atoms with electrons and a heavy particle together: a muon, an antiproton, or a spin-0 boson such as a pion or kaon (via the Klein-Gordon equation). It includes the full set of QED corrections: self-energy and its screening, vacuum polarization to all orders, two-loop terms, and more.
It is the reference code for transition energies in antiprotonic and muonic atoms, and provides the line positions and intensities used to analyze PAX and QUARTET data. More about MCDFGME.
Strong-field QED
Bound-state QED
With V. Yerokhin and V. Shabaev, the team computed the two-loop self-energy to all orders in Zα, which is essential for heavy hydrogen-like ions. Our coordinate-space methods with P. Mohr give self-energy screening in few-electron ions.
Delbrück scattering
Jonas Sommerfeldt’s all-order calculations of Delbrück scattering, the elastic scattering of hard photons by virtual electron-positron pairs in the Coulomb field of a heavy nucleus, resolved a long-standing discrepancy between theory and experiment (Phys. Rev. Lett. 131, 061601 (2023)).
Applications
Our calculations contribute to the NIST X-ray transition database, to atomic masses from Penning-trap measurements on highly charged ions, to the proton radius from muonic hydrogen, to the properties of superheavy elements, and to tests of bound-state QED with kaonic atoms in the SIDDHARTA-2 collaboration.
Recent work
- J. Sommerfeldt et al., Bound-state Compton scattering of linearly polarized photons, Phys. Rev. A 114, 022804 (2026).
- J. Sommerfeldt, V. A. Yerokhin, Z. Harman, C. H. Keitel, Wichmann-Kroll correction to the interelectronic interaction in He- and Li-like ions, arXiv:2607.12168 (2026).
- S. Rathi, K. von Schoeler, P. Indelicato, B. Ohayon, Reference quadrupole moments of transition elements from Lamb shifts in muonic atoms, Phys. Rev. Lett. 137, 023001 (2026).
- S. Rathi, U. D. Jentschura, P. Indelicato, B. Ohayon, Binding energy of muonic beryllium: perturbative versus all-order calculations, J. Phys. B 59, 125002 (2026).
- F. Clozza et al. (SIDDHARTA-2), Bound-state QED test above the Schwinger limit with kaonic fluorine, arXiv:2604.19387 (2026).
- S. Rathi et al., Theory framework for medium-mass muonic atoms, arXiv:2603.22021 (2026).
- S. Manti et al. (SIDDHARTA-2), Precision test of bound-state QED at intermediate Z with kaonic neon, Phys. Rev. A 113, 022815 (2026).
- J. Sommerfeldt, P. Indelicato, All-order Wichmann-Kroll contribution in heavy electronic and exotic atoms, Phys. Rev. A 113, 022806 (2026).
- J. Sommerfeldt, V. A. Yerokhin, A. Surzhykov, Bound–free and free–free pair production channels in forward Delbrück scattering, Atoms 13, 19 (2025).
Reviews and key papers
- P. Indelicato, QED tests with highly charged ions (topical review), J. Phys. B 52, 232001 (2019).
- O. R. Smits et al., Pushing the limits of the periodic table, Physics Reports 1035, 1–57 (2023).
- J. Sommerfeldt et al., All-order Coulomb corrections to Delbrück scattering above the pair-production threshold, Phys. Rev. Lett. 131, 061601 (2023).