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Testing Strong-Field QED to Second Order in the Highly Correlated Atomic System Berylliumlike ${Pb}^{78 +}$ by Electron-Ion Collision Spectroscopy

S. Schippers ^1,2, C. Brandau ^1,3, S. Fuchs ^1,2, M. Lestinsky ³, S. X. Wang ^1,2, C. Y. Zhang ⁴, N. R. Badnell⁴, A. Borovik, Jr.^1,5, M. Fogle ⁶ et al.

V. Hannen ⁷, Z. Harman⁸, P.-M. Hillenbrand ^1,3, E. B. Menz ^3,5, Y. Zhang^8,9, Z. Andelkovic ³, F. Herfurth ³, R. Heß ³, A. Kalinin ³, C. Kozhuharov ³, C. Krantz ³, S. Litvinov ³, B. Lorentz ³, U. Spillmann ³, M. Steck³, G. Vorobyev³, D. Banaś ¹⁰, S. Fritzsche ^3,5,11, E. Lindroth ¹², X. Ma ¹³, A. Müller ¹, R. Schuch ¹², A. Surzhykov ^14,15, M. Trassinelli ¹⁶, K. Ueberholz ⁷, C. Weinheimer ⁷, and Th. Stöhlker ^3,5,17

¹I. Physikalisches Institut, Justus-Liebig-Universität Gießen, 35392 Giessen, Germany
²Helmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung, 64291 Darmstadt, Germany
³GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
⁴Department of Physics, University of Strathclyde, Glasgow G4 0NG, United Kingdom
⁵Helmholtz-Institut Jena, 07743 Jena, Germany
⁶Department of Physics, Auburn University, Alabama 36849, USA
⁷Institut für Kernphysik, Universität Münster, 48149 Münster, Germany
⁸Max-Planck-Institut für Kernphysik, 69117 Heidelberg, Germany
⁹School of Science, Xi’an Jiaotong University, Xi’an 710049, China
¹⁰Institute of Physics, Jan Kochanowski University, 25-406 Kielce, Poland
¹¹Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany
¹²Department of Physics, Stockholm University, AlbaNova, 10691 Stockholm, Sweden
¹³Institute of Modern Physics, Chinese Academy of Sciences, 730000 Lanzhou, China
¹⁴Physikalisch–Technische Bundesanstalt, 38116 Braunschweig, Germany
¹⁵Institut für Mathematische Physik, Technische Universität Braunschweig, 38106 Braunschweig, Germany
¹⁶Institut des NanoSciences de Paris, CNRS, Sorbonne Université, 75005 Paris, France
¹⁷Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany

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Phys. Rev. Lett. 135, 113001 – Published 10 September, 2025

DOI: https://doi.org/10.1103/6j3v-lwxj

Abstract

A low-energy storage ring with an ultracold electron cooler has been coupled with a heavy-ion accelerator facilitating high-resolution electron-ion collision spectroscopy of the heaviest few-electron ions. In the present Letter resonant electron-ion recombination of berylliumlike ${Pb}^{78 +}$ ions was measured in the collision-energy range 9.3–16.5 eV and a value of 244.937(30) eV is derived for the ${Pb}^{78 +} (2 s^{2} {{}^{1}S}_{0} - 2 s 2 p {{}^{3}P}_{1})$ excitation energy. This result agrees with the most recent (less accurate) theoretical value of 244.942(52) eV [Malyshev et al., Phys. Rev. A 110, 062824 (2024)], which has been calculated by applying strong-field QED rigorously up to the second order. The present investigation suggests that further technical improvements can potentially increase the experimental accuracy by an order of magnitude.

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Phys. Rev. Lett. 135, 113001– Published 10 September, 2025

Vol. 135, Iss. 11 — 12 September 2025

Received 16 December 2024
Revised 13 March 2025
Accepted 31 July 2025

DOI: https://doi.org/10.1103/6j3v-lwxj

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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Testing Strong-Field QED to Second Order in the Highly Correlated Atomic System Berylliumlike ${Pb}^{78 +}$ by Electron-Ion Collision Spectroscopy

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Testing Strong-Field QED to Second Order in the Highly Correlated Atomic System Berylliumlike Pb78+ by Electron-Ion Collision Spectroscopy

Abstract

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References (44)

Testing Strong-Field QED to Second Order in the Highly Correlated Atomic System Berylliumlike ${Pb}^{78 +}$ by Electron-Ion Collision Spectroscopy