Measuring the α-particle charge radius with muonic helium-4 ions

Julian J. Krauth*, Karsten Schuhmann, Marwan Abdou Ahmed, Fernando D. Amaro, Pedro Amaro, François Biraben, Tzu Ling Chen, Daniel S. Covita, Andreas J. Dax, Marc Diepold, Luis M.P. Fernandes, Beatrice Franke, Sandrine Galtier, Andrea L. Gouvea, Johannes Götzfried, Thomas Graf, Theodor W. Hänsch, Jens Hartmann, Malte Hildebrandt, Paul IndelicatoLucile Julien, Klaus Kirch, Andreas Knecht, Yi Wei Liu, Jorge Machado, Cristina M.B. Monteiro, Françoise Mulhauser, Boris Naar, Tobias Nebel, François Nez, Joaquim M.F. dos Santos, José Paulo Santos, Csilla I. Szabo, David Taqqu, João F.C.A. Veloso, Jan Vogelsang, Andreas Voss, Birgit Weichelt, Randolf Pohl, Aldo Antognini, Franz Kottmann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


The energy levels of hydrogen-like atomic systems can be calculated with great precision. Starting from their quantum mechanical solution, they have been refined over the years to include the electron spin, the relativistic and quantum field effects, and tiny energy shifts related to the complex structure of the nucleus. These energy shifts caused by the nuclear structure are vastly magnified in hydrogen-like systems formed by a negative muon and a nucleus, so spectroscopy of these muonic ions can be used to investigate the nuclear structure with high precision. Here we present the measurement of two 2S–2P transitions in the muonic helium-4 ion that yields a precise determination of the root-mean-square charge radius of the α particle of 1.67824(83) femtometres. This determination from atomic spectroscopy is in excellent agreement with the value from electron scattering1, but a factor of 4.8 more precise, providing a benchmark for few-nucleon theories, lattice quantum chromodynamics and electron scattering. This agreement also constrains several beyond-standard-model theories proposed to explain the proton-radius puzzle2–5, in line with recent determinations of the proton charge radius6–9, and establishes spectroscopy of light muonic atoms and ions as a precise tool for studies of nuclear properties.

Original languageEnglish
Pages (from-to)527-531
Number of pages5
Issue number7843
StatePublished - 28 Jan 2021


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