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 Indelicato, Lucile 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. Santos, José Paulo Santos, Csilla I. Szabo, David Taqqu, João F. C. A. Veloso, Jan Vogelsang, Andreas Voss, Birgit Weichelt, Randolf Pohl (), Aldo Antognini () and Franz Kottmann
Additional contact information
Julian J. Krauth: Max Planck Institute of Quantum Optics
Karsten Schuhmann: Institute for Particle Physics and Astrophysics, ETH Zurich
Marwan Abdou Ahmed: Universität Stuttgart
Fernando D. Amaro: University of Coimbra
Pedro Amaro: NOVA School of Science and Technology, NOVA University Lisbon
François Biraben: Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France
Tzu-Ling Chen: National Tsing Hua University
Daniel S. Covita: i3N, Universidade de Aveiro
Andreas J. Dax: Paul Scherrer Institute
Marc Diepold: Max Planck Institute of Quantum Optics
Luis M. P. Fernandes: University of Coimbra
Beatrice Franke: Max Planck Institute of Quantum Optics
Sandrine Galtier: Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France
Andrea L. Gouvea: University of Coimbra
Johannes Götzfried: Max Planck Institute of Quantum Optics
Thomas Graf: Universität Stuttgart
Theodor W. Hänsch: Max Planck Institute of Quantum Optics
Jens Hartmann: Ludwig-Maximilians-Universität, Fakultät für Physik
Malte Hildebrandt: Paul Scherrer Institute
Paul Indelicato: Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France
Lucile Julien: Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France
Klaus Kirch: Institute for Particle Physics and Astrophysics, ETH Zurich
Andreas Knecht: Paul Scherrer Institute
Yi-Wei Liu: National Tsing Hua University
Jorge Machado: NOVA School of Science and Technology, NOVA University Lisbon
Cristina M. B. Monteiro: University of Coimbra
Françoise Mulhauser: Max Planck Institute of Quantum Optics
Boris Naar: Paul Scherrer Institute
Tobias Nebel: Max Planck Institute of Quantum Optics
François Nez: Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France
Joaquim M. F. Santos: University of Coimbra
José Paulo Santos: NOVA School of Science and Technology, NOVA University Lisbon
Csilla I. Szabo: Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France
David Taqqu: Institute for Particle Physics and Astrophysics, ETH Zurich
João F. C. A. Veloso: i3N, Universidade de Aveiro
Jan Vogelsang: Max Planck Institute of Quantum Optics
Andreas Voss: Universität Stuttgart
Birgit Weichelt: Universität Stuttgart
Randolf Pohl: Max Planck Institute of Quantum Optics
Aldo Antognini: Institute for Particle Physics and Astrophysics, ETH Zurich
Franz Kottmann: Institute for Particle Physics and Astrophysics, ETH Zurich

Nature, 2021, vol. 589, issue 7843, 527-531

Abstract: Abstract 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.

Date: 2021
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DOI: 10.1038/s41586-021-03183-1

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