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.
Original language | English |
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Pages (from-to) | 527-531 |
Number of pages | 5 |
Journal | Nature |
Volume | 589 |
Issue number | 7843 |
Early online date | 27 Jan 2021 |
DOIs | |
Publication status | Published - 28 Jan 2021 |
Bibliographical note
Funding Information:Acknowledgements This work was performed at HIPA at PSI. We thank the accelerator and beamline support groups for excellent conditions. We also thank L. Simons, U. Röser, M. Nüssli, H. v. Gunten, B. Zehr, W. Lustermann, A. Gendotti, A. Müller, F. Barchetti, B. van den Brandt, P. Schurter, M. Horisberger, A. Weber, S. Spielmann-Jäggi, U. Greuter, P.-R. Kettle, S. Ritt, W. Simons, K. Linner, H. Brückner, K. S. E. Eikema and the PSI, ETH and MPQ workshops and support groups for their help. We acknowledge the support of the following grants: European Research Council (ERC) through StG. 279765 and CoG. 725039, Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Initiative EXC 1098 PRISMA (194673446) and Excellence Strategy EXC PRISMA+ (390831469), EU Horizon 2020 innovation programme STRONG-2020 (grant agreement number 824093), DFG_GR_3172/9–1, MOST of Taiwan under contract number 106-2112-M-007 -021 -MY3, Fundação para a Ciência e a Tecnologia (FCT), Portugal, and FEDER through COMPETE in the framework of project numbers PTDC/FIS-NUC/0843/2012, PTDC/FIS-NUC/1534/2014, PTDC/ FIS-AQM/29611/2017, PEstOE/FIS/UI0303/2011, PTDC/FIS/117606/2010 and UID/04559/2020 (LIBPhys), contract numbers SFRH/BPD/92329/2013, SFRH/BD/52332/2013, SFRH/ BD/66731/2009 and SFRH/BPD/76842/2011, and by SNF 200021L_138175, SNF 200020_159755 and SNF 200021_165854, as well as the ETH-FAST initiative as part of the NCCR MUST programme.
Publisher Copyright:
© 2021, Springer Nature Limited part of Springer Nature.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
Funding
Acknowledgements This work was performed at HIPA at PSI. We thank the accelerator and beamline support groups for excellent conditions. We also thank L. Simons, U. Röser, M. Nüssli, H. v. Gunten, B. Zehr, W. Lustermann, A. Gendotti, A. Müller, F. Barchetti, B. van den Brandt, P. Schurter, M. Horisberger, A. Weber, S. Spielmann-Jäggi, U. Greuter, P.-R. Kettle, S. Ritt, W. Simons, K. Linner, H. Brückner, K. S. E. Eikema and the PSI, ETH and MPQ workshops and support groups for their help. We acknowledge the support of the following grants: European Research Council (ERC) through StG. 279765 and CoG. 725039, Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Initiative EXC 1098 PRISMA (194673446) and Excellence Strategy EXC PRISMA+ (390831469), EU Horizon 2020 innovation programme STRONG-2020 (grant agreement number 824093), DFG_GR_3172/9–1, MOST of Taiwan under contract number 106-2112-M-007 -021 -MY3, Fundação para a Ciência e a Tecnologia (FCT), Portugal, and FEDER through COMPETE in the framework of project numbers PTDC/FIS-NUC/0843/2012, PTDC/FIS-NUC/1534/2014, PTDC/ FIS-AQM/29611/2017, PEstOE/FIS/UI0303/2011, PTDC/FIS/117606/2010 and UID/04559/2020 (LIBPhys), contract numbers SFRH/BPD/92329/2013, SFRH/BD/52332/2013, SFRH/ BD/66731/2009 and SFRH/BPD/76842/2011, and by SNF 200021L_138175, SNF 200020_159755 and SNF 200021_165854, as well as the ETH-FAST initiative as part of the NCCR MUST programme.
Funders | Funder number |
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MOST of Taiwan | 106-2112-M-007 -021 -MY3 |
NCCR MUST | |
Horizon 2020 Framework Programme | 279765, DFG_GR_3172/9–1, 824093, 725039 |
Seventh Framework Programme | |
European Research Council | |
Deutsche Forschungsgemeinschaft | 194673446, 390831469 |
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung | 200020_159755, 200021_165854, 200021L_138175 |
Fundação para a Ciência e a Tecnologia | |
Instituto Nacional de Ciência e Tecnologia para Excitotoxicidade e Neuroproteção | |
European Regional Development Fund | |
Programa Operacional Temático Factores de Competitividade | PTDC/ FIS-AQM/29611/2017, UID/04559/2020, SFRH/BD/52332/2013, SFRH/BPD/76842/2011, PTDC/FIS/117606/2010, PEstOE/FIS/UI0303/2011, SFRH/ BD/66731/2009, PTDC/FIS-NUC/0843/2012, SFRH/BPD/92329/2013, PTDC/FIS-NUC/1534/2014 |