Direct high-precision measurement of the magnetic moment of the proton


One of the fundamental properties of the proton is its magnetic moment, µp. So far µp has been measured only indirectly, by analysing the spectrum of an atomic hydrogen maser in a magnetic field1. Here we report the direct high-precision measurement of the magnetic moment of a single proton using the double Penning-trap technique2. We drive proton-spin quantum jumps by a magnetic radio-frequency field in a Penning trap with a homogeneous magnetic field. The induced spin transitions are detected in a second trap with a strong superimposed magnetic inhomogeneity3. This enables the measurement of the spin-flip probability as a function of the drive frequency. In each measurement the proton’s cyclotron frequency is used to determine the magnetic field of the trap. From the normalized resonance curve, we extract the particle’s magnetic moment in terms of the nuclear magneton: μp = 2.792847350(9)μN. This measurement outperforms previous Penning-trap measurements4,5 in terms of precision by a factor of about 760. It improves the precision of the forty-year-old indirect measurement, in which significant theoretical bound state corrections6 were required to obtain µp, by a factor of 3. By application of this method to the antiproton magnetic moment, the fractional precision of the recently reported value7 can be improved by a factor of at least 1,000. Combined with the present result, this will provide a stringent test of matter/antimatter symmetry with baryons8.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Relative precision achieved in measurements of the proton magnetic moment.
Figure 2: Experimental setup and measurement procedures.
Figure 3: Measured g-factor resonance.


  1. 1

    Winkler, P. F., Kleppner, D., Myint, T. & Walther, F. G. Magnetic moment of the proton in Bohr magnetons. Phys. Rev. A 5, 83–114 (1972)

    ADS  Article  Google Scholar 

  2. 2

    Häffner, H. et al. Double Penning-trap technique for precise g-factor determinations in highly charged ions. Eur. Phys. J. D 22, 163–182 (2003)

    ADS  Article  Google Scholar 

  3. 3

    Dehmelt, H. G. & Ekström, P. Proposed g-2 experiment on single stored electron or positron. Bull. Am. Phys. Soc. 18, 727–731 (1973)

    Google Scholar 

  4. 4

    Rodegheri, C. C. et al. An experiment for the direct determination of the g-factor of a single proton in a Penning trap. New J. Phys. 14, 063011 (2012)

    ADS  Article  Google Scholar 

  5. 5

    DiSciacca, J. & Gabrielse, G. Direct measurement of the proton magnetic moment. Phys. Rev. Lett. 108, 153001 (2012)

    CAS  ADS  Article  Google Scholar 

  6. 6

    Karshenboim, S. G. & Ivanov, V. G. The g-factor of the proton. Phys. Lett. B 566, 27–34 (2003)

    CAS  ADS  Article  Google Scholar 

  7. 7

    DiSciacca, J. et al. One-particle measurement of the antiproton magnetic moment. Phys. Rev. Lett. 110, 130801 (2013)

    CAS  ADS  Article  Google Scholar 

  8. 8

    Bluhm, R., Kostelecký, V. A. & Russell, N. CPT and Lorentz tests in Penning traps. Phys. Rev. D 57, 3932–3943 (1998)

    CAS  ADS  Article  Google Scholar 

  9. 9

    Beringer, J. et al. (Particle Data Group). Review of particle physics. Phys. Rev. D 86, 010001 (2012)

    ADS  Article  Google Scholar 

  10. 10

    Van Dyck, R. S., Jr, Farnham, D. L., Zafonte, S. L. & Schwinberg, P. B. High precision Penning trap mass spectroscopy and a new measurement of the proton’s “atomic mass”. AIP Conf. Proc. 457, 101–110 (1999)

    CAS  ADS  Article  Google Scholar 

  11. 11

    Sturm, S. et al. High-precision measurement of the atomic mass of the electron. Nature 506, 467–470 (2014)

    CAS  ADS  Article  Google Scholar 

  12. 12

    Pohl, R. et al. The size of the proton. Nature 466, 213–216 (2010)

    CAS  ADS  Article  Google Scholar 

  13. 13

    Van Dyck, R. S., Schwinberg, P. B. & Dehmelt, H. G. New high-precision comparison of electron and positron g-factors. Phys. Rev. Lett. 59, 26–29 (1987)

    CAS  ADS  Article  Google Scholar 

  14. 14

    Hanneke, D., Fogwell, S. & Gabrielse, G. New measurement of the electron magnetic moment and the fine structure constant. Phys. Rev. Lett. 100, 120801 (2008)

    CAS  ADS  Article  Google Scholar 

  15. 15

    Brown, L. S. & Gabrielse, G. Geonium theory: physics of a single electron or ion in a Penning trap. Rev. Mod. Phys. 58, 233–311 (1986)

    CAS  ADS  Article  Google Scholar 

  16. 16

    Brown, L. S. Geonium lineshape. Ann. Phys. 159, 62–98 (1985)

    CAS  ADS  Article  Google Scholar 

  17. 17

    Ulmer, S. et al. Observation of spin flips with a single trapped proton. Phys. Rev. Lett. 106, 253001 (2011)

    CAS  ADS  Article  Google Scholar 

  18. 18

    Gabrielse, G. et al. Special relativity and the single antiproton: fortyfold improved comparison of and p charge-to-mass ratios. Phys. Rev. Lett. 74, 3544–3547 (1995)

    CAS  Google Scholar 

  19. 19

    Ulmer, S. et al. Direct measurement of the free cyclotron frequency of a single particle in a Penning trap. Phys. Rev. Lett. 107, 103002 (2011)

    CAS  ADS  Article  Google Scholar 

  20. 20

    Ulmer, S. et al. A cryogenic detection system at 28.9 MHz for the non-destructive observation of a single proton at low particle energy. Nucl. Instrum. Meth. A 705, 55–60 (2013)

    CAS  ADS  Article  Google Scholar 

  21. 21

    Wineland, D. J. & Dehmelt, H. G. Principles of the stored ion calorimeter. J. Appl. Phys. 46, 919–930 (1975)

    ADS  Article  Google Scholar 

  22. 22

    Mooser, A. et al. Demonstration of the double Penning-trap technique with a single proton. Phys. Lett. B 723, 78–81 (2013)

    CAS  ADS  Article  Google Scholar 

  23. 23

    Mooser, A. et al. Resolution of single spin-flips of a single proton. Phys. Rev. Lett. 110, 140405 (2013)

    CAS  ADS  Article  Google Scholar 

  24. 24

    DiSciacca, J., Marshall, M., Marable, K. & Gabrielse, G. Resolving an individual one-proton spin flip to determine a proton spin state. Phys. Rev. Lett. 110, 140406 (2013)

    CAS  ADS  Article  Google Scholar 

  25. 25

    Cornell, E. A., Weisskoff, R. M., Boyce, K. R. & Pritchard, D. E. Mode coupling in a Penning trap: π pulses and a classical avoided crossing. Phys. Rev. A 41, 312–315 (1990)

    CAS  ADS  Article  Google Scholar 

  26. 26

    Sivia, D. S. & Skilling J Data Analysis—A Bayesian Tutorial 1st edn (Oxford Science, 2010)

    Google Scholar 

  27. 27

    Sturm, S. et al. g-factor measurement of hydrogenlike 28Si13+ as a challenge to QED calculations. Phys. Rev. A 87, 030501 (2013)

    ADS  Article  Google Scholar 

  28. 28

    Mittleman, R. K., Ioannou, I. I., Dehmelt, H. G. & Russell, N. Bound on CPT and Lorentz symmetry with a trapped electron. Phys. Rev. Lett. 83, 2116–2119 (1999)

    CAS  ADS  Article  Google Scholar 

  29. 29

    Smorra, C. et al. Towards a high-precision measurement of the antiproton magnetic moment. Hyperfine Interact. (2014)

  30. 30

    Ulmer, S. et al. Technical Design Report BASE CERN Document Server, SPSC-TDR-002, (CERN, 2013)

Download references


We acknowledge the financial support of the BMBF, and of the EU (ERC grant number 290870-MEFUCO), the Helmholtz-Gemeinschaft, HGS-HIRE, the Max-Planck Society, IMPRS-PTFS, and the RIKEN Initiative Research Unit Program.

Author information




S.U., C.C.R., H.K., A.M. and C.L. designed and built the experimental apparatus and the data acquisition system. A.M., C.L. and S.U. took part in the months-long data-taking runs. K.F. and A.M. developed the algorithms for the spin state analysis. A.M., K.F., S.U., C.L. and H.K. analysed the data. S.U., A.M., K.B. and J.W. wrote the initial manuscript, which was then improved and approved by all authors.

Corresponding author

Correspondence to A. Mooser.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Related audio

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mooser, A., Ulmer, S., Blaum, K. et al. Direct high-precision measurement of the magnetic moment of the proton. Nature 509, 596–599 (2014).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing