Blaum, K.

Bräuninger, S. A.

Kracke, H.

Leiteritz, C.

Mooser, A.

Quint, W.

Rodegheri, C. C.

Ulmer, S.

Walz, J.

GSI Repository

Direct measurement of the proton magnetic momentA. Mooser1,2, K. Blaum3,4, S.A. Bra¨uninger3,4, H. Kracke1,2, C. Leiteritz1, W. Quint4,5, C.C.Rodegheri1,4, S. Ulmer6, and J. Walz1,21Institut fu¨r Physik, Johannes Gutenberg-Universita¨t Mainz, Germany; 2Helmholtz Institut Mainz, Mainz, Germany;3Max-Planck-Institut fu¨r Kernphysik, Saupfercheckweg 1, Heidelberg, Germany; 4Ruprecht Karls-Universita¨tHeidelberg, Heidelberg, Germany; 5GSI - Helmholtzzentrum fu¨r Schwerionenforschung, Darmstadt, Germany;6present address: RIKEN Advanced Science Institute, Hirosawa, Wako, Saitama, JapanUp to now the magnetic moment of the proton has neverbeen measured directly. The present most precise valuefor the magnetic moment comes from measurements of thehyperfine splitting in atomic hydrogen by Winkler et al.[1]. Several bound-state corrections have to be includedto extract the magnetic moment of the free proton with aprecision of 8.2 parts in 109 [2]. A direct and precise mea-surement with just one single isolated proton stored in acryogenic Penning trap has the potential to improve thisvalue by one order of magnitude without a need for theo-retical corrections and opens the way for a correspondingmeasurement on the antiproton.An ideal Penning trap is a superposition of a homogeneousmagnetic field and an electrostatic quadrupole potential.In such a trap an ion has three independent eigenmotions:two radial modes, the modified cyclotron motion with fre-quency ω+ and the magnetron motion with frequency ω−,and an axial motion with frequency ωz . The principle of ameasurement of μp is the determination of two frequenciesof the proton: the spin-precession frequency ωL and thefree cyclotron frequency ωc. The frequency ratio yields themagnetic moment ωL/ωc = μp/μN in units of the nuclearmagneton μN .The Larmor frequency is determined by measuring the spintransition probability as a function of the frequency of anexternal magnetic driving field. To this end an inhomoge-neous magnetic field, a so-called magnetic bottle, is usedto couple the spin magnetic moment to the axial motion ofthe proton. Using this continuous Stern-Gerlach effect aspin transition results in a frequency jump of the axial mo-tion. In our magnetic bottle with B2 = 3 · 105 T/m2 a spintransition results in an axial frequency jump of 171 mHz at742 kHz.However, the strong magnetic bottle also couples the mag-netic moments of the radial modes to the axial mode.Thus the axial frequency is extremely sensitive to energychanges in the radial modes. This results in axial frequencyfluctuations. As a measure for these fluctuations the stan-dard deviation of the difference between two subsequentaxial frequency measurements α = νz(t)− νz(t+Δt) canbe defined, Ξ =((N − 1)−1∑(αi − α¯)2)1/2. The mini-mal fluctuation achieved is Ξopt ≈ 150 mHz. This value isnot sufficient to detect spin transitions directly. However, aseries of spin transitions leads to an increase of the fluctu-ations ΞSF ≈√Ξ2opt + PSFΔν2z,SF . A measurement ofΞSF and Ξopt then allows a determination of the spin tran-sition probability [3], thus the Larmor frequency.The spin-flip resonance has been measured by tuning theFigure 1: Larmor resonance of a single proton stored in theanalysis trap. The broadening is due to the coupling of theaxial motion to the thermal bath of the detection system inthe inhomogeneous magnetic field.spin transition drive over the Larmor frequency. The re-sult is presented in Fig. 1. The line broadening is due tothe coupling of the axial motion to the thermal bath of thedetection system in the magnetic bottle. From this the Lar-mor frequency can be determined to 2 parts in 10 6, limitedby the line broadening. Combined with a measurement ofthe free cyclotron frequency the g-factor was determined to5.585696(50) [4].Taking advantage of the so-called double Penning-trapsetup, a narrower spin-flip resonance is expected, which al-lows for a measurement of the g-factor with even higherprecision in the future. To this end spin transitions aredriven in a Penning trap with a homogeneous magneticfield, where no additional line broadening occurs, and sub-sequently detected in a second Penning trap with a mag-netic bottle. This will demand the direct detection of spintransitions, hence lower axial frequency fluctuations. In thefuture, we plan to measure the antiproton magnetic momentas a test of CPT invariance within the FLAIR Collabora-tion.References[1] P. F. Winkler et al., Phys. Rev. A 5, 83 (1972).[2] P. J. Mohr et al., Rev. Mod. Phys. 80, 633 (2008).[3] S. Ulmer et al., Phys. Rev. Lett. 106, 253001 (2011) .[4] C. C. Rodegheri et al., New J. Phys. 14 063011 (2012)GSI SCIENTIFIC REPORT 2012 PHN-HSD-EXP-0511

Direct measurement of the proton magnetic moment

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Direct measurement of the proton magnetic moment

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