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A Measurement of the Neutron to 199Hg Magnetic Moment Ratio

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A Measurement of the Neutron to 199Hg Magnetic Moment Ratio A measurement of the neutron to 199Hg magnetic moment ratio S. Afacha,b,c, C. A. Bakerd, G. Bane, G. Bisonb, K. Bodekf, M. Burghoffg, Z. Chowdhurib, M. Daumb, M. Fertla,b,1, B. Frankea,b,2, P. Geltenborth, K. Greend,i, M. G. D. van der Grintend,i, Z. Grujicj, P. G. Harrisi, W. Heilk, V. Helaine´ b,e, R. Henneckb, M. Horrasa,b, P. Iaydjievd,3, S. N. Ivanovd,4, M. Kasprzakj, Y. Kerma¨ıdicl, K. Kircha,b, A. Knechtb, H.-C. Kochj,k, J. Krempela, M. Kuzniak´ b,f,5, B. Laussb, T. Leforte, Y. Lemiere` e, A. Mtchedlishvilib, O. Naviliat-Cuncice,6, J. M. Pendleburyi, M. Perkowskif, E. Pierreb,e, F. M. Piegsaa, G. Pignoll, P. N. Prashanthm, G. Quem´ ener´ e, D. Rebreyendl, D. Riesb, S. Roccian, P. Schmidt-Wellenburgb, A. Schnabelg, N. Severijnsm, D. Shiersi, K. F. Smithi,7, J. Voigtg, A. Weisj, G. Wyszynskia,f, J. Zejmaf, J. Zennera,b,o, G. Zsigmondb aETH Z¨urich, Institute for Particle Physics, CH-8093 Z¨urich, Switzerland bPaul Scherrer Institute (PSI), CH–5232 Villigen-PSI, Switzerland cHans Berger Department of Neurology, Jena University Hospital, D-07747 Jena, Germany dRutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom eLPC Caen, ENSICAEN, Universit´ede Caen, CNRS/IN2P3, Caen, France fMarian Smoluchowski Institute of Physics, Jagiellonian University, 30–059 Cracow, Poland gPhysikalisch Technische Bundesanstalt, Berlin, Germany hInstitut Laue–Langevin, Grenoble, France iDepartment of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom jPhysics Department, University of Fribourg, CH-1700 Fribourg, Switzerland kInstitut f¨urPhysik, Johannes–Gutenberg–Universit¨at,D–55128 Mainz, Germany lLPSC, Universit´eGrenoble Alpes, CNRS/IN2P3, Grenoble, France mInstituut voor Kern– en Stralingsfysica, Katholieke Universiteit Leuven, B–3001 Leuven, Belgium nCSNSM, Universit´eParis Sud, CNRS/IN2P3, Orsay Campus, France oInstitut f¨urKernchemie, Johannes-Gutenberg-Universitat, D-55128 Mainz, Germany Abstract The neutron gyromagnetic ratio has been measured relative to that of the 199Hg atom with an uncertainty of 0:8 ppm. We employed an apparatus where ultracold neutrons and mercury atoms are stored in the same volume and report the result γn/γHg = 3:8424574(30). Keywords: ultracold neutrons, mercury atoms, magnetic moment, gyromagnetic ratio 1. Introduction spin precession in a magnetic field B0 was measured using the Rabi resonance method, from which the gyromagnetic ra- After Chadwick’s discovery of the neutron in 1932, it became tio γn = 2π fn=B0 and the magnetic moment µn = ~=2 γn were clear that nuclei are made out of protons and neutrons. In this extracted. The precision of this method was then improved by picture the neutron had to bear a nonzero magnetic moment using the proton magnetic resonance technique to measure the in order to account for the magnetic moments of nuclei. The magnetic field B0 [2, 3]. In 1956, Cohen, Corngold and Ramsey observation that the neutron, an electrically neutral particle, has achieved an uncertainty of 25 ppm, using Ramsey’s resonance a nonzero magnetic moment is in conflict with the prediction technique of separated oscillating fields [4]. Then, challenged of the relativistic Dirac equation valid for elementary spin 1/2 by the possible discovery of a nonzero neutron electric dipole arXiv:1410.8259v2 [nucl-ex] 31 Oct 2014 particles. This fact was an early indication of the existence of a moment (nEDM), Ramsey’s technique was further developed. sub-structure for neutrons and protons. Profiting from these developments, Greene and coworkers [5] The first direct measurement of the neutron magnetic mo- measured in 1977 the neutron-to-proton magnetic moment ratio ment was reported by Alvarez and Bloch in 1940 [1] with an with an improvement of two orders of magnitude in accuracy. uncertainty of one percent. The frequency fn of the neutron In the latter experiment, the separated field resonance technique was applied simultaneously to a beam of slow neutrons and a Email address: [email protected] (G. Pignol) flow of protons in water precessing in the same magnetic field. 1Now at University of Washington, Seattle WA, USA. Since 1986 the neutron gyromagnetic ratio has been consid- 2Now at Max-Planck-Institute of Quantum Optics, Garching, Germany. ered by the Committee on Data for Science and Technology 3On leave from INRNE, Sofia, Bulgaria. (CODATA) as a fundamental constant. In the 2010 evaluation 4 On leave from PNPI, St. Petersburg, Russia. of the fundamental constants [6], the accepted value 5Now at Queen’s University, Kingston ON, Canada. 6 Now at Michigan State University, East-Lansing, USA. γn 7 = 29:1646943(69) MHz=T [0:24 ppm] (1) Deceased. 2π Preprint submitted to Elsevier August 23, 2018 0 was obtained by combining Greene’s measurement [5] of γn/γp with the determination of the shielded proton gyromagnetic ra- 0 Top CsM tio in pure water γp. Precession chamber In this letter we report on a measurement of the neutron mag- 25.1 cm netic moment with an accuracy of better than 1 ppm, using an 12 cm I/V amplifier apparatus that was built to search for the neutron electric dipole Hg lamp 47 cm PMT: moment [7]. The experimental method differs in two essen- photomultiplier tial aspects from the one reported in Ref. [5]. First, we use tube stored ultracold neutrons (UCNs) rather than a beam of cold Bottom CsM neutrons. Second, the magnetic field is measured using a co- Hg polarization UCN guide UCN chamber magnetometer based on the nuclear spin precession of 199Hg atoms. The result presented is, in fact, a measurement of the ra- 199 tio γn/γHg of the neutron to mercury Hg magnetic moments. Figure 1: Vertical cut through the inner part of the nEDM apparatus. Schemat- Although not as suitable as the proton, the 199Hg atom ically indicated are the precession chamber, the mercury comagnetometer and can also be used as a magnetic moment standard. In 1960 the Cs magnetometer array. 0 Cagnac measured γHg/γp in Kastler’s lab using the newly in- vented Brossel’s double resonance method [8]. Since the mag- netic field was calibrated using nuclear magnetic resonance described below, the UCN valve is opened again and the neu- in water, the mercury magnetic moment was effectively mea- trons fall down into a detector where they are counted. On the sured in units of the proton magnetic moment. Cagnac’s re- way to the detector they pass through a magnetized iron foil that 0 serves as a spin analyzer, providing a spin-dependent counting sult γHg/γp = 0:1782706(3) can be combined with the cur- 0 of the neutrons. rent accepted value of the shielded proton moment (γp=2π = 42:5763866(10) MHz/T [6]) to extract a mercury gyromagnetic The precession chamber is exposed to a static vertical mag- ratio of netic field of B0 ≈ 1030 nT, either pointing upwards or down- wards, corresponding to a neutron Larmor precession frequency γHg γn ≈ = 7:590118(13) MHz=T [1:71 ppm]: (2) of fn = 2π B0 30 Hz. This highly homogeneous magnetic 2π field (δB=B ≈ 10−3) is generated by a cos θ coil. In addition, a set of trim coils permits the optimization of the magnetic field Our result for γn/γHg with an accuracy better than 1 ppm pro- vides an interesting consistency check on results (1) and (2). It uniformity or the application of magnetic field gradients. These confirms the currently accepted value of the neutron magnetic coils are wound on the outside of the cylindrical vacuum tank, moment, which was inferred from a single experiment [5]. Al- which is surrounded by a four-layer mu-metal magnetic shield. ternatively, our result can be used to produce a more accurate During the storage of polarized UCN, the Ramsey method of value for the mercury magnetic moment. separated oscillatory fields is employed in order to measure fn accurately. At the beginning of the storage period, a first os- cillating horizontal field pulse of frequency fRF ≈ fn is applied 2. The measurement with the nEDM spectrometer for t = 2 s, thereby flipping the neutron spins by π/2. Next, the UCN spins are allowed to precess freely in the horizontal The measurement was performed in fall 2012 with the nEDM plane around the B0 field, for a precession time of T = 180 s. A spectrometer, currently installed at the Paul Scherrer Institute second π/2-pulse, at the same frequency fRF and in phase with (PSI). A precursor of this room-temperature apparatus, oper- the first pulse, is then applied. The Ramsey procedure is reso- ated at Institut Laue Langevin (ILL), has produced the cur- nant in the sense that it flips the neutron spins by exactly π only rently lowest experimental limit for the neutron EDM [9]. A when fRF = fn. detailed description of the apparatus, when operated at ILL, can In order to monitor the magnetic field B0 within the preces- be found in [10]. A schematic view of the core of the apparatus, sion chamber, a cohabiting mercury magnetometer is used [12]. as installed now at PSI, is depicted in Fig. 1. A gas of 199Hg mercury atoms is continuously polarized by op- The spectrometer uses UCNs, neutrons with kinetic energies tical pumping in a polarization chamber situated below the pre- of ≈ 100 neV that can be stored in material bottles for a few cession chamber. At the beginning of a measurement cycle, the minutes. In a typical measurement cycle, UCNs from the new precession chamber is filled with polarized atoms, and a π/2 PSI source [11] are guided to the precession chamber, filling the mercury pulse is applied immediately before the first neutron volume for 34 s before closing the UCN valve.
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