A Free Precession Determination of the Proton Gyromagnetic Ratio

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    A Free Precession Determination of theProton Gyromagnetic Ratio*


    ITHIN the last decade the proton gyromagnetic absolute values of the magnetic fields used, which areratio has come to play an important role in de- measured in terms of the proton precession frequency,termining the fundamental constants of physics. an improvement in the value of the proton gyromag-

    A new measurement of this quantity by the National netic ratio automatically gives an improvement in theBureau of Standards is now nearing completion and a values of the fundamental constants.preliminary value has been obtained. Before discussing The first precise measurement of the proton gyromag-this experiment, however, it is perhaps desirable to em- netic ratio was made at the National Bureau of Stand-phasize the relevance of the proton gyromagnetic ratio ards in 1949 by Thomas, Driscoll, and Hipple.2 Theto magnetic measurements and electrical standards. estimated accuracy was 22 ppm. This permitted farThe proton, which is just the nucleus of the hydrogen more precise measurements of magnetic fields than had

    atom, has an inherent magnetic moment. A magnetic previously been possible. The experiment was done withfield will exert a force on it which tends to line up the a strong electromagnet. The field was found from themagnetic moment along the field direction. However, force on a currenit-carrying wire placed in the magnetthe proton also spins rapidly about its axis. Its resulting gap. The frequency for resonant absorption of energyangular momentum causes it to act like a gyroscope. by the proton sample from an RF field, which is theInstead of lining up with the field, the proton will precess same as the precession frequency, was measured quiteabout the field direction like a spinning top. As might be simply. However, the magnetic field measurement wasexpected, the precession, or Larmor, frequency is di- very difficult and contributed most of the uncertaintyrectly proportional to the magnetic induction B. The in the result.ratio of the angular precession frequency in radians per The present method of measuring the proton gyromag-second to the magnetic induction in gauss is known as netic ratio was designed to keep the uncertainty in thethe proton gyromagnetic ratio yp. magnetic field as small as possible. A precision solenoid3

    Since all protons have the same magnetic moment 100 cm long and 28 cm in diameter, wounid with a singleand angular momentum, they will all have the same layer of bare copper wire, was used to supply the field.gyromagnetic ratio. Also, if the protons are contained in The wire was wound under constant tension in a care-relatively nonmagnetic molecules such as water or fully lapped groove on a fused silica form. With thishydrocarbon molecules, they will act almost as if they solenoid the pitch and other dimensions can be measuredwere free protons. Thus one can work with convenient accurately enough so that the field near the center forsamples such as water or mineral oil. Actually, the mag- a known current can be calculated to about one ppm.netic field which a proton in a molecule sees may differ Since the present uncertainty in the ampere as main-from the applied field because of shielding caused by the tained by the National Bureau of Standards is aboutdiamagnetism of the electrons in the molecules, but such 5 ppm,4 the absolute accuracy of the field produced byshifts are only of the order of 30 ppm and are known to the solenoid is limited almost entirely by this uncer-about one ppm.1 tainty. If the resonance frequency can be measured moreTo measure magnetic fields accurately it is thus neces- accurately than this, the gyromagnetic ratio measure-

    sary only to measure the proton precession frequency ment becomes an excellent check on the constancy offor a sample such as water in the unknown field. Fortu- the NBS ampere.nately, measurement. of the precession frequency to a In order to avoid damage to the solenoid due to heat-part in 106or better is very simple compared with almost ing, it was necessary to keep the current down to 1any other type of precise measurement. We can thus ampere. The resulting magnetic field was 12 gauss. Sinceeasily find the field strength in absolute units to the ac- small variations in the earth's magnetic field wouldcuracy with which the proton gyromagnetic ratio is cause fluctuations in the total field, it was necessary toknown. Since the largest single uncertainty up to the minimize the effects of disturbances from other appa-present time in determinations of the fundamental con- ratus, cars, power lines, etc. For this reason the experi-

    stantsofphsicsas coe fro the ncertinty n the 2 H. A. Thomas, R. L. Driscoll, and J. A. Hipple, Phys. Rev., vol.78, p. 787; 1950.

    * Manuscript received by the PGI, September 22, 1958. Also see J. Res. NBS, vol. 44, RP2104, p. 569; 1950.t NVational Bureau of Standards, XVashington, D. C. 3This solenoid also has been used in a recent determination of the[H. A. Thomas, Phys. Rev., vol. 80, p. 901; 1950. ampere: R. L. Driscoll, J. Res. NBS, vol. 60, RP2845, p. 287; 1958.H. S. Gutowsky and R. E. McClure, Phys. Rev>., vol. 81, p. 277; 4R. L. Driscoll and R. D. Cutkosky, f. Res. NBS, vol. 60,

    1951. RP2846, p. 297; 1958.

  • 1958 Bender and Driscoll: Free Precession Determination of Proton Gyromagnetic Ratio 177

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    Fig. I-Fredericksburg Magnetic Observatory; the main building onthe right contains offices and workshops. The other buildings arenon-magnetic and are used for observation. The solenoid waslocated in the nearest building on the left.

    Fig. 3-The apparatus in the foreground is for controlling the currentthrough the solenoid. Automatic controls for the large coils whichbuck out the earth's magnetic field can be seen at the rear.

    the center of the solenoid. Since the relaxation time forFig. 2-The nonmagnetic building containing the solenoid is located the magnetizationi of the sample is several seconds, the

    at the left. The shed contains the polarizing magnet and pumps.The pneumatic tube goes from the shed into the solenoid building. magnetization was still large when the sample reachedThe two buildings at the right contain the controls for the cur- the solenioid. The shed containing the magnet and therent through the solenoid and the batteries, pneumatic tube going into the solenoid can be seen in

    Fig. 2. In this way a large magnetization was pro-ment was carried out at the Fredericksburg Magnetic duced in the sample without disturbing the solenoidObservatory of the U. S. Coast and Geodetic Survey, field. In goinig through the pneumatic tube the mag-The Observatory, shown in Fig. 1, is located on a site nietization of the sample followed the instantaneouschosen to be as free from magnetic disturbances as magnetic field directioni and ended up pointed along thepossible. A nonmagnetic building with large coils for axis of the solenoid. A short pulse of RF magnetic fieldcompensating the earth's field was made available for at about the precession frequency of the protons in thethe experiment. Fig. 2 shows a view of this buildinig field of the solenoid was then applied perpendicular to(left) and of the buildings (right) housing the apparatus the solenoid field. This pulse, lasting about 10 msec,for controlling and measuring the current through the caused the magnetization to spiral out from the solenoidsolenoid. The current was passed through a standard axis and end up nearly perpendicular to the field direc-resistance maintained in an oil bath anid the resulting tion and precessing around it. The precessing magnetiza-voltage was compared with a set of saturated standard tion induced a signal in a pick-up coil which surroundedcells in a thermostated case. These were then compared the sample, and the period of this signal was measured.with the bank of standard cells at the Bureau of Stand- The solenoid and the coils for compensating theards. The equipment used is shown in Fig. 3. With this earth's field are shown in Fig. 4. Extra compensatingarrangement the solenoid current could be measured in coils inside it served to reduce the inhomogeneity nearterms of the electrical standards maintainied at the the center due to enid effects. These coils, with the sole-Bureau to about 1 ppm. noid removed, can be seen in Fig. 5. The sample came

    In the solenoid field of 12 gauss the proton precession into place through the lucite tube at the top. The con-frequency was 52 kc. At such a low frequency the reso- tribution to the field from the compensating coils wasnance signals which can be obtained with conventional only one part in a thousand and the coil dimensions aremethods are quite weak unless a large sample is used. known well eniough so that the uncertainty in the totalHowever, by employing a variationi of the free preces- field is niot increased appreciably. All materials goingsioii techniques initroduced by Hahnf and by Packard into the solenoid were carefully tested for magnietism.and Varian f a good signal-to-noise ratio was obtained The carriage holding the solenoid, the rails on whichwith a 2-cm diameter sample. it runs, and the support at the end for the compensatingThe sample consisted of a spherical glass or lucite coils were made of aluminium which had also been tested.

    shell filled with distilled water. It was polarized in a The immediate surroundings of the sample can befield of about 5000 gauss produced by a permanent mag- seen in Fig. 6. The pick-up coil was supported on thenet and then shot through a 40-foot pnieumatic tube into lucite tube bringinig the sample into place inside the

    E. L. Hahn, Phys. Rev., vol. 77, p. 297; 1950. compensating coils. The pair of coils which can be seenM. Packard and R. Varian, Phys. Rev., vol. 93, p. 941; 1954. were used to apply the short RF pulse for reorienting the


    Fig. 6 TIhe immiedliate stirrotintiuiigs of the sampleinisidlethe soleioitIcan be seeni. TIhe small coil att the center SLorroonids the sample andpicks tip the signail. TIhe aluimintlm rinig holds the compensatingcoils in place. 'rhe otitsi(le coils provi dethe IRF ptilse to reorieiitthe sample.

    Fig. 4-The large Fanselati coils belonging to the Observatory wereise(d to btick otIt the earth's liel(l. 'T'he precision solenoi(i c,an heseen at the center, with the pileniliatic tube enterinig throughi thefar eiid.

    Fig. 7-T'he apparattis shown is used to measure the freqtiency of thesignial fromi the pick-tip coil to abotit onie part in 101~. It is located

    - in the niaii building about 150 mieters away fromi the solenioidbuildiiig, which cani be seeni at the left.

    Fig. 5--IThe compensattinig coils for smoothinig ouit the liel(d from thesolenoid are showii with the solenoid moved otit of the wav. All mittedl the perio(d for any preassigne(d number of cyclesmaterials usecl for the solenoi(d carriage, the rails, and the stip- of the precessioni freqtueu cy to be measLired. 'I'he tincer-ports for the compensating coils have been careftillv checked formagnetisimi. The samilple enters through the ILICite ttlbe at the top tainty in the total periodnmeasurement was less thanand returins the same way. 0.3 ,usec, and since measuring times of 3 second(s or more

    couldi be used, the period measuremenit intro(luce(d verymagnetization of the sampl)le. 'T'he signal from the piick- little uncertainity in the result.up coil was sent throtigh a preamplifier and theni to the Since the magnetic field was quite homogenieous overmain Observatory buildlings where the perio(I was meas- the sample, the factor which limited the duration of thetired. 'I'he apparatus for cloing this is showin in Fig. 7. signal was dlecay of the samrple magnetization clue to in-'I'he building containing the solenoid can be seen teractions between protons in the sample. For water thethrough the window at the left. 'I'he signal was passed decay time at room temperature is about 3 seconds,through a 500-cycle blan(lwidth amplifier and theni to a while for benzeiie it is about 18 seconds. When the ampli-circuit which ptLt out a sharl) pulse each time the volt- fied output from the pick-up coil was displaye(l on aage passed throughi zero positively. These ptilses wenit to slow-sweep oscilloscope, the envelope of the inu(ticeda gating circuit, preset couniter, and timer, which per- voltage was seen. Such a trace is showni at the bottom

  • 1958 Bender and D)riscoll: Free Precession Determnination of Pvroton Gyromagnetic Ratio 179