GENERAL ASPECTS OF METROLOGY AND MEASUREMENT ENGINEERING

MEASUREMENT OF THE GYROMAGNETIC RATIO OF THE PROTON IN A

WEAK MAGNETIC FIELD

Yu. V. Tarbeev, V. Ya. Shifrin, V. N. Khorev, and N. V. Studentsov

UDC 537.624.2:539.125.4

In the coordination of the fundamental physical constants one of the most important constants is the gyromagnetic ratio of the proton ~. Measurements of the gyromagnetic ratio in strong and weak magnetic fields permit reproducing the ampere, i.e., determining the factor for converting from the current force unit employed to the (absolute) SI ampere, finding at the same time the value of X~ in (absolute) SI units. Here it is unimportant in which units the current force is measured in these two experiments; it is only important that the unit be the same in both experiments. For this reason, since the time that proton mag- netic resonance was realized in practice (1954) in some countries this constant was syste- matically determined and refined by two methods - in a weak magnetic field (USA, USSR, England, Japan, etc.) and in a strong magnetic field (USSR, England, and others). In the last CODATA bulletin on coordinating the constants [I] values are given for 7~ which were measured in different countries up to 1984 and which in 1985 were scaled to the current force unit stored at the ITB.

The measurements of the gyromagnetic ratio of the proton discussed below were performed at the All-Union Scientific-Research Institute of Metrology (AUSRIM) in 1987 after the measuring apparatus and techniques were improved.

Attention was first directed toward lowering the errors owing to the drift of the EMF of the normal cells (NC) employed for measuring the force of the current. It was not possible to rely directly on the EMF standard stored under stationary conditions because it

! was located 40 km from the suburban laboratory where 7p was determined. Nine NC, studied over a number of years, were employed as the measure of EMF. The normal cells are employed at a temperature of 25~ which is maintained in a transportable thermostat with an in- stability of less than 0.001~ and are checked under the same conditions with standard elements whose EMF is periodicaly monitored on a Josephson setup. The error is measuring the temperature in the checks and the use of NC when measuring 7~ did not exceed 5.10-41~ In the course of the measurements one reference NC, whose EMF was compared with the other eight immediately prior to and after the measurements of the nuclear precession frequency, was singled out. A correction of +0.22 DV for the drift in the average value of the EMF of the group of NC employed was made based on the measured difference of the average value of the EMF of the nine NC which were checked with the primary standard before (September 25, 1987) and after (January 18, 1988) X~ was measured, taking into account moments of the mea- surements. The error in determining this correction does not exceed 0.I ~V.

A resistance measure consisting of 10-ohm foil resistors, connected in parallel and having an instability of not greater than 1"10 -6 per year, was employed as the resistance coil, the voltage drop on which was compared with the EMF of the NC. Since the resistance measures do not depend critically on the length of time they are held after being transported, the error in determining the resistance was reduced to 0.5"10 -7 .

The errors in the measurements of ~6 were also lowered due to the use of a current stab- ilizer, which made it possible to maintain a constant current with a given value at a level of 2"10 -8 [2]. This facilitated measurement of the current force and it primarily enabled determining the load coefficient of the resistance coil, which was checked with the primary ohm standard at i0 mW and used at i W; this coefficient turned out to be equal to 2.5"10 -6 . In addition it was possible to study indetail the distribution of the magnetic field of the working quartz coil in the zone of the sample and to correct it by changing the points of the contacts of the conductors feeding current to the winding and by insignificantly changing their configuration. Both factors were taken into account in calculating the field of the coil, employed earlier in measurements of ~ [3] performed in 1980.

Translated from Izmeritel'naya Tekhnika, No. 4, pp. 3-4, April, 1989.

0543-1972/89/3204-0279512.50 �9 1989 Plenum Publishing Corporation 279

TABLE 1

Source of the error component Value of the error component, 10 -7

Measurement of the diameters of the loops of the quartz coil Measurement of the distance between the loops Measurement of the diameter of the wire Distribution of the current over the cross section of the wire

Uncertainty in the shape of the winding of the quartz coil Change in the position of the connecting conductors and of

the return wire Magnetism of the material of the coil Measurement of the temperature of the quartz coil Measurement of the ratio of the precession frequencies of

SHe nuclei and protons Checking of ~4F measures with primary volt standard Instability of ~ measure Checking of resistance measures with primary ohm standard Instability of resistance measures Thermo KMF in the voltage checking circuits Measurement of the load coefficient of the resistance mea- sure Measurement of the coefficient of the effect of the

quartz coil on the autocompensator of the external filed Measurement of the magnetic resonance frequency 3 He

1.4 1.6 1.0

1.0 1.7

0.5 0.5 0.5

0.6 0.7 1.0 0.4 0.i 0.2

0.4

0.I 0.4

It is shown in [3] that the largest error is introduced when measuring the diameter of the coil, so that in our experiment we improve the setup for measuring the diameter in

order to increase the accuracy of the measurements. In addition, the measurements were more complete: each loop was measured in 12 sections. We also introduced corrections for the temperature of the quartz foil, the effect of the magnetic field of the quartz coil on the system for compensating the,Earth's field, etc.

We used the following procedure to eliminate the screening or other effects of the polarizing coil, which is necessary in order to observe the free procession of protons. In the quartz coil we determined the gyromagnetic ratio not of the proton but rather of SHe nuclei, for which a polarizing coil is not required. We first determined in the same field with inductions of 5.7 and 9.7"10 -4 T the ratio of the frequency of precession of protons and SHe nuclei with spherical samples having identical parameters and in the same receiving coil in the presence of a polarizing coil. This procedure made it possible to eliminate

' owing to the the effect of the polarization coil on the result of the determination of yp high accuracy of the measurement of the ratio of the frequencies, which, in its turn, was ensured by the high stability of the field.

Table 1 gives the main components of the error in measuring ~.

The following new value was obtained for the gyromagnetic ratio of the proton (at t = 23~

,y' =26751 4660.104 rad.sec -1 .T-IAusRIM

In addition, we obtain the value

?,He=20378.~ll.10~rad.sec-Z.T-~uSRiM

I n V I - 8 5 u n i t s (1 AAUSRIM = 1 .00000295 AVI-85) t h e v a l u e s o f t h e g y r o m a g n e t i c r a t i o s o f t h e p r o t o n and SHe a r e a s f o l l o w s :

? p = 2 6 7 5 1 . 3 8 7 0 ( 9 3 ) . 1 0 4 r a d . s e c _ i . T - l VI-85

? 3 H e = 2 0 3 7 8 , 3 4 0 1 ( 7 1 ) . 1 0 4 r a d . s e c - I - 3 "TvI-85

280

Only the value of the gyromagnetic ratio of the proton obtained at the National Bureau of Standards, the error in which equals 2.4"10 -7 , is more accurate than our result for the gyromagnetic ratio of the proton.

The new determination of ~low by AUSRIM can be employedtogetherwith the values of ylow obtained by NBS and the more accurate value of y'high obtained at NPL in a strong P , P

magnetic field to calculate 7p in the SI system and to calculate the factor for converting from the ITB ampere to the SI ampere. Using

' low ?p,NBS=26751,372, 104 rad. sec- 1.T2 ZVI_85 ' (2.4. 10 -7) and 'h'~h _ _ ?p,NPL---26751.676 �9 [0~ rad.sec/.]T-Zvl_85 , (I .0. i0-6),

we obtain the average

{1] :

u -. 104 rad. sec- t .T -lvI_85 ,(2, I '10-1) and

g,s =V r 10,

(5. I. 1o-7).

T h i s r e s u l t i s c l o s e t o t h e r e s u l t o b t a i n e d f r o m c o o r d i n a t i n g t h e c o n s t a n t s i n 1986

7~=26751 526.104 rad -sec- ~ _ i (3.10-7).

The conversion factor K A for converting from the ITB ampere to the SI ampere is

KA, VI = V ?'~o~/y'~IZh =I--5,53.10 -6, (5. I. I0-7),

i.e., I AVI-85 = 1ASI = 5.53 BA (•

Analogous calculations for the conversion factor for converting from the AUSRIM ampere to the SI ampere give

K AOSRIM=I--3.33.10 -~ .

We shall employ this result to calculate the constant Ej ~ 2e/h with the accuracy accessible to us. At AUSRIM the value.EjAUSRI M = 483596,176"109 Hz/V was used to realize the volt based on the Josephson effect. If it is assumed that the AUSRIM ohm equals the SI ohm, and this was confirmed in checks performed in 1983-1985 of the ohm standards at ITB with an error of less than 1"10 -7 , then we have

EJAUSRIM87 ~ E JAUSRIM 80 ( I n u 3.33. 10 -6) =483597 ~ 786. I 0 '~ Hz / V ,

which agrees within the limits of error with the numerical value of Es0, which is recommended by the working work of KKE ITB for practical application starting in 1990 based on the results of more accurate (absolute) measurements of the volt and ampere in the national laboratories of different countries.

The calculations performedshow that all results compared agree well with one another and that their errors were correctly evaluated. In conclusion we note that work on deter- mining more accurately the distances between the loops of the winding of the working quartz magnetic induction coil and reducing the uncertainty in the shape of the coil is being continued at AUSRIM.

LITERATURE CITED

i. CODATA Bul. JN, No. 63, 36 (1986).

281

2. E. V. Blinov, et al., "Creation of measurement means for metrological support of pre- cision nanoteslameters," Tr. VNIIM (1988).

3. N. V. Studentsov, V. N. Khorev, and V. Ya. Shifrin, Izmer. Tekh., No. 6, 56 (1981).

282