measurement of the proton gyromagnetic ratio in a weak magnetic field

3
MEASUREMENTS OF ELECTRICAL AND MAGNETIC QUANTITIES MEASUREMENT OF THE PROTON GYROMAGNETIC RATIO IN A WEAK MAGNETIC FIELD N. V. Studentsov, T. N. Malyarevskaya, and V. Ya. Shifrin UIX: 539.125.4.001,24 Measurements of the proton gyromagnetic ratio r were carried out since 1958 at the VNIIM (All-Union Scien- tific-Research Institute of Metrology), The first results and the measurement technique were published in 1960 and 1962 i"1-31. However, experiments continued at the VNIIM in connection with the recommendation of the Consultative Committee on Electricity to obtain a more trustworthy value for the gyromagnefic ratio of the proton. Investigations were continued also for the purpose of discovering systematic errors in the first results mentioned above [2]. In recent years careful experiments were carried out for discovering systematic measurement errors. Experi- ments were first continued with one of the existing Helmholtz coils (No. 13) without inserting into it the massive polarizing coil which could have produced a screening effect. For this purpose an equipment was produced with the specimen being shot out of the magnetic field of an armoured electromagnet into the magnetic field of the Helm- holtz coil "wound on a quartz former. This experiment produced a negative result, i.e., within the precision of this experiment no screening effect could be discovered. Further investigations dealt with studying the frequency errors of the decaying proton precession signal. As long ago as 1958, it was noticed that frequency measurements of a decaying proton precession by means of the heterodyne method with a preliminary frequency multiplication lead to errors approaching 0.01%, if the muhi- plying device consists of a robe stage with a tuned anode circuit whose inductance comprises a ferromagnetic materi- al. This error is due to the variations of the resonant frequency produced by the fact that the dc anode current of a tube which operates in a nonlinear condition varies with the amplitude of the input signal. Therefore, the phase of the multiplier output vohage is a function of the exponentially decaying amplitude. All the amplifying tubes or semiconductor devices consist of a quadrupole which contains elements with a cer- tain degree of nonlinearity. Therefore, variations of the input signal amplitude in the course of measurements (of frequency) always lead to phase changes at the quadrupole output. These phase changes in turn produce variations in the time interval consisting of a given number of the measured frequency periods. Since the measuring time is determined by the duration of the proton precession sig- TABLE 1 Year i Mean values t~ ~.~t of r' 10% U i . 10 -2 T -1 ,sec- 1 Ui.10-4 T -2 sec -2 1960 1961 1962 1966 1967 2675160 2675177 2675135 2675153 2677564 +2 +19 --23 --5 T6 4 361 529 25 36 av. 2675158 X=955 o . . . . . 15,5.10 9 T "I, sec'l; arlt=5,8.10--6; s= a =7.102T--l,.sec-t Srlt=2.6" 10--6 g~- hal (i.e., 0.5-1 sec), the effect of phase errors which change the counting time of standard pulses by fractions of a period will decrease with a rising measured frequency. The same can be said about the errors due to vari- ations in the tripping instant of the digital frequency me- ter's shaping device by the first and last periods of the decaying voltage. It can be shown that, if time interval 7- is formed by a stationary amplitude, the decaying am- plitude will change it in the first approximation by the amount of AT ---~ Uo (1 AUo \ oUf [ Ui § Vo ' Translated from Izmeritel'naya Tekhnika, No. 11, pp. 29-31, November, 1968. Original article submitted August 7, 1968. 1483

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Page 1: Measurement of the proton gyromagnetic ratio in a weak magnetic field

MEASUREMENTS OF ELECTRICAL AND MAGNETIC QUANTITIES

M E A S U R E M E N T OF T H E P R O T O N G Y R O M A G N E T I C R A T I O

IN A WEAK M A G N E T I C F I E L D

N. V. S t u d e n t s o v , T. N. M a l y a r e v s k a y a , a n d V. Ya . S h i f r i n

UIX: 539.125.4.001,24

Measurements of the proton gyromagnetic ratio r were carried out since 1958 at the VNIIM (All-Union Scien- tific-Research Institute of Metrology), The first results and the measurement technique were published in 1960 and 1962 i"1-31.

However, experiments continued at the VNIIM in connection with the recommendation of the Consultative Commit tee on Electricity to obtain a more trustworthy value for the gyromagnefic ratio of the proton. Investigations were continued also for the purpose of discovering systematic errors in the first results mentioned above [2].

In recent years careful experiments were carried out for discovering systematic measurement errors. Experi- ments were first continued with one of the existing Helmholtz coils (No. 13) without inserting into it the massive polarizing coil which could have produced a screening effect. For this purpose an equipment was produced with the specimen being shot out of the magnetic field of an armoured electromagnet into the magnetic field of the Helm- holtz coil "wound on a quartz former. This experiment produced a negative result, i.e., within the precision of this experiment no screening effect could be discovered. Further investigations dealt with studying the frequency errors of the decaying proton precession signal.

As long ago as 1958, it was noticed that frequency measurements of a decaying proton precession by means of the heterodyne method with a preliminary frequency multiplication lead to errors approaching 0.01%, if the muhi- plying device consists of a robe stage with a tuned anode circuit whose inductance comprises a ferromagnetic materi- al. This error is due to the variations of the resonant frequency produced by the fact that the dc anode current of a tube which operates in a nonlinear condition varies with the amplitude of the input signal. Therefore, the phase of the multiplier output vohage is a function of the exponentially decaying amplitude.

All the amplifying tubes or semiconductor devices consist of a quadrupole which contains elements with a cer- tain degree of nonlinearity. Therefore, variations of the input signal amplitude in the course of measurements (of frequency) always lead to phase changes at the quadrupole output. These phase changes in turn produce variations in the time interval consisting of a given number of the measured frequency periods. Since the measuring time is

determined by the duration of the proton precession sig- TABLE 1

Year i Mean values

t~ ~.~t of r ' 10% U i . 10 - 2

T -1 ,sec- 1 Ui.10 - 4

T -2 sec -2

1960 1961 1962 1966 1967

2675160 2 6 7 5 1 7 7 2675135 2675153 2 6 7 7 5 6 4

+ 2 +19 --23 --5 T6

4 361 529

25 36

av. 2675158 X=955

o . . . . . 1 5 , 5 . 1 0 9 T "I, sec ' l ; arlt=5,8.10--6;

s = a = 7 . 1 0 2 T - - l , . s e c - t Sr l t=2 .6" 10--6 g ~ -

hal (i.e., 0.5-1 sec), the effect of phase errors which change the counting time of standard pulses by fractions of a period will decrease with a rising measured frequency.

The same can be said about the errors due to vari- ations in the tripping instant of the digital frequency me- ter's shaping device by the first and last periods of the decaying voltage. It can be shown that, if time interval 7- is formed by a stationary amplitude, the decaying am- plitude will change it in the first approximation by the amount of

AT ---~ Uo (1 AUo \ oUf [ Ui

§ V o '

Translated from Izmeri te l 'naya Tekhnika, No. 11, pp. 29-31, November, 1968. Original article submitted August 7, 1968.

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Page 2: Measurement of the proton gyromagnetic ratio in a weak magnetic field

TABLE 2

I 2 Value o f u i . l o - 2 u ~.1o - 4 Coil

y.lO--2 ' ,

No. T" I sec- 1 ' T- 1 see" 1 T- 2 sec- 2

4 26775167 +4,5 i 20,25 5 152 --10,5 110,25 6 162 --0,5 0,25 7 158 --4,5 20,25 8 137 --25,5 650,25 9 162 --0,5 0,25

10 146 --16,5 272,25 II 164 q-l,5 2,25 12 156 --6,5 42,25 13 ,180 -}-17,5 306,25 14 200 ff-37,5 1406,25 15 166 -t-3,5 I 12,25

av. 267516~.5 ~ = 284a

] / z v ~ T.~ =__~ ( ~ = ~ = 1 6 ' 1 0 2 s e e ' l ; % I t = 6 ' 0 " 1 0 - - 6 n - - I y

S = ~ = 4 , 7 . 1 0 2 T - i s e c - I ; S r l t = 1 , 7 , 1 0 - 6 . Kn

TABLE 3

YKhGNIIM

YVNIIM

Y N B S

YNPL

Value of y. 1 o - - 2 , T - l s e c --1

L

2 675 071 2 675

2 675 162 2 675

2 675 150 2 675

2 6 7 5 171 2 675

oOk)

~'~.,~ o .~ O ~

094 2 675 123

139 2 6 7 5 1 1 0

150 2 675 121

154 2 6 7 5 I25

�9 ,-4 �9

t ' ~

2 675 i 16

2 6 7 5 116

2 675 128

2 675 132

a v . 675 123

where U 0 is the tripping vol tage of the shaping device; w is the measured frequency; U i and Uf are the in i t ia l and

final ampli tudes of the shaping pulse with duration r ; AU0 is the variat ion of the shaping-device tripping vol tage during the frequency measurement.

A detai led study of the frequency errors is impeded by the complex i ty of their separation. Therefore, only their total effect was studied. The method of measuring the frequency simultaneously with two or three frequency meters was used for investigating this effect, These frequency meters were employed for evaluating the t ime inter- val formed by 4096 periods of the proton-precession decaying signal. The s imultaneously-operat ing frequency me-

ters were connected either to the output of the common ampl i f ier whose parameters were varied in the course of the investigation, or to the output of different amplifiers which had a common preamplif ier stage, or else to an ampl i -

fier with a narrow and another one with a wide bandwidth. The tripping instants of the frequency meters were then staggered by 0.05 to 0.2 sec.

Let us note that in measuring the frequency of the s ta t ionary-ampl i tude vol tage the discrepancies between the readings of the frequency meters did not exceed 0.00012%, whereas in measuring the frequency of the decaying am-

pl i tude they sometimes exceeded 0.001%. The error in measuring the frequency of the decaying precession signal was reduced to 0.0005~ (discrepancy in the f requency-meter readings) by reducing the shaping-device tripping volt-

age to a level approaching noise and by l inearizing the amplifying stages. This error was classified as random.

In addition to investigating the equipment for measuring the proton precession frequency and the current in the coils, we also repeated the measurements of the geomet r ica l dimensions of coils. The theoret ical investigation of the errors produced in the computed field strength of the Helmholtz coils by the errors in measuring the d iameter

and pitch of their windings has shown that the coi l constant is effected mostly by the error in measuring the distance between the turns of the winding sections. Therefore, a new device was developed for measuring the distance be-

tween the turns, with the Abbd principle adhered to in this case with part icular precision. The new measurements of the geomet r ica l dimensions of coils made in 1966-1968 served to apply corrections to theirconstants and to amend the gyromagnet ic proton ratio 7 which was obtained in previous years.

The proton gyromagnefic ratio was measured in the field of 12 Helmholtz coils in the period from 3.960 to 1968. Seven coils (numbers 4-10) produced a magnet ic induction of about 5 .10 -5 T and the five remaining coils (numbers 11-15) produced an induction of 1" 10 .4 T.

Table 1 shows as an example the proton gyromagnetic ratio of measurements made in the period of 1960-1967 with coi l number 7. Each series of measurements consisted of 10-15 observations.

Table 2 carries results of ~, measurements made in the magnet ic field of each coil . The results for each coi l were taken as a mean ofmeasurements made over two to four years. The discrepancies thus obtained in the ~, mea-

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Page 3: Measurement of the proton gyromagnetic ratio in a weak magnetic field

surements made with different coils agree fair ly wel l with the theoret ical and exper imental investigations of the method and the equipment.

The mean value of the proton gyromagnet ic ratio expressed with a d iamagnet ic correction in the USSR nat ion-

al units and measured in weak magnet ic fields amounts to

71 = (2675162 • 14): 102 T - 1 sec - I ,

whose error 14" 102 T -1 sec -1 corresponds to a f iducial probabi l i ty of 99%.

The value of the proton gyromagnet ic ratio also expressed in the USSR nat ional units and measured in a strong magnet ic field at the KhGNIIM (Khar 'kov State Scientif ic-Research Institute of Metrology) [4] amounts to

Y~ -~ (2675071+16)-102 T --1 sec - - 1

It is known that the measurements of the proton gyromagnet ic ratio in the magnet ic field of an e lec t romagnet

and a weak field of a computed coi l can be used for discovering the systematic discrepancy between the unit of cur- rent represented by the volt and ohm reference standards and the absolute ampere [1].

It can be shown that the proton gyromagnet ic ratio in absolute units can be determined from its exper imenta l - ly obtained values ) ' i and 72 in a weak and strong magnet ic fields respectively and ca lcu la ted from the formula

The factor (C a = I a / I e) for converting the current values I e used in experiments to their values I a expressed

in absolute units is d.etermined from

C a = V~7--~2.

Thus, from the VNIIM and the KhGNIIM measurement results we obtained

7 = (2675117 +__ 10). 102 T --i sec- - I

C a = = l + ( 1 7 + 4).10 - 6 .

Therefore, the current unit used in experiments was larger than the absolute ampere by an amount of 17 .10 -6 , in other words there are good reasons for decreasing the value of our nat ional volt by 0.0017%.

From s imi lar operations with 71 and ?'2, after they have been converted to the internat ional ampere by using the data of the 1964 internat ional comparisons, we find that

Cia = 1 -{- (8 -+ 4)..10--~.

This agrees within the expected errors with the Internat ional Bureau of Weights and Measures conversion factor C i = 1+ (11 ~ 3) ' 10 -6 [5].

Table 3 provides the values of the proton gyroscopic ratio.

The good agreement of results after they have been converted to the absolute ampere indicates the high leve l

of the work thus carried out and confirms the difference between the internat ional and the absolute amperes.

L I T E R A T U R E C I T E D

1. B.M. Yanovskii, N. V. Studentsov, and T. N. Tikhomirova, Izmer i te l . ' Tekh., No. 2 (1959).

2. N .V . Studentsov and B. M. Yanovskii, Transactions of the Commi t t ee of Standards' Institutes, No. 54 (114) (1961).

3. B.M. Yanovskii and N. V, Studentsov, Izmer i te l . ' Tekh., No. 6 (1962), 4. G .K . Yagola, V. I, Zingerman, and V. N. Sepetyi , Izmeri te l ' . Tekhn., No. 7 (1966). 5. 1. Terrien, Metrologia, 1, No, 3 (1965).

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