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THE GYROMAGNETIC RATIO FOR THE PROTON AND REFINEMENT OF THE VALUE OF $e/m$
The development of magnetic resonance methods has made it possible to measure, with a high degree of accuracy, the gyromagnetic ratios for various nuclei. At the same time, the accuracy of relative measurements has proved to be considerably higher than that of absolute measurements, since the latter is limited by—
* The main features of the method and some results are already contained in the work of A. B. Migdal, JETP 15, 81 (1945).
errors in the measurements of the induction of the applied magnetic field, reaching, in the best cases, 0.5%. The authors of the paper under review set themselves the goal of improving the method for measuring the induction of a magnetic field and, with the aid of the method of nuclear resonance absorption, obtaining a more accurate value of the gyromagnetic ratio for the proton. As an indicator of the magnetic field they used the ponderomotive force experienced by a conductor with a current placed in this field. As a result of a number of precautions, they succeeded in reducing the root-mean-square error in determining the induction of the magnetic field to \(2.2\cdot 10^{-5}\) of the measured quantity. (The measurement consisted of a series of auxiliary measurements, the errors of which fluctuated within \((1 \div 10)\cdot 10^{-6}\) of the measured quantity.) The error in measuring the resonance frequency was \(1\cdot 10^{-6}\).
As a result, they obtained the following value of the gyromagnetic ratio for the proton (without introducing the correction for the diamagnetic effect):
\[ \gamma_p = (2.67523 \pm 0.00006)\cdot 10^4\ \mathrm{sec}^{-1}\mathrm{gauss}^{-1}. \]
After introducing the correction for the diamagnetic effect, the value obtained is:
\[ \gamma_p = (2.67528 \pm 0.00006)\cdot 10^4\ \mathrm{sec}^{-1}\mathrm{gauss}^{-1}, \]
whence, taking the value of Planck’s constant
\[ h = (6.6234 \pm 0.0011)\cdot 10^{-27}\ \mathrm{erg}\cdot\mathrm{sec}, \]
one obtains the value for the magnetic moment of the proton:
\[ \mu_p = (1.4100 \pm 0.0002)\cdot 10^{-23}\ \frac{\mathrm{dyn}\cdot\mathrm{cm}}{\mathrm{gauss}}, \]
and in this case the accuracy is limited by the accuracy of the determination of Planck’s constant.
To calculate the specific charge of the electron, the authors use the ratio, measured by Gardner and Purcell, of the proton precession frequency \(\omega = \gamma_p B\) to the rotation frequency of a free electron
\[ \omega_e = \]
\[ = \frac{e}{m}B \]
in the same magnetic field \(B\), which expresses the magnetic moment of the proton in Bohr magnetons:
\[ \frac{\omega}{\omega_e} = (1.52100 \pm 0.0002)\cdot 10^{-3}. \]
(The correction for the diamagnetic effect has been taken into account.) This quantity is in good agreement with the somewhat less accurate measurements of Taub and Kusch\(^3\):
\[ \mu_p = (1.52106 \pm 0.00007)\cdot 10^{-3}\mu_B, \]
where \(\mu_B\) is the Bohr magneton.
As a result, for the specific charge of the electron one obtains the value:
\[ \frac{e}{m} = (1.75890 \pm 0.00005)\cdot 10^7\ \frac{\mathrm{el.\!-\!m.\ units}}{\mathrm{g}}. \]
The figure gives a comparison of various measurements of the specific charge of the electron.
Figure. Comparison of measurements of \(e/m\) in units of \(10^7\) el.-m. units/gram. Values and labels shown in the figure include:
- \(1.75890 \pm 0.00005\) — Thomas, Driscoll, and Hipple, 1949; Gardner and Purcell
- \(1.75936 \pm 0.00018\) — Dumond and Cohen, 1947; weighted mean
- \(1.75903 \pm 0.00050\) — Bearden, 1941; revised by Dumond and Cohen
- \(1.75877 \pm 0.00080\) — Gleditsch, 1939
- \(1.75827 \pm 0.00130\) — Shaw, 1938
- \(1.75986 \pm 0.00040\) — Dunnington, 1937
- \(1.75704 \pm 0.00070\) — electron magnetic moment; Zeeman effect
- \(1.75908 \pm 0.00070\) — Kinster and Houston, 1934
- \(1.75901 \pm 0.00090\) — Kirchner, 1932
- \(1.76111 \pm 0.00100\) — Perry and Chaffee, 1930
G. R.
CITED LITERATURE
- H. A. Thomas, R. L. Driscoll and J. A. Hipple, Phys. Rev. 78, 787 (1950).
- J. H. Gardner and E. M. Purcell, Phys. Rev. 76, 1262 (1949).
- H. Taub and P. Kusch, Phys. Rev. 75, 1477, 1481 (1949).