Further Data on the Spin Gyromagnetic Ratio of the Electron

Abstract

The atomic beam magnetic resonance method has been used to compare the $g_J$ values of In in the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ states in order to obtain a value of the spin gyromagnetic ratio of the electron. The determination of the $g_J$ ratio involved only the measurement of frequencies of lines in the h.f.s. spectra of both states at constant magnetic field. Lines with widely different frequency dependence on field were selected to avoid possible systemic errors arising from inhomogeneities in the field. The result of these measurements is $\frac{g_J\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)}{g_J\left({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)}=2(1.00200\mathrm{}\pm 0.00006)$. Assuming Russell-Saunders coupling, and $g_L=1\mathrm{}$, the spin gyromagnetic ratio of the electron may be calculated. The result is $g_S=2(1.00133\mathrm{}\pm 0.00004)$, which is to be compared with the value $g_S=2(1.00119\mathrm{}\pm 0.00005)$ obtained by Kusch and Foley. The discrepancy is greater than the sum of the experimental errors. The ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state of In is believed to be free of significant perturbations which might affect the total electronic $g$ value. However, in view of possible perturbations of the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state, the agreement must be considered as very good. The present result confirms the conclusions of the previous experiment, both as to the existence of the intrinsic magnetic moment of the electron, and as to its approximate magnitude.