A Comparison of thegValue of the Electron in Hydrogen with That in Deuterium

Abstract

The $g$ value of the electron in the ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state of $H$ has been compared with the $g$ value of the electron in the corresponding state of $D$ by the atomic beam magnetic resonance method. The frequencies, $f_H$, of the transition (1, 0 ⇄ 1, -1) in $H$, and $f_D$, of the transition ($\frac{3}{2},-\frac{1}{2}\leftrightarrow \frac{3}{2},-\frac{3}{2}$) in $D$ were observed in the same magnetic field and the ratio $\frac{{\left(g_J\right)}_H}{{\left(g_J\right)}_D}$ was computed from the Breit-Rabi formula. The principal uncertainty is caused by the drift of the magnetic field. The average of 36 observations in 4 runs in which $f_H$ and $f_D$ were measured alternately is $\frac{{\left(g_J\right)}_H}{{\left(g_J\right)}_D}=1.000004\mathrm{}\pm 0.000025$. The average of 3 runs in which the two resonances were observed simultaneously is $\frac{{\left(g_J\right)}_H}{{\left(g_J\right)}_D}=0.999991\mathrm{}\pm 0.000010$. The uncertainty indicated in each result is the mean deviation of the residuals. We conclude that the $g$ value of the electron when bound to the proton differs from that when bound to the deuteron by less than 0.001 percent.