An experimental determination ofgJ(He4, 2S13)gJ(H1, 1S122)

The ratio of the $g_J$ factor of ${}_{}{}^4{}_{}{}^{}\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\right)$ to that of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}\left(5\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)$ has been measured to a fractional accuracy of ±5×${10}^{-8\mathrm{}}$. The Rb atoms were optically pumped, and the ${}_{}{}^4{}_{}{}^{}\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\right)$ Zeeman resonance was observed through a combination of spin-exchange collisions and spin-dependent Penning ionization. Linewidths as narrow as 220 Hz were observed for the ${}_{}{}^4{}_{}{}^{}\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\right)$ Zeeman resonance. The accuracy of this experiment was limited by a systematic shift in the He $g_J$ factor that depended upon the intensity of the discharge used to excite the He atoms to the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state. Calculations indicate that transfer of coherence in spin-exchange collisions with free electrons contributes to this shift. The measured ratio $\frac{g_J({}_{}{}^4{}_{}{}^{}\mathrm{He}, 2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{})}{g_J({}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}, 5{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{})}=1-46.798\mathrm{}\left(50\right)\mathrm{}\times {10}^{-6\mathrm{}}$. Using the previously measured ratio of the $g_J$ factors of the ground state of rubidium to the ground state of hydrogen, we determine the ratio