Measurement ofgJ(Rb87)gJ(K39)by spin-exchange optical pumping

The method of spin-exchange optical pumping has been used to measure the ratio $\frac{g_J\left({\mathrm{Rb}}^{87}\right)}{g_J\left({\mathrm{K}}^{39}\right)}$ for the alkalis in their ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ ground states. Zeeman hyperfine splittings of the atomic ground states were produced in a magnetic field of 43 G, and the rf transition frequencies between the states were measured. A best fit of the data was then made using the Breit-Rabi expression for the energy levels, and constants were adjusted for best fit. Possible systematic effects of pumping light, buffer pressure, etc., were considered in obtaining the final result $\frac{g_J\left({\mathrm{Rb}}^{87}\right)}{g_J\left({\mathrm{K}}^{39}\right)}=1.000\mathrm{}01845\left(7\right)\mathrm{}$. The ${\mathrm{K}}^{39}$ $g_I$ and the $g_J$ and $\frac{g_I}{g_J}$ ratios of the rubidium isotopes obtained in check runs were in good agreement with published high-precision data.