A Determination ofgJ(S122)of Potassium in Terms of the Proton Gyromagnetic Ratio

The ratio of the $g$ value of potassium ${\mathrm{K}}^{39}$ in the ground state to the gyromagnetic ratio of the proton in mineral oil has been measured in an experiment combining atomic beam and nuclear resonance techniques. It is found to be $\frac{g_J\left(\mathrm{K}\right)}{g_p}=658.2274\mathrm{}\pm 0.0023$. This result, when combined with the measurement of $\frac{g_J\left(\mathrm{H}\right)}{g_p}$ by Koenig, Prodell, and Kusch, yields $\frac{g_J\left(\mathrm{K}\right)}{g_J\left(\mathrm{H}\right)}=1.000016\mathrm{}\pm 0.0004 \mathrm{percent}.$ This is to be compared with the recent direct measurement by Pohlman, Bederson, and Eisinger: $\frac{g_J\left(\mathrm{K}\right)}{g_J\left(\mathrm{H}\right)}=1.00016\mathrm{}\pm 0.006 \mathrm{percent}$. The present experiment is of superior precision and is in agreement with independent experimental evidence. The present result is found to agree with the theoretically predicted value.