ElectrongValue in the Ground State of Deuterium

Abstract

The ratio of the electron $g_J$ in the deuterium ground state to the proton $g_p$ in a cylindrical mineral oil sample has been measured. The measurement was made using the microwave magnetic resonance absorption method and apparatus which Beringer and Heald used to determine $-\frac{g_J}{g_p}$ for hydrogen. The three strong-field Zeeman transitions having $\Delta m_J=\pm 1$, $\Delta m_I=0\mathrm{}$ were observed at a frequency of 9200 Mc/sec. The accuracy was limited by the minimum observed line widths of 20 parts per million resulting principally from magnetic field inhomogeneities. When one uses the Breit-Rabi formula, the unweighted mean of 68 observations yields $-\frac{g_J\left(\mathrm{D}\right)}{g_p}=658.2162\mathrm{}$ with an assigned error of ±0.0008. The ratio of this value to the value of $-\frac{g_J\left(\mathrm{H}\right)}{g_p}$ obtained by Beringer and Heald, who used an identical mineral oil sample is $\frac{g_J\left(\mathrm{D}\right)}{g_J\left(\mathrm{H}\right)}=0.9999983\mathrm{}\pm 0.0000015$, and to the value of $-\frac{g_J\left(\mathrm{H}\right)}{g_p}$ of Koenig, Prodell, and Kusch, after suitable diamagnetic corrections, is $\frac{g_J\left(\mathrm{D}\right)}{g_J\left(\mathrm{H}\right)}=0.9999997\mathrm{}\pm 0.0000023$. These values are in agreement with the theoretically expected value of $\frac{g_J\left(\mathrm{D}\right)}{g_J\left(\mathrm{H}\right)}=1\mathrm{}$ and with the less precise direct measurement of Nelson and Nafe.