Interaction of Molecular Oxygen with a Magnetic Field

The dominant interaction of ${\mathrm{O}}_2$ with a magnetic field is through the electronic spin magnetic moment. However, a precise comparison with experiment of the results of calculating the microwave paramagnetic spectrum, assuming only this interaction, shows a systematic discrepancy. This discrepancy is removed by introducing two corrections. The larger (approximately 0.1 percent, or 7 gauss) is a correction for the second-order electronic orbital moment coupled in by the spin-orbit energy. Its magnitude is proportional to the second-order term ${\mu }^{\prime \prime }$ in the spin-rotation coupling constant. The smaller (approximately 1 gauss) is a correction for the rotation-induced magnetic moment of the molecule. Since the dependence of this contribution on quantum numbers is quite unique, this coefficient can also be determined by fitting the magnetic spectrum. A total of 120 $X$-band and 78 $S$-band lines were observed. The complete corrections have been made on 26 lines with a mean residual error of roughly 0.5 Mc/sec. This excellent agreement confirms the anomalous electronic moment to 60 parts per million (ppm) and also confirms the validity of the Zeeman-effect theory.