The Zeeman Effect in Oxygen

This paper describes the calculation of the energy of magnetic sub-levels belonging to the ${}_{}{}^3{}_{}{}^{}\Sigma$-state of ${\mathrm{O}}_2$ in an external magnetic field. A general secular determinant is derived, the roots of which yield the desired energies. The results are particularly useful in the investigation of levels associated with a low value of the rotational quantum number. The perturbation representing the external magnetic field is introduced together with the perturbations leading to the rotational triplets; thus the distortion of the rotational triplets is considered from the beginning of the calculation. The work is performed in two stages to avoid the mathematical difficulties of treating a ninth-order secular determinant. Comparison between theory and experiment is satisfactory.