Magnetic Hyperfine Structure in Diatomic Molecules

A general theory of the magnetic hyperfine structure in diatomic molecules, including states other than ${}_{}{}^1{}_{}{}^{}\Sigma$ states, is given. The magnetic hyperfine interaction is derived from the Dirac equation for the electron in the molecular potential field. First-order hyperfine structure formulas are given for the various vector coupling schemes characteristic of molecular states. The ${}_{}{}^1{}_{}{}^{}\Sigma$ magnetic hyperfine structures are obtained from second order hyperfine interactions. Applications to the ${\mathrm{N}}^{14}$ ${\mathrm{O}}^{16}$ and ${\mathrm{O}}^{16}$ ${\mathrm{O}}^{17}$ microwave spectra are discussed.