Theory of Molecular Hydrogen and Deuterium in Magnetic Fields

Abstract

The hamiltonian of a diatomic homonuclear molecule in a magnetic field is discussed. Included in the hamiltonian are the effects of the nuclear and rotational magnetic moments interacting with the external magnetic field, magnetic shielding, molecular diamagnetism, the spin-spin magnetic interaction of the two nuclei, the interaction of the nuclear magnetic moments with the field due to the rotation of the molecule, and the interaction of nuclear electric quadrupole moments. Perturbation theory expressions for the energy of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ in the first rotational state are obtained in both strong and weak field limits. The secular equation is numerically solved for intermediate fields. Curves are given showing the theoretical dependence of the energy and the transition frequencies upon the field.