Hydrogen molecular ion in a high magnetic field

The ground and several excited states of the hydrogen molecular ion in a homogeneous magnetic field aligned along the molecular axis are studied. A pair of self-consistent equations is derived in prolate spheroidal coordinates and solved numerically. The results are exact at the limit of vanishing magnetic field and more accurate than previous results up to about 10⁹ G. The equilibrium internuclear separation and binding energy for a number of electronic states are reported as functions of the magnetic field strength. The dissociation energy is deduced from the study of the hydrogen atom in the same coordinate system.