Non-aligned hydrogen molecular ion in strong magnetic fields

The hydrogen molecular ion in a strong magnetic field is studied for arbitrary orientations of the molecular axis. A gauge preserving the parity symmetry and leading to real matrix elements for a class of basis states is introduced. The calculations are performed in prolate spheroidal coordinates with the Lagrange-mesh method. The simple resulting mesh equations provide a high accuracy with short computing times for magnetic fields *g = 1 and 10 in atomic units of 2.35 X 105 T. Less accurate results are obtained at the field *g = 100, typical of neutron stars where the size of the matrix becomes very large. The present results allow evaluation of the accuracy of published variational results. At high field strengths, the rotational motion becomes strongly hindered. Simple estimates of rotational energies are compared with other works.