Polarizability of the ground state of the hydrogen molecular ion

The dipole polarizabilities of the ground states of the ions H₂⁺ and D₂⁺ have been calculated without making use of the Born-Oppenheimer approximation. Instead, the ions were treated as three-body systems whose ground states are spherically symmetric, and the polarizabilities were calculated using second-order perturbation theory with intermediate p pseudostates. The wave functions of both the ground and intermediate states are taken to be of generalized Hylleraas form, but it is necessary to use quite high powers of the internuclear coordinate to simulate the localized motion of the nuclei. We obtain good values of the ground-state energies, and report values of the polarizabilities, to be compared with recent measurements.