Adiabatic hyperspherical treatment ofHD+

We have calculated approximate hyperspherical adiabatic ${\mathrm{HD}}^{+}$ potential curves. In contrast to the Born-Oppenheimer adiabatic potential curves, the hyperspherical ones exhibit the correct dissociation limits. The lowest-order vibrational spectrum that we obtain compares favorably with conventional higher-order calculations. The implications of our results for continuum states of ${\mathrm{HD}}^{+}$ and for ion-atom scattering in general are discussed. We show that translation factors are not needed in the hyperspherical formulation.