Hyperspherical treatment of three-body molecular states

The hyperspherical treatment of ${\mathrm{HD}}^{+}$ is extended to make it suitable for a multichannel approach including the rotational coupling. For this purpose, a new and symmetric set of coordinates is introduced. The approximate hyperspherical adiabatic potential curves are calculated. In contrast to the Born-Oppenheimer adiabatic potential curves, the hyperspherical ones exhibit the correct dissociation limits. The lowest-order vibrational spectrum obtained compares favorably with the conventional higher-order calculations. It is shown that this approach is better suited to describing the dynamics of three-body systems.