Classification of Coulombic three-body systems in hyperspherical coordinates

Hyperspherical coordinates are used to study properties of Coulombic three-body systems of arbitrary masses. Consider a system ABA, which consists of two identical particles A and a third particle B, each with one unit of charge. We examine the evolution of the approximate quantum numbers that are used for classifying bound and resonance states of the system as the mass ratio {λ}=mA/mB changes from the atomic limit ({λ}{→}0 as in H^-) to the diatomic molecular limit ({λ}{}1 as in H₂⁺). It is shown that for states which exhibit rovibrational behaviors in the atomic limit ({λ}{→}0), a single set of approximate quantum numbers can be used to describe three-body systems of any {λ}'s. For states that display independent-particle behavior in the atomic limit, such as singly excited states, it is shown that these states display rovibrational behaviors only in the large-{λ} limit. The evolution of the spectroscopy of the three-body systems from the shell model of atoms to the rovibrational model of molecules is thus analyzed. Calculations of potential curves in hyperspherical coordinates were carried out for Ps^- and d⁺{{{μ}}}^{{{-}}}d⁺ that serve as the intermediate steps for the study of the evolution of the approximate quantum numbers from H^- to H₂⁺.