An asymptotic expansion of the wave functions for the fragmentation channels of three-body systems is developed in hyperspherical coordinates. It is shown that, to any finite power in 1/R, where ${\mathrm{mR}}^2$= is the trace of the inertia tensor, the expanded wave function is an analytic finite sum of Sturmian functions. The expansion is carried out explicitly through order 1/$R^4$. These asymptotic states converge (as R→∞) to polarized orbitals for two-electron systems, and also provide improved dissociation channels for molecular ions, such as ${\mathrm{HD}}^{+}$. Asymptotic potential curves for He and ${\mu }^{\mathrm{-}}$-H systems are presented as illustrations.

• Received 10 August 1989

DOI:https://doi.org/10.1103/PhysRevA.41.1225