Hyperradial-adiabatic approach to Coulombic three-body systems

Abstract

The variational approach to the solution of the hyperradial-adiabatic three-body Hamiltonian is analysed in a new way. The hyperspheroidal coordinates, introduced earlier by Matveenko and Abe, are used to construct the channel-independent pair-collision- and triple-collision-limit solutions of the HA problem. The breakdowns of the adiabaticity in the vicinity of the avoided-crossing points and in the regions of the two-body dissociation limits are critically overlooked. In order to treat the avoided-crossing regions we define the separable HA Hamiltonian which naturally follows from the exact one, and has proper behaviour at the singular points and is simpler than the one introduced recently by Tolstikhin et al. The dissociation-limit problem is clearly demonstrated to be the asymptotic tail of the unphysical hyperradial coupling: we discuss the possibility of the general solution of the problem for a rearrangement scattering process in the hyperradial-adiabatic approach.