Spheroidal and hyperspheroidal coordinates in the adiabatic representation of scattering states for the Coulomb three-body problem

Recently, an involved approach has been used by Abramov (2008 J. Phys. B: At. Mol. Opt. Phys. 41 175201) to introduce a separable adiabatic basis into the hyperradial adiabatic (HA) approximation. The aim was to combine the separability of the Born-Oppenheimer (BO) adiabatic basis and the better asymptotic properties of the HA approach. Generalizing these results we present here three more different separable bases of the same type by making use of a previously introduced adiabatic Hamiltonian expressed in hyperspheroidal coordinates (Matveenko 1983 Phys. Lett. B 129 11). In addition, we propose a robust procedure which accounts in a stepwise procedure for the unphysical couplings that are inherently present in the hyperradial adiabatic multichannel scattering approach. The advantages of the new approach are demonstrated on the example of the basic reaction in muon-catalyzed fusion physics dμ + t → tμ + d.