Long-range interactions and artificial poles

Abstract

The structure of the three-body continuum of the 6 He nucleus within the hyperspherical harmonic calculation scheme has been the subject of extensive study. An approximate treatment of the long-range couplings inherent in such models gives rise to unphysical poles in the deduced Smatrix at complex energies. We consider here a simple two-channel example, which includes long-range interactions, and demonstrates the existence of these artificial S-matrix poles. This is also illustrated in a physical context by considering the extreme adiabatic approximation of the hyperspherical harmonics technique for 6 He. A correct treatment of the long-range (1/ρ λ ) behaviour of the channel potentials is shown to remove the artificial poles from the physically significant region of the complex energy plane.