Quantum three‐body scattering problem in the adiabatic hyperspherical representation

The adiabatic hyperspherical (AH) approach to the quantum three‐body problem is considered. It is proven that the AH harmonics are complete and differentiable with respect to the hyperradius for a large class of two‐body potentials. For the case of short‐range potentials, the scattering theory is studied in the framework of the AH approach. The asymptotics of the AH potential curves, harmonics, and coupling matrix elements are derived, as well as the structure of the three‐body wave operators and, the S‐matrix in the AH representation is investigated.