  For a particular case of three-body scattering in two dimensions, and
matching analytical expressions at a transition point, we obtain accurate
solutions for the hyperspherical adiabatic basis and potential. We find
analytical expressions for the respective, asymptotic, inverse logarithmic and
inverse power potential behaviors, that arise as functions of the radial
coordinate. The model that we consider is that of two particles interacting
with a repulsive step potential, a third particle acting as a spectator. The
model is simple but gives insight, as the 2-body interaction is long ranged in
hyperspherical coordinates. The fully interacting 3-body problem is known,
numerically, to yield similar behaviors that we can now begin to
understand.That, clearly, is the ultimate aim.
