  For a particular case of three-body scattering in 2 dimensions, we
demonstrate analytically that the behaviour of the adiabatic potential is
different from that of the hyperspherical coupling matrix elements, thereby
leading to a phase shift that tends to zero, as the energy goes to zero,
instead of to a constant. We consider two particles interacting with binary
repulsive step potentials, one acting as a spectator, and solve analytically
for the adiabatic eigenvalues and eigenvectors, for all values of rho. We are
thereby able to obtain the leading terms in the long range behaviour of the
effective potentials, and confirm its inverse logarithmic nature, suggested
from a previous numerical study.
