The quantum mechanical third cluster for a binary step potential

Abstract

We calculate the quantum mechanical third cluster coefficient b ₃ in two dimensions. The model of the interaction is a binary repulsive step potential with finite range. We expand the continuum three-body wave functions in hyperspherical harmonics and solve large finite sets of coupled equations in the hyper radius ρ, by using an adiabatic approximation. We obtain the eigenphase shifts of the three to three scattering and integrate a phase shift sum (weighted by a Boltzmann factor), over the energy, to give us the cluster as a function of temperature. We note that we do obtain the correct threshold behaviour for the crucial phase shift sum.