Three-Particle Unitarity in Potential Scattering

A three-particle wave function arising out of a Schr\"odinger equation with two-body potentials is considered. For simplicity in analysis, the potentials are taken to be of the nonlocal separable type. It is found that at bound-state energies of a three-particle system, the "phase" of the three-particle amplitude is not equal to that of a pair of its members whose relative energy allows them to be in a physical scattering state. This result disagrees with the prediction of a "multiplicative" three-particle structure suggested by Blankenbecler, according to which these two phases are necessarily equal.