Boundary-Condition Approach to Three-Particle Final States

It is shown that the wave function for a three-particle system outside the range of forces may be uniquely determined by imposing a suitable set of boundary conditions. This result is expressed in terms of a one-variable integral equation with a square-integrable kernel, the solutions of which specify the three-body $t$ matrix. The input to this equation consists of the two-particle phase shifts and two independent real-valued functions which characterize the three-body wave function in specific regions. The formalism yields an exactly unitary three-particle $t$ matrix for arbitrary values of this input, and thus provides a practical scheme for the analysis of three-body final states.