The Exterior Three - Particle Wave Function

For three particles interacting via forces of finite range, it is shown that the wave function interior to the finite volume where all three force ranges overlap completely determines the exterior wave function, provided only the wave functions (half off-shell t matrices) of the isolated two-particle subsystems are also known inside their own range of force. The determination is provided by the solution of a one-variable integral equation with a compact kernel, whose resolvent applied to any parametrization of the interior wave function supplies the equivalent of a phase shift analysis for three-particle final states (exact description of overlapping resonances throughout the Dalitz plot), and (if the interior three-particle fordes are also known) a matrix equation for the interior wave function. (Submitted to Physical Review Letters) * Supported in part by the U. S. Atomic Energy Commission.