Three-particle scattering rates and singularities of the T matrix. I.

We construct a quantum ensemble to describe nonrelativistic three-particle scattering, and derive expressions for the observable scattering rates. These expressions are seen to reduce to the familiar expressions involving the modulus squared of the T matrix, provided the final momenta are chosen to avoid the disconnected and double-scattering singularities. We show that our expressions remain finite in the neighborhood of the disconnected singularities, and that the predicted rates are consistent with the physical interpretation of the disconnected processes.