Scattering theory in three-body kinetic equations

The relationship between the collision kernel of the three-body quantum mechanical kinetic equation (quantum version of the Choh-Uhlenbeck equation) and modern scattering theory is examined utilizing the work of Faddeev and Weinberg. Recognizing that the collision kernel is related to the M⊘ller scattering operator it is shown that the collision kernel is “well-defined” for suitable interaction potentials and contains only connected three particle collisions in the sense of Weinberg. The collision kernel is interpreted physically and is shown to contain a generalization of the ordinary Boltzmann collision term to three particle processes plus a distorted-wave-impulse approximation correction to the two particle Boltzmann collision term.