Projection Operators in the Unified Reaction Theory

A simple form of the projection operators applicable for general rearrangement and exchange processes with full recoil effect is constructed for the unified reaction theory of Feshbach. Channels of different cluster configurations are not orthogonal and the overlap of their wave functions is important. Multidimensional generalization of the wave functions and corresponding wave equations takes this effect into account in a simple way without the complication of solving the integral equations with overlap kernels. Introduction of the projection operators makes it possible to reduce the multiparticle scattering problem in a natural way to that of multiclusters and the dispersive part which involves intermediate states of the compound system. The formalism is compared with the Faddeev equations for the case of three-particle two-cluster reactions, and also with other theories.