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Abstract
The unified nuclear reaction theory that employs the channel projection operators is generalized to include explicitly the cluster structures of a many-body system. It facilitates not only the construction of asymptotic boundary conditions, but also the incorporation of the cluster models in the interaction region. A matrix representation of the scattering equations and the multi-component wavefunctions in the cluster channel space naturally resolves the difficulty associated with the non-commuting channel operators for different cluster structures, thus removing the principal limitation of the previous formulation. The critical problems of over-completeness and cluster channel orthogonality inherent in the multi-component formulation are discussed in detail for the first time, providing the essential mathematical basis for the validity of the generalized theory.
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