Asymptotic Channel States and Matrix Equations in the Unified Reaction Theory

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Abstract
The multidimensional formulation of the unified reaction theory with asymptotic channel states of different cluster compositions is discussed and extended. Modified sets of projection operators and Hermitian orthoprojectors are derived using the channel-mixing operator and it is shown that the Hermiticity of the operators may be an unnecessarily stringent requirement for the formulation of the theory. The simple diagonal form of the orthoprojectors given earlier is shown, however, to be sufficient to construct a reaction theory consistent with the asymptotic boundary conditions if the matrix equations are suitably modified. Based on the many-particle scattering theory, a useful reduction method for the modification of the matrix equations is developed. Application of the method provides a series of sets of coupled equations for the description of direct processes, which contains a sufficient amount of desirable properties in the restricted direct-channel spaces to give consistent solutions.