Theory of Rearrangement Collisions and Resonances

Abstract

The theory of rearrangement collisions is examined in terms of the channel-projection method, and the singularities in the wave functions are analyzed in detail. Ambiguities in the coupled equations are pointed out, which are the direct consequence of the nonuniqueness in the multicomponent wave functions. Boundary conditions on the wave functions play a crucial role in determining the boundedness of the closed-channel operators. A convenient set of equations whose solutions describe the resonances is derived, and an explicit variational procedure is given to calculate the resonance energies. The method used in deriving the different equivalent sets of coupled equations in terms of the channel-mixing operator is based on the multidimensional formulation of the reaction theory and is quite general. Nonorthogonality of the rearrangement channels allows essentially such arbitrariness, and this can be used to simplify the theory.