Multiple scattering and few-body Hamiltonian models of nuclear reactions

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Abstract
The multiple-scattering structure of various scattering operators as well as the integral equations they satisfy are investigated for Hamiltonians consisting of terms of definite but arbitrary connectivities. This is done in order to encompass the effective interactions which arise in few-body models of nuclear reactions. The counterparts of the Watson and other kinds of multiple-scattering expansions are developed under these circumstances. Connected-kernel scattering integral equations which have the unique and practical feature of being both partition labeled and possessing a multiple-scattering structure are obtained for the transition operators. These extended versions of both the multiple-scattering expansions and partition-labeled multiple-scattering integral equations are applied to the specific class of few-body Hamiltonian reaction models found by Polyzou and Redish. The concept of a well-structured reaction mechanism is introduced and it is established that for such a reaction mechanism an appropriately modified multiple-scattering picture carries over to the approximate few-body models. It is shown, for example, that for a well-structured reaction mechanism the analogs of the Born and impulse approximations emerge directly from the extended partitionlabeled multiple-scattering equations in contrast to alternative formulations.