DOMINANT PARTITION METHOD

Employing the L'Huillier, Redish, and Tandy (LRT) wave function formalism we develop a partially connected method for obtaining few-body reductions of the many-body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. This method for systematically constructing fewer body models for the N-body LRT and BRS equations is termed the dominant partition method (DPM). The DPM maps the many-body problem to a fewer-body one using the criterion that the truncated formalism must be such that consistency with the full Schrödinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few-body reaction mechanism prevails. We also show that the dominant-partition-truncated form of the BRS equations may be obtained by distributing the residual interaction in the exit channel in a manner consistent with the dominant partition truncations of the irreducible cluster potential. © 1980 American Institute of Physics.