Unified Theory of antisymmetrized elastic two-fragment scattering

The relationship between a new antisymmetrized optical potential formulation based on the Alt, Grassberger, and Sandhas off-shell extension of the transition operator and the Feshbach effective Hamiltonian approach to elastic two-fragment scattering is established. Explicit relationships among the unsymmetrized and symmetrized projection operators of the two methods are found and exploited in order to determine several interpolative operatore identities. The resonance signatures of both the potential and the Feshbach formalisms are found to be identifical. An explicit operator identical connecting the effective Hamiltonian and the optical potential, which is stated in terms of a nonsingular dynamically independent mapping, is the principal result obtained. This identity leads to the unambiguous solution of the problem of the imposition of the correct elastic scattering boundary conditions upon Feshbach's projected forms of the Schroedinger equation and also completes the unification of two superfically distinct methods for dealing with elastic nuclear scattering with all effects of antisymmetry taken into account