Redundant solutions, scattering solutions, and nonsymmetric nonlocal potentials

Increasingly, nonsymmetric nonlocal potentials are occurring in formulations which include descriptions of antisymmetrization and other nuclear phenomena. In studying such potentials, it is found that the characteristics of solutions of the scattering equation differ in some cases significantly from those associated with symmetric nonlocal potentials. For example, it has been demonstrated that when redundant solutions are present due to antisymmetrization, a scattering solution does not exist unless a consistency condition is satisfied. In the present paper this and other such aspects of nonsymmetric nonlocal potentials are investigated. The importance of the adjoint potential to these discussions is particularly emphasized. Conditions on scattering solutions for nonsymmetric nonlocal potentials and their adjoints are discussed in detail, and an example is presented