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Multichannel scattering with nonlocal and confining potentials. I. General theory.

A general discussion of nonrelativistic multichannel scattering for nonlocal potentials is presented. The approach is based on the extensive use of the Fredholm determinants that are associated with the integral equations occurring at various points of the theory. Special attention is paid to situations where confining potentials are present, as in nonrelativistic quark models of hadron-hadron interactions. Some standard results of multichannel scattering theory for local potentials and one-channel theory for nonlocal ones are generalized in this context, including Levinson's theorem.