Theory of multichannel potential scattering with permanently confined channels

A detailed investigation of a class of nonrelativistic multichannel potential scattering models is presented. A subset of the channels contain confinement potentials that allow only a discrete spectrum with an accumulation at $+\infty$ (like the states of the quark model); the remaining channels contain the usual scattering states, which are allowed to communicate with the states of the permanently confined channel through an off-diagonal local potential. We formulate the problem in this paper in such a way that many of the usual properties of partial-wave scattering theory can be extended to this case. We generalize the Levinson theorem to include this class of models and attempt to use it to make a distinction between two types of resonances: those related to the fundamental states of the quark model and accidental resonances not associated with quark-model states.