Coulomb two-body problem with internal structure

The methods of the theory of extensions to an enlarged Hilbert space are used to construct a model of the interaction of the external (Coulomb) and internal (quark) channelsin the two-body problem. The mutual influence of the spectra of the corresponding channel Hamiltonians is studied; it leads, in particular, to a rearrangement of the spectra of hadronic atoms. An explicit representation is obtained for the $S$ matrix, and its singularities on the energy shell are studied.