Model of a zero-range potential with internal structure

A zero-range potential with internal structure is constructed using the methods of the theory of extensions from the space $L_2(\mathbb R^3)$ to the larger Hilbert space $L_2(\mathbb R^3)\oplus H$. A spectral analysis of a Schrödinger operator with such a potential is made; the S matrix is investigated and shown to be nontrivial in the $s$ channel; and the eigenvalues and resonances are calculated for small coupling constants.