Pseudopotential in resonant regimes

The zero-range potential approach is extended for the description of situations where two-body scattering is resonant in arbitrary partial waves. The formalism generalizes the Fermi pseudopotential which can be used only for s-wave broad resonances. In a given channel, the interaction is described either in terms of a contact condition on the wave function or with a family of pseudopotentials. We show that it is necessary to introduce a regularized scalar product for wave functions obtained in the zero-range potential formalism (except for the Fermi pseudopotential). This metrics shows that the geometry of these Hilbert spaces depends crucially on the interaction.