Pseudopotential in resonant regimes

TL;DR

This paper extends the zero-range potential approach to describe resonant two-body scattering in arbitrary partial waves, generalizing the Fermi pseudopotential and emphasizing the importance of a regularized scalar product.

Contribution

It introduces a generalized formalism for zero-range potentials in resonant regimes across all partial waves, including a regularized scalar product for accurate wave function description.

Findings

Generalization of zero-range potential formalism to arbitrary partial waves

Introduction of a regularized scalar product for wave functions

Demonstration of the impact of interaction on Hilbert space geometry

Abstract

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.