Modeling interactions for resonant p-wave scattering

TL;DR

This paper extends the zero-range potential approach to resonant p-wave scattering in ultra-cold polarized fermions, revealing geometric insights and providing a simple interpretation of transfer rates near resonance, with energy varying linearly with density.

Contribution

It introduces a modified scalar product linking Hilbert space geometry to interactions, offering new insights into p-wave resonant scattering and atom-molecule transfer processes.

Findings

Energy varies linearly with density at resonance.

A modified scalar product reveals geometric structure of the Hilbert space.

Transfer rates between atomic and molecular states are interpreted simply.

Abstract

In view of recent experiments on ultra-cold polarized fermions, the zero-range potential approach is generalized to situations where two-body scattering is resonant in the p-wave channel. We introduce a modified scalar product which reveals a deep relation between the geometry of the Hilbert space and the interaction. This formulation is used to obtain a simple interpretation for the transfer rates between atomic and molecular states within a two branches picture of the many-body system close to resonance. At resonance, the energy of the dilute gas is found to vary linearly with density.