A two-channel R-matrix analysis of magnetic field induced Feshbach resonances

TL;DR

This paper develops a simplified two-channel R-matrix model to analyze magnetic field induced Feshbach resonances in cold atom scattering, capturing essential physics with minimal parameters.

Contribution

It introduces a method to construct an effective two-channel Feshbach model from key parameters, validated by comparison with exact calculations.

Findings

The two-channel model accurately reproduces bound state spectra.

The scattering properties match well with full coupled channels calculations.

The approach simplifies analysis of Feshbach resonances.

Abstract

A Feshbach resonance arises in cold atom scattering due to the complex interplay between several coupled channels. However, the essential physics of the resonance may be encapsulated in a simplified model consisting of just two coupled channels. In this paper we describe in detail how such an effective Feshbach model can be constructed from knowledge of a few key parameters, characterizing the atomic Born-Oppenheimer potentials and the low energy scattering near the resonance. These parameters may be obtained either from experiment or full coupled channels calculations. Using R-matrix theory we analyze the bound state spectrum and the scattering properties of the two-channel model, and find it to be in good agreement with exact calculations.