# Width and shift of Fano-Feshbach resonances for van der Waals interactions

## TL;DR

This paper analyzes the properties of Fano-Feshbach resonances in ultracold atoms with van der Waals interactions, revealing that the width-to-shift ratio depends on both background and closed-channel scattering lengths, challenging previous assumptions.

## Contribution

It introduces a two-channel model to accurately relate the width and shift of resonances, accounting for both background and closed-channel scattering lengths, and verifies predictions with lithium-6 data.

## Key findings

- The width-to-shift ratio depends on closed-channel scattering length.
- Different limits are identified for optical and magnetic resonances.
- Model predictions are validated for lithium-6 resonance.

## Abstract

We revisit the basic properties of Fano-Feshbach resonances in two-body systems with van der Waals tail interactions, such as ultracold neutral atoms. Using a two-channel model and two different methods, we investigate the relationship between the width and shift of the resonances and their dependence on the low-energy parameters of the system. Unlike what was previously believed [Rev. Mod. Phys. 82, 1225 (2010)] for magnetic resonances, we find that the ratio between the width and the shift of a resonance does not depend only on the background scattering length, but also on a closed-channel scattering length. We obtain different limits corresponding to different cases of optical and magnetic resonances. Although the generalisation of the theory to the multi-channel case remains to be done, we found that our two-channel predictions are verified for a specific resonance of lithium-6.