# Time delays in ultracold atomic and molecular collisions

## TL;DR

This paper investigates the behavior of collisional time delays near Feshbach resonances in ultracold atomic and molecular collisions, revealing how these delays depend on energy, field, and resonance width through coupled-channels calculations.

## Contribution

It provides a detailed analysis of time delays around Feshbach resonances using coupled-channels calculations and multichannel quantum defect theory, highlighting the dependence on resonance parameters.

## Key findings

- Time delay is proportional to scattering length at low energy.
- Time delay exhibits a Lorentzian peak at high energy.
- Crossover energy scales with resonance strength parameter.

## Abstract

We study the behavior of the Eisenbud-Wigner collisional time delay around Feshbach resonances in cold and ultracold atomic and molecular collisions. We carry out coupled-channels scattering calculations on ultracold Rb and Cs collisions. In the low-energy limit, the time delay is proportional to the scattering length, so exhibits a pole as a function of applied field. At high energy, it exhibits a Lorentzian peak as a function of either energy or field. For narrow resonances, the crossover between these two regimes occurs at an energy proportional to the square of the resonance strength parameter $s_\textrm{res}$. For wider resonances, the behavior is more complicated and we present an analysis in terms of multichannel quantum defect theory.