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.
Highlights
Scattering resonances are important in many fields, from nuclear physics to physical chemistry
There are important applications in ultracold atomic physics, where magnetically tunable Feshbach resonances are used to control the behavior of ultracold atoms
We have studied the behavior of the collisional time delay in cold and ultracold atomic and molecular collisions
Summary
Scattering resonances are important in many fields, from nuclear physics to physical chemistry. A resonance occurs when a collision occurs at an energy close to that of a quasibound state of the collision complex so that scattering flux is temporarily trapped at short range. The resulting dense pattern of scattering resonances may produce long-lived sticky collisions in the ultracold regime. Gregory et al [10] have demonstrated that the kinetics of the loss process are second order for ultracold RbCs. It is important to understand collisional time delays in the ultracold regime. There has been little work on understanding the basic properties and behaviors of the time delay in ultracold collisions. We will illustrate the behavior with calculations on resonances in ultracold atomic collisions and discuss the transition from the threshold regime to higher energy
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