Time delays in ultracold atomic and molecular collisions

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 sres. For wider resonances, the behavior is more complicated and we present an analysis in terms of multichannel quantum defect theory.

Unified model of ultracold molecular collisions

“…These two contributions comprise a mean cross section, denoted the "shape elastic" cross section; and a contribution from the fluctuations, denoted the "compound elastic" cross section [20,24]. Since the lifetime of a collisional process is proportional to the energy derivative of the S-matrix [28][29][30][31], writing the cross section in this way elegantly separates out the cross section for direct scattering, the shape elastic part, from indirect scattering, the compound elastic part. Meanwhile, the average absorption cross section is…”

Complexes formed in collisions between ultracold alkali-metal diatomic molecules and atoms

“…The actual widths of the resonances are thus likely to be considerably smaller than the estimates of Mayle et al, and the lifetimes of the complexes, once formed, are likely to be considerably larger than τ = 2π ρ. In general, if the temperature T is high enough to average over many resonances, k B T d, then τ = 2π ρ is still the correct mean collisional time delay [81], but only a fraction of collisions form complexes and those that do have extended lifetimes.…”

Complexes formed in collisions between ultracold alkali-metal diatomic molecules and atoms

“…The actual widths of the resonances are thus likely to be considerably smaller than the estimates of Mayle et al, and the lifetimes of the complexes, once formed, are likely to be considerably larger than τ = 2πhρ. In general, if the temperature T is high enough to average over many resonances, k B T d, then τ = 2πhρ is still the correct mean collisional time delay [81], but only a fraction of collisions form complexes and those that do have extended lifetimes.…”