Signature of the $s$-wave regime high above ultralow temperatures

TL;DR

This paper demonstrates that the $s$-wave scattering contribution can accurately approximate the total cross section even at high energies well above ultracold temperatures, simplifying analysis of resonant scattering processes.

Contribution

The authors derive an analytical expression for the exchange cross section that remains valid at high energies, extending the applicability of $s$-wave approximations beyond the ultracold regime.

Findings

The $s$-wave contribution approximates the full cross section across a wide energy range.

An analytical expression for the exchange cross section is derived.

The approximation enables extracting ultracold scattering information from higher-temperature data.

Abstract

Physical processes involving charge transfer, spin exchange, or excitation exchange often occur in conditions of resonant scattering. We show that the $s$-wave contribution can be used to obtain a good approximation for the full cross section. This approximation is found to be valid for a wide range of scattering energies, including high above the Wigner regime, where many partial waves contribute. We derive an analytical expression for the exchange cross section and demonstrate its relationship to the Langevin cross section. We give examples for resonant charge transfer as well as spin-flip and excitation exchange. Our approximation can be used to gain information about the $s$-wave regime from data obtained at much higher temperatures, which would be advantageous for systems where the ultracold quantum regime is not easily reachable.