Signature of the s-Wave Regime High above Ultralow Temperatures

Resonant exchange is a general process playing a key role in many-body dynamics and transport phenomena, such as spin, charge, or excitation diffusion. The underlying process is described by the resonant exchange cross section. We show that the s-wave scattering, generally thought to contribute mainly in the ultracold (or Wigner) regime, dictates the overall cross section over a broad range of energies. We derive an analytical expression and explain its applicability high above the Wigner regime. In particular, we demonstrate its relationship to the classical capture (Langevin) cross section and apply it to three very different resonant processes: namely, resonant charge transfer, spin flip, and excitation exchange. This expression explains large variations for different isotopes that cannot otherwise be accounted for by the small change in mass. The s-wave signature also allows us to gain information about the Wigner regime from data obtained at much higher temperatures, which is especially advantageous for systems where the ultracold regime is not reachable.