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

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