Collision cross sections for the thermalization of cold gases

The collision cross section that controls thermalization of gas mixtures is the transport cross section σ_η⁽¹⁾ and not the elastic cross section σₑₗ. The two are the same for pure s-wave scattering but not when higher partial waves contribute. We investigate the differences between them for prototype atomic mixtures and show that the distinction is important at energies above 1000.28em0exμK for LiYb and 30.28em0exμK for RbYb and RbCs. For simple systems, both σ_η⁽¹⁾ and σₑₗ follow universal energy dependence that depends only on the s-wave scattering length when expressed in reduced length and energy units.