Universality constraints on three-body recombination for cold atoms: From {sup 4}He to {sup 133}Cs

For atoms with large scattering length, the dependence of the three-body recombination rate on the collision energy is determined by the scattering length and the Efimov three-body parameters and can be expressed in terms of universal functions of a single scaling variable. We use published results on the three-body recombination rate for {sup 4}He atoms to constrain the universal functions. We then use those universal functions to calculate the three-body recombination rate for other atoms with large scattering length at nonzero temperature. The constraints from the {sup 4}He results are strong if the scattering length is near the minimum of the three-body recombination rate at threshold. We apply our results to {sup 133}Cs atoms with a large positive scattering length, and compare them with experimental results from the Innsbruck group.