Energy-scaling of the Product State Distribution for Three-Body Recombination of Ultracold Atoms

Three-body recombination is a chemical reaction where the collision of threeatoms leads to the formation of a diatomic molecule. In the ultracold regime itis expected that the production rate of a molecule generally decreases with itsbinding energy E_b, however, its precise dependence and the physics governingit have been left unclear so far. Here, we present a comprehensive experimentaland theoretical study of the energy dependency for three-body recombination ofultracold Rb. For this, we determine production rates for molecules in astate-to-state resolved manner, with the binding energies E_b ranging from0.02 to 77 GHz× h. We find that the formation rate approximately scalesas E_b^-α, where α is in the vicinity of 1. The formation ratetypically varies only within a factor of two for different rotational angularmomenta of the molecular product, apart from a possible centrifugal barriersuppression for low binding energies. In addition to numerical three-bodycalculations we present a perturbative model which reveals the physical originof the energy scaling of the formation rate. Furthermore, we show that thescaling law potentially holds universally for a broad range of interactionpotentials.