  Three-body recombination is a chemical reaction where the collision of three
atoms leads to the formation of a diatomic molecule. In the ultracold regime it
is expected that the production rate of a molecule generally decreases with its
binding energy $E_b$, however, its precise dependence and the physics governing
it have been left unclear so far. Here, we present a comprehensive experimental
and theoretical study of the energy dependency for three-body recombination of
ultracold Rb. For this, we determine production rates for molecules in a
state-to-state resolved manner, with the binding energies $E_b$ ranging from
0.02 to 77 GHz$\times h$. We find that the formation rate approximately scales
as $E_b^{-\alpha}$, where $\alpha$ is in the vicinity of 1. The formation rate
typically varies only within a factor of two for different rotational angular
momenta of the molecular product, apart from a possible centrifugal barrier
suppression for low binding energies. In addition to numerical three-body
calculations we present a perturbative model which reveals the physical origin
of the energy scaling of the formation rate. Furthermore, we show that the
scaling law potentially holds universally for a broad range of interaction
potentials.
