  We study three-body recombination of Ba$^+$ + Rb + Rb in the mK regime where
a single $^{138}$Ba$^{+}$ ion in a Paul trap is immersed into a cloud of
ultracold $^{87}$Rb atoms. We measure the energy dependence of the three-body
rate coefficient $k_3$ and compare the results to the theoretical prediction,
$k_3 \propto E_{\textrm{col}}^{-3/4}$ where $E_{\textrm{col}}$ is the collision
energy. We find agreement if we assume that the non-thermal ion energy
distribution is determined by at least two different micro-motion induced
energy scales. Furthermore, using classical trajectory calculations we predict
how the median binding energy of the formed molecules scales with the collision
energy. Our studies give new insights into the kinetics of an ion immersed into
an ultracold atom cloud and yield important prospects for atom-ion experiments
targeting the s-wave regime.
