  The immersion of a single ion confined by a radiofrequency trap in an
ultracold atomic gas extends the concept of buffer gas cooling to a new
temperature regime. The steady state energy distribution of the ion is
determined by its kinetics in the radiofrequency field rather than the
temperature of the buffer gas. Moreover, the finite size of the ultracold gas
facilitates the observation of back-action of the ion onto the buffer gas. We
numerically investigate the system's properties depending on atom-ion mass
ratio, trap geometry, differential cross-section, and non-uniform neutral atom
density distribution. Experimental results are well reproduced by our model
considering only elastic collisions. We identify excess micromotion to set the
typical scale for the ion energy statistics and explore the applicability of
the mobility collision cross-section to the ultracold regime.
