  We study atom-ion scattering in the ultracold regime. To this aim, an
analytical model based on the multichannel quantum defect formalism is
developed and compared to close-coupled numerical calculations. We investigate
the occurrence of magnetic Feshbach resonances focusing on the specific 40Ca+ -
Na system. The presence of several resonances at experimentally accessible
magnetic fields should allow the atom-ion interaction to be precisely tuned. A
fully quantum-mechanical study of charge exchange processes shows that
charge-exchange rates should remain small even in the presence of resonance
effects. Most of our results can be cast in a system-independent form and are
important for the realization of the charge-neutral ultracold systems.
