  We theoretically investigate the trap-assisted formation of complexes in
atom-ion collisions and their impact on the stability of the trapped ion. The
time-dependent potential of the Paul trap facilitates the formation of
temporary complexes by reducing the energy of the atom, which gets temporarily
stuck in the atom-ion potential. As a result, those complexes significantly
impact termolecular reactions leading to molecular ion formation via three-body
recombination. We find that complex formation is more pronounced in systems
with heavy atoms, but the mass has no influence on the lifetime of the
transient state. Instead, the complex formation rate strongly depends on the
amplitude of the ion's micromotion. We also show that complex formation
persists even in the case of a time-independent harmonic trap. In this case, we
find higher formation rates and longer lifetimes than the Paul trap, indicating
that the atom-ion complex plays an essential role in atom-ion mixtures in
optical traps.
