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A charged particle in a magnetic field possesses discrete energy levelsassociated with particle's rotation around the field lines. The radiativetransitions between these levels are the well-known cyclotron transitions. Weshow that a bound complex of particles with a non-zero net charge displaysanalogous transitions between the states of confined motion of the entirecomplex in the field. The latter {\em bound-ion cyclotron transitions} areaffected by a coupling between the collective and internal motions of thecomplex and, as a result, differ from the transitions of a "reference" bare ionwith the same mass and charge. We analyze the cyclotron transitions for complexions by including the coupling within a rigorous quantum approach. Particularattention is paid to comparison of the transition energies and oscillatorstrengths to those of the bare ion. Selection rules based on integrals ofcollective motion are derived for the bound-ion cyclotron transitionsanalytically, and the perturbation and coupled-channel approaches are developedto study the transitions quantitatively. Representative examples are consideredand discussed for positive and negative atomic and cluster ions.

Cyclotron transitions of bound ions