  A charged particle in a magnetic field possesses discrete energy levels
associated with particle rotation around the field lines. A bound complex of
particles with a nonzero net charge possesses an analogous levels associated
with its center-of-mass motion and, in addition, the levels associated with
internal degrees of freedom, that is with relative motions of its constituent
particles. The center-of-mass and internal motions are mutually dependent,
which complicates theoretical studies of the binding energies, radiative
transitions and other properties of the complex ions moving in quantizing
magnetic fields. In this work, we present a detailed derivation of practical
expressions for the numerical treatment of such properties of the hydrogenlike
ions moving in strong quantizing magnetic fields, which follows and supplements
the previous works of Bezchastnov et al. Second, we derive asymptotic analytic
expressions for the binding energies, oscillator strengths, and photoionization
cross sections of the moving hydrogenlike ions in the limit of an ultra-strong
magnetic field.
