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One-electron ion in a quantizing magnetic field

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.