  The nuclear-polarization corrections to the energy levels of highly charged
ions are systematically investigated to leading order in the fine-structure
constant. To this end, the notion of effective photon propagators with
nuclear-polarization insertions is employed, where the nuclear excitation
spectrum is calculated by means of the Hartree-Fock-based random-phase
approximation. The effective Skyrme force is used to describe the interaction
between nucleons, and the model dependence is analyzed. To leading order, the
formalism predicts two contributions given by the effective vacuum-polarization
and self-energy diagrams. The existing ambiguity around the vacuum-polarization
term is resolved by demonstrating that it is effectively absorbed in the
standard finite-nuclear-size correction. The self-energy part is evaluated with
the full electromagnetic electron-nucleus interaction taken into account, where
the importance of the effects of the nuclear three-currents is emphasized.
