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A systematic investigation of the nuclear-polarization effects in one- and few-electron heavy ions is presented. The nuclear-polarization corrections in the zeroth and first orders in are evaluated to the binding energies, the hyperfine splitting, and the bound-electron g factor. It is shown, that the nuclear-polarization contributions can be substantially canceled simultaneously with the rigid nuclear corrections. This allows for new prospects for probing the QED effects in strong electromagnetic field and the determination of fundamental constants.

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