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The theoretical treatment of Rydberg states in one-electron ions isfacilitated by the virtual absence of the nuclear-size correction, andfundamental constants like the Rydberg constant may be in the reach of plannedhigh-precision spectroscopic experiments. The dominant nuclear effect thatshifts transition energies among Rydberg states therefore is due to the nuclearmass. As a consequence, spectroscopic measurements of Rydberg transitions canbe used in order to precisely deduce nuclear masses. A possible application ofthis approach to the hydrogen and deuterium, and hydrogen-like lithium andcarbon is explored in detail. In order to complete the analysis, numerical andanalytic calculations of the quantum electrodynamic (QED) self-energy remainderfunction for states with principal quantum number n=5,...,8 and with angularmomentum L=n-1 and L=n-2 are described (j = L +/- 1/2).

Proposal for the determination of nuclear masses by high-precision spectroscopy of Rydberg states