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

The theoretical treatment of Rydberg states in one-electron ions is facilitated by the virtual absence of the nuclear-size correction, and fundamental constants like the Rydberg constant may be in the reach of planned high-precision spectroscopic experiments. The dominant nuclear effect that shifts transition energies among Rydberg states therefore is due to the nuclear mass. As a consequence, spectroscopic measurements of Rydberg transitions can be used in order to precisely deduce nuclear masses. A possible application of this approach to the hydrogen and deuterium, and hydrogen-like lithium and carbon is explored in detail. In order to complete the analysis, numerical and analytic calculations of the quantum electrodynamic (QED) self-energy remainder function for states with principal quantum number n=5,...,8 and with angular momentum L=n-1 and L=n-2 are described (j = L +/- 1/2).