  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).
