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Relativistic and Radiative Energy Shifts for Rydberg States
We investigate relativistic and quantum electrodynamic effects for
highly-excited bound states in hydrogenlike systems (Rydberg states). In
particular, hydrogenic one-loop Bethe logarithms are calculated for all
circular states (l = n-1) in the range 20 <= n <= 60 and successfully compared
to an existing asymptotic expansion for large principal quantum number n. We
provide accurate expansions of the Bethe logarithm for large values of n, for
S, P and circular Rydberg states. These three expansions are expected to give
any Bethe logarithms for principal quantum number n > 20 to an accuracy of five
to seven decimal digits, within the specified manifolds of atomic states.
Within the numerical accuracy, the results constitute unified, general formulas
for quantum electrodynamic corrections whose validity is not restricted to a
single atomic state. The results are relevant for accurate predictions of
radiative shifts of Rydberg states and for the description of the recently
investigated laser-dressed Lamb shift, which is observable in a strong
coherent-wave light field.Comment: 8 pages; RevTeX