  Processes mediated by two virtual low-energy photons contribute quite
significantly to the energy of hydrogenic S states. The corresponding level
shift is of the order of (alpha/pi)^2 (Zalpha)^6 m_e c^2 and may be ascribed to
a two-loop generalization of the Bethe logarithm. For 1S and 2S states, the
correction has recently been evaluated by Pachucki and Jentschura [Phys. Rev.
Lett. vol. 91, 113005 (2003)]. Here, we generalize the approach to higher
excited S states, which in contrast to the 1S and 2S states can decay to P
states via the electric-dipole (E1) channel. The more complex structure of the
excited-state wave functions and the necessity to subtract P-state poles lead
to additional calculational problems. In addition to the calculation of the
excited-state two-loop energy shift, we investigate the ambiguity in the energy
level definition due to squared decay rates.
