Two-photon decay of excited levels in hydrogen: the ambiguity of the
  separation of cascades and pure two-photon emission
  The problem of the evaluation of the two-photon decay width of excited states
in hydrogen is considered. Two different approaches to the evaluation of the
width including cascades channels are employed: the summation of the transition
probabilities for various decay channels and the evaluation of the imaginary
part of the Lamb shift. As application the decay channels for the 3s level of
the hydrogen atom are evaluated, including the cascade transition probability
3s-2p-1s as well as "pure" two-photon decay probability and the interference
between both channels. An important role should be assigned to the "pure"
two-photon probability in astrophysics context, since processes of this kind
provide a possibility for the decoupling of radiation and matter in the early
Universe. We demonstrate the ambiguity of separation of the "pure" two-photon
contribution and criticize the existing attempts for such a separation.
