Two-photon decay of excited levels in hydrogen: The ambiguity of the separation of cascades and pure two-photon emission

Abstract

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 two-photon decay channels for the $3s$ level of the hydrogen atom are evaluated, including the cascade transition probability $3s\text{\ensuremath{-}}2p\text{\ensuremath{-}}1s$. An important role is assigned to the two-photon decays 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 methods for such a separation.