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

TL;DR

This paper examines the calculation of two-photon decay widths in hydrogen, highlighting ambiguities in separating cascade and pure two-photon processes, with implications for astrophysics and early Universe studies.

Contribution

It compares two approaches for evaluating two-photon decay widths and critically analyzes the ambiguity in distinguishing cascade and pure two-photon contributions.

Findings

Demonstrates ambiguity in separating cascade and pure two-photon decay channels.

Highlights the significance of pure two-photon processes in astrophysics.

Critiques existing methods for separating decay contributions.

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 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.