Virtual Resonant States in Two-Photon Decay Processes: Lower-Order Terms, Subtractions, and Physical Interpretations

TL;DR

This paper examines the two-photon decay of highly excited atomic states, highlighting the need for subtracting lower-order terms in naive models and demonstrating how QED naturally accounts for these corrections.

Contribution

It clarifies the role of lower-order terms in two-photon decay calculations and shows how QED inherently performs the necessary subtractions.

Findings

Naive decay models include lower-order terms that must be subtracted.

Sum of lower-order terms equals the one-photon decay rate of the initial state.

QED approach automatically subtracts lower-order contributions.

Abstract

We investigate the two-photon decay rate of a highly excited atomic state which can decay to bound states of lower energy via cascade processes. We show that a naive treatment of the process, based on the introduction of phenomenological decay rates for the intermediate, resonant states, leads to lower-order terms which need to be subtracted in order to obtain the coherent two-photon correction to the decay rate. The sum of the lower-order terms is exactly equal to the one-photon decay rate of the initial state, provided the naive two-photon decay rates are summed over all available two-photon channels. A quantum electrodynamics (QED) treatment of the problem leads to an "automatic" subtraction of the lower-order terms.