Redefined vacuum approach and gauge-invariant subsets in two-photon-exchange diagrams for a closed-shell system with a valence electron

CThe two-photon-exchange diagrams for atoms with single valence electrons are investigated. Calculation formulas are derived for an arbitrary state within the rigorous bound-state QED framework utilizing the redefined vacuum formalism. In contrast to other methods, the redefined vacuum approach enables the identification of eight gauge-invariant subsets and, thus, efficiently checks the consistency of the obtained results. The gauge invariance of found subsets is demonstrated both analytically (for an arbitrary state) as well as numerically for 2s, 2p(1/2), and 2p(3/2) valence electrons in Li-like ions. Identifying gauge-invariant subsets in the framework of the proposed approach opens a way to tackle more complex diagrams, e.g., three-photon exchange, where the fragmentation on simpler subsets is crucial for its successful calculation.

Automated summary

This study investigates the two-photon-exchange diagrams for atoms with single valence electrons using a redefined vacuum formalism within the bound-state QED framework. It derives calculation formulas for arbitrary states, identifies gauge-invariant subsets, and efficiently checks consistency of results. Analytical and numerical demonstrations on Li-like ions confirm the gauge invariance of found subsets, highlighting the importance of this approach for tackling more complex diagram calculations.