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

TL;DR

This paper introduces a redefined vacuum formalism within bound-state QED to identify gauge-invariant subsets in two-photon-exchange diagrams for atoms with a single valence electron, improving the analysis of complex atomic interactions.

Contribution

The paper develops a novel redefined vacuum approach that allows for the systematic identification of gauge-invariant subsets in two-photon-exchange diagrams, enhancing the consistency and complexity of atomic QED calculations.

Findings

Derived calculation formulas for arbitrary states in bound-state QED.

Demonstrated gauge invariance analytically and numerically for specific ions.

Enabled potential extension to more complex multi-photon exchange diagrams.

Abstract

The 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, 2p1/2, and 2p3/2 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.