Abstract
The redefined vacuum approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool for formula derivation. Here, we elaborate this approach within the bound-state QED perturbation theory. In addition to general formulation, we consider the particular example of a single particle (electron or vacancy) excitation with respect to the redefined vacuum. Starting with simple one-electron QED diagrams, we deduce first- and second-order many-electron contributions: screened self-energy, screened vacuum polarization, one-photon exchange, and two-photon exchange. The redefined vacuum approach provides a straightforward and streamlined derivation and facilitates its application to any electronic configuration. Moreover, based on the gauge invariance of the one-electron diagrams, we can identify various gauge-invariant subsets within derived many-electron QED contributions.
Highlights
Charged ions are considered as one of the best available natural laboratories to access strong field effects at the moment; highlighting the need to go beyond the perturbative regime since for high Z, the αZ expansion parameter is comparable to one
quantum electrodynamics (QED) can be applied to any many-electron atoms even though it is most deeply developed for hydrogen and helium [3], and hydrogen-like ions [4], where the accuracy of the calculations has reached a remarkably high level
To date there are several methods employed within the bound-state QED perturbation theory: the adiabatic Smatrix approach [50], the two-time Green’s function (TTGF) method [42,49], the covariantevolution-operator method [51], and the line profile approach [52]
Summary
Charged ions are considered as one of the best available natural laboratories to access strong field effects at the moment; highlighting the need to go beyond the perturbative regime since for high Z, the αZ expansion parameter is comparable to one (where Z is the nuclear charge number and α is the fine-structure constant). Following the motivation outlined above, in our recent paper [43], we have derived the two-photon-exchange contribution within the redefined vacuum QED approach for the case of an atom with a single electron above closed shells. In order to illustrate the developed method, the first- (one-photon exchange) and secondorder (screened QED and two-photon exchange) many-electron QED diagrams are derived for the case of single-vacancy atoms Such an example is chosen due to the fact that twophoton-exchange correction is still uncalculated for fluorine-like ions [44,45,46] as well as due to recent experimental efforts for such systems [47,48]. All integrals are meant to be on the interval (−∞, ∞)
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