Highly precise QED predictions for measurements at the CRYRING at FAIR

An ab initio QED approach to treat a valence-hole excitation in closed-shell systems is developed in the framework of the two-time Green's-function method. The derivation considers a redefinition of the vacuum state and its excitation as a valence-hole pair. The proper two-time Green's function, whose spectral representation confirms the poles at valence-hole excitation energies, is proposed. An contour integral formula which connects the energy corrections and the Green's function is also presented. First-order corrections to the valence-hole excitation energy involving self-energy, vacuum polarization, and one-photon-exchange terms are explicitly derived in the redefined vacuum picture. Reduction to the usual vacuum electron propagators is shown, which agrees in the Breit approximation with the many-body perturbation theory expressions for the valence-hole excitation energy.