PAX (antiProtonic Atom X-ray spectroscopy) is a new experiment with the aim to test strong-field quantum electrodynamics (QED) effects by performing high-precision x-ray spectroscopy of antiprotonic atoms. By utilizing advanced microcalorimeter detection techniques and a low-energy antiproton beam provided by the ELENA ring at CERN, gaseous targets will be used for the creation of antiprotonic atoms, and the measurement of transitions between circular Rydberg states will be conducted with up to two orders of magnitude improved accuracy over previous studies using high-purity germanium detectors. %\cite{Gotta2008, Ullom2015} Our approach eliminates the longstanding issue of nuclear uncertainties that have hindered prior studies using highly charged ions, thus enabling direct and purely QED-focused measurements. %\cite{Paul2021} By precisely probing atomic systems with electric fields up to two orders of magnitude above the Schwinger limit, PAX will test vacuum polarization and second-order QED corrections, opening new frontiers in fundamental physics and uncovering potential pathways to physics beyond the Standard Model.

The total two-photon decay rate of hydrogenlike ions is studied using relativistic quantum electrodynamics. In particular, we analyze how finite nuclear size and QED vacuum polarization corrections affect the decay rate. To calculate these corrections, a finite basis set method based on $B$ splines is used for the generation of quasicomplete atomic spectra and, hence, of the relativistic Green's function. By making use of this $B$-spline approach, high precision calculations have been performed for the $2s_{1/2}\to 1s_{1/2}+2\gamma$ and $2p_{1/2}\to 1s_{1/2}+2\gamma$ decay of hydrogenlike ions along the entire isoelectronic sequence. The results of these calculations show that both QED and finite nuclear size effects are comparatively weak for the $2s_{1/2}\to 1s_{1/2}+2\gamma$ transition. In contrast, they are much more pronounced for the $2p_{1/2}\to 1s_{1/2}+2\gamma$ decay, where, for hydrogenlike uranium, the decay rate is reduced by 0.484% due to the finite nuclear size and enhanced by 0.239% if the vacuum polarization is taken into account.

We present a theoretical method to calculate Delbrück scattering amplitudes. Our formalism is based on the exact analytical Dirac-Coulomb Green's function and therefore accounts for the interaction of the virtual electron-positron pair with the nucleus to all orders, including the Coulomb corrections. The numerical convergence of our calculations is accelerated by solving the radial integrals that are involved analytically in the asymptotic region. Numerical results for the collision of photons with energies 102.2 and 255.5 keV with bare neon and lead nuclei are compared with the predictions of the lowest-order Born approximation. We find that our method can produce accurate results within a reasonable computation time and that the Coulomb corrections enhance the absolute value of the Delbrück amplitude by a few percent for the studied photon energies.

We present a theoretical study of the inelastic scattering of vortex electrons by a hydrogen atom. In our study, special emphasis is placed on the effects of the Coulomb interaction between a projectile electron and a target atom. To understand these effects, we construct vortex electron wave functions both from free space and distorted solutions of the Schrödinger equation. These wave functions give rise to the first Born and distorted wave scattering amplitudes, respectively. The derived theory has been employed to investigate the 1 s → 2 p transition of a hydrogen atom induced by electrons with the kinetic energies in the range from 20 to 100 eV. The results of the calculations have clearly indicated that the Coulomb interaction can significantly affect the phase pattern and probability density of a vortex electron beam as well as the squared transition amplitudes. For the latter, the most pronounced effect was found for the excitation to the | 2 p m f = 0 ⟩ sublevel and large scattering angles.

We report calculations of Delbrück scattering that include all-order Coulomb corrections for photon energies above the threshold of electron-positron pair creation. Our approach is based on the application of the Dirac-Coulomb Green’s function and accounts for the interaction between the virtual electron-positron pair and the nucleus to all orders in the nuclear binding strength parameter $\alpha Z$. Practical calculations are performed for the scattering of 2.754 MeV photons off plutonium atoms. We find that including the Coulomb corrections enhances the scattering cross section by up to 50% in this case. The obtained results resolve the long-standing discrepancy between experimental data and theoretical predictions and demonstrate that an accurate treatment of the Coulomb corrections is crucial for the interpretation of existing and guidance of future Delbrück scattering experiments on heavy atoms.