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.

In this study, comprehensive calculations of energies, hyperfine structure constants, Landé $g_J$ factors and isotope shifts have been performed for the lowest 71 states of Na-like Ar${}^{7+}$, Kr${}^{25+}$ and Xe${}^{43+}$ ions. Radiative parameters viz., wavelengths, transition rates, oscillator strengths and lifetimes are estimated for the electric dipole E1 transitions among these levels. The states under consideration include $1s^{2}2s^{2}2p^{6}nl$ for n = 3–9, l = 0–6, and the fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) method integrated in the latest version of the general-purpose relativistic atomic structure package (GRASP2018) is used for the calculations. The additional corrections, such as the Breit interaction and quantum electrodynamics effects are included in the relativistic configuration interaction calculations, and their effects on energies and other parameters are analysed. We examined the impact of including the core–core and core–valence correlations on level energies. Furthermore, to inspect the reliability of our MCDHF results, we performed another set of calculations using the many-body perturbation theory built into the Flexible Atomic Code (FAC). Moreover, we estimated the uncertainties in the computed lifetimes and transition parameters and assigned their accuracy class. A thorough comparison between the two obtained calculations and with the previous theoretical and experimental results, wherever available, is carried out and a good agreement is observed.

A collisional radiative model for Kr III in the ultraviolet regime is developed. For this purpose, atomic parameters for $4s^{2}4p^4$, $4s4p^5$, $4s^{2}4p^{3}nl$, and $4s^{2}4p^{3}5d$ configurations with n ranging from 5 to 7 and $l=s,p$, using the multiconfiguration Dirac–Hatree–Fock method are calculated. The effects of Breit and radiative quantum electrodynamic corrections are also included. Electron impact excitation cross-sections from the ground state, along with four metastable states arising from the $4s^{2}4p^4$ configuration to all fine structure levels of interest, are calculated using the relativistic distorted wave method. The reliability of the model is tested by comparing the predicted results with the previous measurements.

We compute the ground-state binding energy of muonic 9 Be in two ways: first, the fully perturbative treatment of the nuclear-size effect often employed in light systems, and second, an approach that accounts for the finite-nuclear-size to all orders (and is inspired by calculations otherwise employed for heavy muonic ions). The results are compared term by term and show that both approaches agree to better than one part-per-million of the total energy. The objective of this work is twofold. The first is practical: to provide a parametrization that allows the extraction of the 9 Be charge radius from recent and forthcoming experiments with high precision. The second is more conceptual: to act as a bridge between the community working on calculations for light systems and those focusing on heavy systems, demonstrating that the fully relativistic approach otherwise chosen for heavy systems can be enhanced to cover theoretical predictions for all charge numbers.

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. 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. 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.

We present a novel method for accurately measuring the absolute electric quadrupole moments of light transition elements (23≤Z≤30). Our approach is based on performing precision muonic x-ray spectroscopy of the 2s-2p manifold, which is also referred to as the Lamb shift. These transitions are too weak to be detected with dispersive methods and too overlapping to be resolved by solid-state detectors. Here, we propose the use of cryogenic microcalorimeters, which possess high efficiency and excellent energy resolution in the relevant energy regime, coupled with state-of-the-art theoretical calculations. We demonstrate the feasibility of this approach by performing extensive calculations and realistic simulations. In this way, we establish that the uncertainty in the absolute moment, which is transferred to the quadrupole moments of all isotopes in the chain, could be reduced by up to an order of magnitude within a day of measurement. These precise reference quadrupole moments serve as valuable inputs for nuclear structure studies and for benchmarking state-of-the-art quantum chemistry calculations in open-shell elements.