arXiv subjects

J. Sommerfeldt

Publications and source records attributed to J. Sommerfeldt.

10 recordsLinked to original sources

arXiv2026

Wichmann-Kroll Correction to the Interelectronic Interaction in He- and Li-Like Ions

We present a theoretical study of the higher-order QED contribution to the interelectronic interaction in He- and Li-like ions, where a virtual electron-positron loop is inserted into the photon line of the one-photon exchange diagram. Our approach is based on the Dirac-Coulomb Green's function and accounts for the interaction of the virtual $e^+e^-$ pair with the electric field of the nucleus to all orders in $αZ$, with $α$ being the fine-structure constant and $Z$ the atomic charge number. We show that the numerical convergence of the involved integrals can be significantly improved by explicitly subtracting the non-gauge-invariant spurious contributions from the integrands. We present improved numerical values for this contribution to the Lamb shift over a wide range of nuclear charge numbers $Z$. Our calculations agree well with previous results by Artemyev and co-workers [Phys. Rev. A 56, 3529 (1997); Phys. Rev. A 60, 45 (1999)] for He-like ions, but we find a discrepancy in the Li-like case. Moreover, we calculate the finite nuclear size correction to this diagram, which can reduce its size by more than 5% for heavy ions. The improved QED calculations not only decrease the uncertainty of theoretical predictions for the interelectronic interaction in few-electron ions but the methods could also be used in the future to improve calculations of closely related one-electron two-loop QED diagrams.

physics.atom-ph↗

arXiv2026

Bound-state QED test above the Schwinger limit with kaonic fluorine

Kaonic atoms, formed when a negatively charged kaon replaces an electron in an atomic orbit, provide access to bound-state quantum electrodynamics (BSQED) in electromagnetic fields far stronger than in ordinary atoms. Here, we report an experimental test of BSQED in a regime where the mean Coulomb field exceeds the Schwinger limit. Using high-precision x-ray spectroscopy of kaonic fluorine with the SIDDHARTA-2 experiment at DA$Φ$NE, corresponding to an integrated luminosity of 22.4 pb$^{-1}$, we observe transitions involving the 4f and 3d levels, probing field-to-Schwinger-limit ratios of 1.11 and 3.70, respectively. The measured transition energies agree with state-of-the-art Dirac-Fock calculations. In particular, the 5g-4f transition showing a residual of 5.8 $\pm$ 4.7 (stat.) $\pm$ 5.5 (syst.) eV and a $\sim$ 9$σ$ sensitivity to QED contributions. These results provide a direct test of BSQED in the strong-field regime of QED above the Schwinger limit, opening a new avenue for precision studies in extreme electromagnetic fields.

physics.atom-ph↗

arXiv2025

Precision Test of Bound-State QED at Intermediate-Z with Kaonic Neon

We report Dirac-Fock calculations of transition energies for kaonic neon (KNe). For the most intense line, the 7-6 transition, the calculated energy is 9450.28 eV, which includes a bound-state QED (BSQED) contribution of 12.66 eV. This is in excellent agreement with the recent SIDDHARTHA-2 measurement at DA$Φ$NE of 9450.23 $\pm$ 0.37 (stat.) $\pm$ 1.50 (syst.) eV. With the QED shift far exceeding experimental uncertainty, these results establish kaonic atoms as powerful platforms for precision tests of BSQED in intermediate-Z systems.

physics.atom-ph↗

arXiv2024

Inelastic scattering of vortex electrons beyond the Born approximation

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 $1s \rightarrow 2p$ 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 $\ket{2p\, m_f=0}$ sublevel and large scattering angles.

physics.atom-ph↗

arXiv2023

Delbrück scattering above the pair production threshold: Going beyond the Born approximation

We present a theoretical method to calculate Delbrück scattering amplitudes for photon energies above the electron-positron pair production threshold. The method is based on the application of the relativistic Dirac-Coulomb Green function and describes the interaction of the virtual $e^+e^-$ pair with the Coulomb field of a target to all orders in the coupling strength parameter $αZ$. To illustrate the application of the developed approach, detailed calculations have been performed for the scattering of 2.754~MeV photons off bare ions with a wide range of nuclear charge numbers. Results of these calculations clearly indicate that the higher-order terms beyond the Born approximation lead to a strong enhancement of the imaginary part of the Delbrück amplitude and have to be taken into account for the analysis and guidance of gamma-ray scattering experiments.

physics.atom-ph↗

arXiv2023

Low-energy tests of Delbrück scattering

We present a theoretical study of elastic photon scattering by atomic targets. This process is of special interest since various channels from atomic and nuclear physics as well as quantum elctrodynamics (QED) contribute to it. In this work, we focus on Delbrück scattering which proceeds via production of virtual $e^+e^-$ pairs. In particular, we explore whether and how the Delbrück channel can be "seen" in present synchrotron experiments which employ strongly linearly polarized light in the energy range of a few hundred keV. In order to answer this question, detailed calculations have been performed for the scattering of 300 keV and 889.2 keV photons off helium-like tin ions. Based on these calculations, we argue that the Delbrück scattering for the energies below the threshold for $e^+e^-$ pair creation leads to a shift in the angular distribution and the polarization of the scattered photons which can be observed by state-of-the-art solid-state detectors.

physics.atom-ph↗

arXiv2023

All-order Coulomb corrections to Delbrück scattering above the pair production threshold

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 function and accounts for the interaction between the virtual electron-positron pair and the nucleus to all orders in the nuclear binding strength parameter $αZ$. 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.

physics.atom-ph↗

arXiv2022

Calculations of Delbrück scattering to all orders in $αZ$

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 keV 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.

hep-th↗

arXiv2020

Vacuum polarization and finite nuclear size effects in the two-photon decay of hydrogen-like ions

The total two-photon decay rate of hydrogen-like ions is studied using relativistic quantum electrodynamics. In particular, we analyse 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 quasi-complete 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 $2s_{1/2} \to 1s_{1/2} + 2γ$ and $2p_{1/2} \to 1s_{1/2} + 2γ$ decay of hydrogen-like 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 $2s_{1/2} \to 1s_{1/2} + 2γ$ transition. In contrast, they are much more pronounced for the $2p_{1/2}\to 1s_{1/2} + 2γ$ decay, where, for hydrogen-like 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.

physics.atom-ph↗

arXiv2019

Polarization effects in bound-free pair production

We present a theoretical study of bound-free electron-positron pair production in the interaction of $γ$-rays with bare ions. Special attention is paid to the longitudinal polarization of both the emitted positrons and the produced hydrogen-like ions. To evaluate this polarization we employed exact solutions of the relativistic Dirac equation and treat the electron-photon coupling within the framework of first-order perturbation theory. Detailed calculations have been performed for both, low- and high-Z ions and for a wide range of photon energies. The results of these calculations suggest that bound-free pair production can be a source of strongly polarized positrons and ions.

physics.atom-ph↗