# Peer-Review Publications

## 2020

**Lifetime measurements of ultrashort-lived excited states in Be-like ions**

**49**, 165 (2020)

**Abstract:** We propose to measure the lifetime of short-lived excited states in highly charged ions by pump-probe experiments. Utilizing two synchronized and delayed Femtosecond pulses allows accessing these lifetimes with Femtosecond precision. Such measurements could provide sensitive tests of state-of-the art atomic structure calculations beyond the capabilities of established methods.

**K-line X-ray fluorescence from highly charged iron ions under dense astrophysical plasma conditions**

**49**, 29 (2020)

**Abstract:** In the present work, we report an investigation of plasma environment effects on the atomic parameters associated with the K-vacancy states in highly charged iron ions within the astrophysical context of accretion disks around black holes. More particularly, the sensitivity of K-line X-ray fluorescence parameters (wavelengths, radiative transition probabilities, and Auger rates) in Fe XVII–Fe XXV ions has been estimated for plasma conditions characterized by an electron temperature ranging from 105 to 107 K and an electron density ranging from 1018 to 1022 cm−3. In order to do this, relativistic multiconfiguration Dirac-Fock atomic structure calculations have been carried out by considering a time averaged Debye-Hückel potential for both the electron–nucleus and electron–electron interactions.

**The photon-ion merged-beams experiment PIPE at PETRA III—The first five years**

**49**, 11 (2020)

**Abstract:** The Photon-Ion Spectrometer at PETRA III—in short, PIPE—is a permanently installed user facility at the 'Variable Polarization XUV Beamline' P04 of the synchrotron light source PETRA III operated by DESY in Hamburg, Germany. The careful design of the PIPE ion-optics in combination with the record-high photon flux at P04 has lead to a breakthrough in experimental studies of photon interactions with ionized small quantum systems. This short review provides an overview over the published scientific results from photon-ion merged-beams experiments at PIPE that were obtained since the start of P04 operations in 2013. The topics covered comprise photoionization of ions of astrophysical relevance, quantitative studies of multi-electron processes upon inner-shell photoexcitation and photoionization of negative and positive atomic ions, precision spectroscopy of photoionization resonances, photoionization and photofragmentation of molecular ions, and of endohedral fullerene ions.

**Probing Vacuum Polarization Effects with High-Intensity Lasers**

**3**, 39 (2020)

**Abstract:** These notes provide a pedagogical introduction to the theoretical study of vacuum polarization effects in strong electromagnetic fields as provided by state-of-the-art high-intensity lasers. Quantum vacuum fluctuations give rise to effective couplings between electromagnetic fields, thereby supplementing Maxwell’s linear theory of classical electrodynamics with nonlinearities. Resorting to a simplified laser pulse model, allowing for explicit analytical insights, we demonstrate how to efficiently analyze all-optical signatures of these effective interactions in high-intensity laser experiments. Moreover, we highlight several key features relevant for the accurate planning and quantitative theoretical analysis of quantum vacuum nonlinearities in the collision of high-intensity laser pulses.

**Quantum Collisions and Confinement of Atomic and Molecular Species, and Photons**

**Abstract:** We study strong-field ionization of a hydrogenic target by few-cycle Bessel pulses. In order to investigate the interplay between the carrier envelope phase (CEP) and the orbital angular momentum of a few-cycle pulse (OAM), we apply a semiclassical two-step model. In particular, we here compute and discuss photoelectron momentum distributions (PEMD) for localized atomic targets. We show how these momentum distributions are affected by the CEP and TAM of the incident pulse. In particular, we find that the OAM affects the PEMD in a similar way as the CEP, depending on the initial position of our target.

## 2019

**Simulation of the multiphase configuration and phase transitions with quantum walks utilizing a step-dependent coin**

**100**, 062115 (2019)

**Abstract:** Quantum walks are versatile simulators of topological phases and phase transitions as observed in condensed-matter physics. Here, we utilize a step-dependent coin in quantum walks and investigate what topological phases we can simulate with it, their topological invariants, bound states, and possibility of phase transitions. These quantum walks simulate nontrivial phases characterized by topological invariants (winding number) ±1, which are similar to the ones observed in topological insulators and polyacetylene. We confirm that the number of phases and their corresponding bound states increase step dependently. In contrast, the size of topological phase and distance between two bound states are decreasing functions of steps resulting into formation of multiple phases as quantum walks proceed (multiphase configuration). We show that, in the bound states, the winding number and group velocity are ill defined and the second moment of the probability density distribution in position space undergoes an abrupt change. Therefore, there are phase transitions taking place over the bound states and between two topological phases with different winding numbers.

**Near L-edge Single and Multiple Photoionization of Triply Charged Iron Ions**

**887**, 189 (2019)

**Abstract:** Relative cross sections for m-fold photoionization (m = 1,…, 5) of Fe3+ by single-photon absorption were measured employing the photon-ion merged-beams setup PIPE at the PETRA III synchrotron light source operated at DESY in Hamburg, Germany. The photon energies used spanned the range of 680–950 eV, covering both the photoexcitation resonances from the 2p and 2s shells, as well as the direct ionization from both shells. Multiconfiguration Dirac–Hartree–Fock (MCDHF) calculations were performed to simulate the total photoexcitation spectra. Good agreement was found with the experimental results. These computations helped to assign several strong resonance features to specific transitions. We also carried out Hartree–Fock calculations with relativistic extensions taking into account both photoexcitation and photoionization. Furthermore, we performed extensive MCDHF calculations of the Auger cascades that result when an electron is removed from the 2p and 2s shells of Fe3+. Our theoretically predicted charge-state fractions are in good agreement with the experimental results, representing a substantial improvement over previous theoretical calculations. The main reason for the disagreement with the previous calculations is their lack of inclusion of slow Auger decays of several configurations that can only proceed when accompanied by de-excitation of two electrons. In such cases, this additional shake-down transition of a (sub)valence electron is required to gain the necessary energy for the release of the Auger electron.

**Propagator from nonperturbative worldline dynamics**

**100**, 105020 (2019)

**Abstract:** We use the worldline representation for correlation functions together with numerical path integral methods to extract nonperturbative information about the propagator to all orders in the coupling in the quenched limit (small-Nf expansion). Specifically, we consider a simple two-scalar field theory with cubic interaction (S²QED) in four dimensions as a toy model for QED-like theories. Using a worldline regularization technique, we are able to analyze the divergence structure of all-order diagrams and to perform the renormalization of the model nonperturbatively. Our method gives us access to a wide range of couplings and coordinate distances. We compute the pole mass of the S²QED electron and observe sizable nonperturbative effects in the strong-coupling regime arising from the full photon dressing. We also find indications for the existence of a critical coupling where the photon dressing compensates the bare mass such that the electron mass vanishes. The short distance behavior remains unaffected by the photon dressing in accordance with the power-counting structure of the model.

**Modeling terahertz emission from the target rear side during intense laser-solid interactions**

**100**, 053204 (2019)

**Abstract:** Relativistic laser-solid target interaction is a powerful source of terahertz radiation where broadband terahertz radiation is emitted from the front and rear surfaces of the target. Even though several experimental works have reported the generation of subpicosecond duration gigawatt peak power terahertz pulses from the target rear surface, the underlying physical process behind their origin is still an open question. Here we discuss a numerical model that can accurately reproduce several aspects of the experimental results. The model is based on the charged particle dynamics at the target rear surface and the evolution of the charge separation field. We identify the major contributors that are responsible for broadband terahertz emission from the rear surface of the target.

**Spatiotemporal visualization of the terahertz emission during high-power laser-matter interaction**

**100**, 053203 (2019)

**Abstract:** Single-cycle pulses with multimillion volts per centimeter field strengths and spectra in the terahertz (THz) band have attracted great interest due to their ability to coherently manipulate molecular orientations and electron spins resonantly and nonresonantly. The tremendous progress made in the development of compact and powerful terahertz sources have identified intense laser-thin foil interaction as a potential candidate for high-power broadband terahertz radiation. They are micrometers in size and deliver radially polarized terahertz pulses with millijoule energy and gigawatt peak power. Although several works have been carried out to investigate the terahertz generation process, their origin and angular distribution are still debated. We present here an indisputable study on their spatiotemporal characteristics and elaborate the underlying physical processes via recording the three-dimensional beam profile along with transient dynamics. These results are substructured with the quantitative visualization of the charge particle spectra.

**Characterization of laser-driven proton acceleration from water microdroplets**

**9**, 17169 (2019)

**Abstract:** We report on a proton acceleration experiment in which high-intensity laser pulses with a wavelength of 0.4 mm and with varying temporal intensity contrast have been used to irradiate water droplets of 20 mm diameter. Such droplets are a reliable and easy-to-implement type of target for proton acceleration experiments with the potential to be used at very high repetition rates. We have investigated the influence of the laser's angle of incidence by moving the droplet along the laser polarization axis. This position, which is coupled with the angle of incidence, has a crucial impact on the maximum proton energy. Central irradiation leads to an inefficient coupling of the laser energy into hot electrons, resulting in a low maximum proton energy. The introduction of a controlled pre-pulse produces an enhancement of hot electron generation in this geometry and therefore higher proton energies. However, two-dimensional particle-in-cell simulations support our experimental results confirming, that even slightly higher proton energies are achieved under grazing laser incidence when no additional pre-plasma is present. Illuminating a droplet under grazing incidence generates a stream of hot electrons that flows along the droplet's surface due to self-generated electric and magnetic fields and ultimately generates a strong electric field responsible for proton acceleration. The interaction conditions were monitored with the help of an ultra-short optical probe laser, with which the plasma expansion could be observed.

**Efficient Laser-Driven Proton Acceleration from a Cryogenic Solid Hydrogen Target**

**9**, 16534 (2019)

**Abstract:** We report on the successful implementation and characterization of a cryogenic solid hydrogen target in experiments on high-power laser-driven proton acceleration. When irradiating a solid hydrogen filament of 10 mm diameter with 10-Terawatt laser pulses of 2.5 J energy, protons with kinetic energies in excess of 20?MeV exhibiting non-thermal features in their spectrum were observed. The protons were emitted into a large solid angle reaching a total conversion efficiency of several percent. Two-dimensional particle-in-cell simulations confirm our results indicating that the spectral modulations are caused by collisionless shocks launched from the surface of the the high-density filament into a low-density corona surrounding the target. The use of solid hydrogen targets may significantly improve the prospects of laser-accelerated proton pulses for future applications.

**Modification of multipole transitions by twisted light**

**100**, 043416 (2019)

**Abstract:** A theoretical analysis is presented for the excitation of single many-electron atoms and ions by twisted (or vortex) light. Special emphasis is put on excitations that can proceed via several electric and magnetic multipole channels. We argue that the relative strength of these multipoles is very sensitive to the topological charge and kinematic parameters of the incident light and can be strongly modified with respect to the plane-wave case. Most remarkably, the modification of multipole transitions by twisted radiation can be described by means of a geometrical factor. This factor is independent of the shell structure of a particular target atom and just reflects the properties of the light beam as well as the position of an atom with respect to the vortex axis. An analytical expression for the geometrical factor is derived for Bessel photons and for a realistic experimental situation in which the position of an atom is not well determined. To illustrate the use of the geometrical factor for the analysis of (future) measurements, detailed calculations are presented for the presented for the 3s 3p 3P1 -> 3s 3p 1P1 excitation in neutral Mg.

**g Factor of Lithiumlike Silicon: New Challenge to Bound-State QED**

**123**, 173001 (2019)

**Abstract:** The recently established agreement between experiment and theory for the g factors of lithiumlike silicon and calcium ions manifests the most stringent test of the many-electron bound-state quantum electrodynamics (QED) effects in the presence of a magnetic field. In this Letter, we present a significant simultaneous improvement of both theoretical gth=2.000 889 894 4 (34) and experimental gexp=2.000 889 888 45 (14) values of the g factor of lithiumlike silicon 28Si11+. The theoretical precision now is limited by the many-electron two-loop contributions of the bound-state QED. The experimental value is accurate enough to test these contributions on a few percent level.

**How to Observe the Vacuum Decay in Low-Energy Heavy-Ion Collisions**

**123**, 113401 (2019)

**Abstract:** In slow collisions of two bare nuclei with the total charge larger than the critical value Zcr≈173, the initially neutral vacuum can spontaneously decay into the charged vacuum and two positrons. The detection of the spontaneous emission of positrons would be direct evidence of this fundamental phenomenon. However, the spontaneously produced particles are indistinguishable from the dynamical background in the positron spectra. We show that the vacuum decay can nevertheless be observed via impact-sensitive measurements of pair-production probabilities. The possibility of such an observation is demonstrated using numerical calculations of pair production in low-energy collisions of heavy nuclei.

**A scintillator‐based particle detector for CRYRING@ESR**

**n/a**, 1 (2019)

**Abstract:** With the unprecedented range of ion species and energies offered by the newly commissioned CRYRING facility, the availability of single ion detectors is of significant importance as part of standard instrumentation as well as for novel experiments. A detector system was constructed on the basis of the YAP:Ce crystal scintillator, which is at once radiation‐hard, fast, and affordable. Results of a characterization experiment confirmed the feasibility of the setup for incident ion rates on the order of MHz and found a critical fluence of some 10¹³ cm⁻² upon which the crystal is rendered locally blind to further ion irradiation. The device was first used in CRYRING commissioning runs in August and November 2018. Future efforts will complete the integration of the detector into the GSI control and data acquisition system MBS.

**Roadmap on photonic, electronic and atomic collision physics: III. Heavy particles: with zero to relativistic speeds**

**52**, 171003 (2019)

**Abstract:** We publish three Roadmaps on photonic, electronic and atomic collision physics in order to celebrate the 60th anniversary of the ICPEAC conference. Roadmap III focusses on heavy particles: with zero to relativistic speeds. Modern theoretical and experimental approaches provide detailed insight into the wide range of many-body interactions involving projectiles and targets of varying complexity ranging from simple atoms, through molecules and clusters, complex biomolecules and nanoparticles to surfaces and crystals. These developments have been driven by technological progress and future developments will expand the horizon of the systems that can be studied. This Roadmap aims at looking back along the road, explaining the evolution of the field, and looking forward, collecting nineteen contributions from leading scientists in the field.

**Scattering of twisted light from a crystal**

**94**, 105402 (2019)

**Abstract:** Recent years have seen significant progress in the generation and application of twisted beams carrying orbital angular momentum. Here we study the elastic scattering of twisted Bessel light from a crystal and compare our predictions with the results for incident plane-wave radiation. Based on form-factor approximation our numerical calculations of the differential scattering cross sections have been carried out for a crystal of lithium at x-ray energies. It is shown that the use of twisted light can lead to a measurable change in the scattering cross section for the nanocrystals approaching a few nm in size.

**X-ray photon scattering at a focused high-intensity laser pulse**

**100**, 033002 (2019)

**Abstract:** We study x-ray photon scattering in the head-on collision of an XFEL pulse and a focused high-intensity laser pulse, described as paraxial Laguerre-Gaussian beam of arbitrary mode composition. For adequately chosen relative orientations of the polarization vectors of the colliding laser fields, this gives rise to a vacuum birefringence effect manifesting itself in polarization flipped signal photons. Throughout this article the XFEL is assumed to be mildly focused to a waist larger than that of the high-intensity laser beam. As previously demonstrated for the special case of a fundamental paraxial Gaussian beam, this scenario is generically accompanied by a scattering phenomenon of x-ray energy signal photons outside the forward cone of the XFEL beam, potentially assisting the detection of the effect in experiment. Here, we study the fate of the x-ray scattering signal under exemplary deformations of the transverse focus profile of the high-intensity pump.

**Ab initio QED Treatment of the Two-Photon Annihilation of Positrons with Bound Electrons**

**123**, 093401 (2019)

**Abstract:** The process of a positron—bound-electron annihilation with simultaneous emission of two photons is investigated theoretically. A fully relativistic formalism based on an ab initio QED description of the process is worked out. The developed approach is applied to evaluate the annihilation of a positron with K-shell electrons of a silver atom, for which a strong contradiction between theory and experiment was previously stated. The results obtained here resolve this longstanding disagreement and, moreover, demonstrate a sizable difference with approaches so far used for calculations of the positron—bound-electron annihilation process, namely, Lee’s and the impulse approximations.

**Boosting Quantum Vacuum Signatures by Coherent Harmonic Focusing**

**123**, 091802 (2019)

**Abstract:** We show that coherent harmonic focusing provides an efficient mechanism to boost all-optical signatures of quantum vacuum nonlinearity in the collision of high-intensity laser fields, thereby offering a promising route to their first experimental detection. Assuming two laser pulses of given parameters at our disposal, we demonstrate a substantial increase of the number of signal photons measurable in experiments where one of the pulses undergoes coherent harmonic focusing before it collides with the fundamental-frequency pulse. Imposing a quantitative criterion to discern the signal photons from the background of the driving laser photons and accounting for the finite purity of polarization filtering, we find that signal photons arising from inelastic scattering processes constitute a promising signature. By contrast, quasielastic contributions which are conventionally assumed to form the most prospective signal remain background dominated. Our findings may result in a paradigm shift concerning which photonic signatures of quantum vacuum nonlinearity are accessible in experiment.

**A fresh computational approach to atomic structures, processes and cascades**

**240**, 1 (2019)

**Abstract:** Electronic structure computations of atoms and ions have a long tradition in physics with applications in basic research, spectroscopy, life sciences and technology. Various theoretical methods (and codes) have therefore been developed to account for the many-particle structure of atoms, from simple semi-empirical estimates to accurate predictions of selected data, and up to highly advanced time-independent and time-dependent numerical techniques. — Here, I present a fresh concept and implementation of (relativistic) atomic structure theory that supports the computation of interaction amplitudes, properties as well as a large number of excitation and decay processes for open-shell atoms and ions across the whole periodic table. This implementation will facilitate also studies on atomic cascades, responses as well as the time-evolution of atoms and ions. It is based on Julia, a new programming language for scientific computing, and provides an easy-to-use but powerful platform to extent atomic theory towards new applications.

**Modeling of the 3D spatio-temporal thermal profile of joule-class Yb³⁺-based laser amplifiers**

**7**, E42 (2019)

**Abstract:** Thermal profile modification of an active material in a laser amplifier via optical pumping results in a change in the material’s refractive index, and causes thermal expansion and stress, eventually leading to spatial phase aberrations, or even permanent material damage. For this purpose, knowledge of the 3D spatio-temporal thermal profile, which can currently only be retrieved via numerical simulations, is critical for joule-class laser amplifiers to reveal potentially dangerous thermal features within the pumped active materials. In this investigation, a detailed, spatio-temporal numerical simulation was constructed and tested for accuracy against surface thermal measurements of various end-pumped Yb³⁺-doped laser-active materials. The measurements and simulations show an excellent agreement and the model was successfully applied to a joule-class Yb³⁺-based amplifier currently operating in the POLARIS laser system at the Friedrich-Schiller-University and Helmholtz-Institute Jena in Germany.

**High harmonic generation with Laguerre-Gaussian beams**

**21**, 094001 (2019)

**Abstract:** We summarize the development of high harmonic generation (HHG) with linearly polarized Laguerre–Gaussian (LG) beams and their superpositions to explain the non-perturbative aspects of HHG. Furthermore, we show that circularly polarized extreme ultraviolet vortices with well-defined orbital angular momentum (OAM) can be generated by HHG with bicircular LG beams. We introduce photon diagrams in order to explain how to calculate the OAM and the polarization of the generated harmonics by means of simultaneous conservation of spin angular momentum and OAM. Moreover, we show how the intensity ratio of the driving fields in HHG with bicircular LG beams further enhances the generation of circularly polarized twisted attosecond pulse trains.

**Properties of a cylindrical Penning trap with conical endcap openings**

**94**, 075401 (2019)

**Abstract:** We describe the results of analytical calculations and numerical simulations of the confinement properties of a mechanically compensated cylindrical Penning trap which has conical endcap openings for large-solid-angle access for example with highly focused laser beams. While the analytical calculations show that under the common geometrical conditions the harmonicity of the confining fields near the centre of the trap does not change when a conical shape of the endcap electrodes is introduced, numerical simulations show significant changes when the opening angle of the cone exceeds a certain critical angle. We also show that these sharp features are due to the fringe-field effects above the critical angle, which are not described by the analytical calculations. These effects are also observed in a cylindrical Penning trap when the length of the endcap electrodes is reduced below a certain critical value.

**Coherence control in high-order harmonic generation with Laguerre-Gaussian beams**

**100**, 013422 (2019)

**Abstract:** We investigate phase matching for high-order harmonic generation with linearly polarized Laguerre-Gaussian (LG) beams with nonzero orbital angular momentum (OAM). We compare the conditions for efficient phase matching for LG beams with those of Gaussian beams. In particular, we show how the OAM of the incident beams affects the phase-matching conditions for the short and long trajectories that arise from the saddle-point approximation of the dipole moment. Thereby we illustrate that the coherence length for the short trajectories decreases for LG beams near the focus compared to Gaussian beams, whereas efficient phase matching can be achieved before and behind the focus. Furthermore, we demonstrate that the coherence length for the long trajectory behind the focus plane can be controlled by the OAM. This paper provides a route for the experiment in order to have good coherence control to enhance the conversion efficiency for high-order harmonic generation with beams carrying OAM.

**Fluorescence polarization as a precise tool for understanding nonsequential many-photon ionization**

**100**, 011401 (2019)

**Abstract:** Nonsequential two-photon ionization of inner-shell np subshell of neutral atoms by circularly polarized light is investigated. Detection of subsequent fluorescence as a signature of the process is proposed and the dependence of fluorescence degree of polarization on incident photon beam energy is studied. It is generally expected that the degree of polarization remains approximately constant, except when the beam energy is tuned to an intermediate n′ resonance. However, strong unexpected change in the polarization degree is discovered for nonsequential two-photon ionization at specific incident beam energy due to a zero contribution of the otherwise dominant ionization channel. Polarization degree of the fluorescence depends less on the beam parameters, and its measurements at this specific beam energy, whose position is very sensitive to the details of the employed theory, are highly desirable for evaluation of theoretical calculations of nonlinear ionization at hitherto unreachable accuracy.

**QED radiative corrections to the ²P₁/₂-²P₃/₂ fine structure in fluorinelike ions**

**100**, 010502 (2019)

**Abstract:** calculations of QED radiative corrections to the 2P1/2 - 2P3/2 fine-structure transition energy are performed for selected F-like ions. These calculations are nonperturbative in αZ and include all first-order and many-electron second-order effects in α. When compared to approximate QED computations, a notable discrepancy is found especially for F-like uranium for which the predicted self-energy contributions even differ in sign. Moreover, all deviations between theory and experiment for the 2P1/2 - 2P3/2 fine-structure energies of F-like ions, reported recently by Li et al., Phys. Rev. A 98, 020502(R) (2018), are resolved if their highly accurate, non-QED fine-structure values are combined with the QED corrections ab initially evaluated here.

**High-order implicit particle-in-cell method for plasma simulations at solid densities**

**100**, 013207 (2019)

**Abstract:** A high-order implicit multidimensional particle-in-cell (PIC) method is developed for simulating plasmas at solid densities. The space-time arrangement is based on Yee and a leapfrog algorithm for electromagnetic fields and particle advancement. The field solver algorithm completely eliminates numerical instabilities found in explicit PIC methods with relaxed time step and grid resolution. Moreover, this algorithm eliminates the numerical cooling found in the standard implicit PIC methods by using a pseudo-electric-field method. The particle pusher algorithm combines the standard Boris particle pusher with the Newton-Krylov iteration method. This algorithm increases the precision accuracy by several orders of magnitude when compared with the standard Boris particle pusher and also significantly decreases the iteration time when compared with the pure Newton-Krylov method. The code is tested with several benchmarks, including Weibel instability, and relativistic laser plasma interactions at both low and solid densities.

**High-precision X-ray spectroscopy of Fe ions in an EBIT using a micro-calorimeter detector: First results**

**n/a**, 1 (2019)

**Abstract:** A micro-calorimeter X-ray detector of the maXs-30 type was used to record the X-ray radiation from Fe ions, being produced in the S-EBIT-I electron beam ion trap at the site of GSI. The resulting spectra demonstrate the superior energy resolving power of micro-calorimeter detectors compared with conventional semiconductor detectors. The experiment serves as another proof of principle for the application of calorimeters as dedicated high-resolution X-ray spectrometers at an ion facility. Together with the development of an improved analysis algorithm for online readout, these results present a step towards the use of maXs-type detectors as standard instrumentation at GSI/FAIR.

**Opportunities for measurements of astrophysical-relevant alpha-capture reaction rates at CRYRING@ESR**

**n/a**, 1 (2019)

**Abstract:** The heavy-ion storage ring CRYRING@ESR has recently been installed and commissioned at GSI as one of the first installations of the upcoming Facility for Antiproton and Ion Research (FAIR). It is designed to store highly charged ions in the energy range between 300?keV/u and about 10?MeV/u. It will incorporate a gas-jet target providing high-density jets of, among other gases, hydrogen and helium. This will allow to study alpha-capture reaction rates of astrophysical interest in the energy range of the Gamow window for core-collapse supernovae. Special interest comes from the long-lived radio-isotope 44Ti (t1/2?=?58.9?years), which is supposed to be produced in the alpha-rich freeze-out during such an event. The nucleosynthesis of this isotope is of great interest, as the amount of material produced can be estimated by direct observation in remnants of recent supernovae. The disagreements between the observations and the estimations from astrophysical models show the need of more experimental data for the production and consumption reactions in the energy range of a core-collapse supernova. In this article, we will describe the proposed method of injecting beams of 44Ti into CRYRING@ESR and performing the actual reaction rate measurements.

**Gamma Factory at CERN - Novel Research Tools Made of Light**

**50**, 1191 (2019)

**Abstract:** We discuss the possibility of creating novel research tools by producing and storing highly relativistic beams of highly ionised atoms in the CERN accelerator complex, and by exciting their atomic degrees of freedom with lasers to produce high-energy photon beams. Intensity of such photon beams would be by several orders of magnitude higher than offered by the presently operating light sources, in the particularly interesting gamma-ray energy domain of 0.1-400 MeV. In this energy range, the high-intensity photon beams can be used to produce secondary beams of polarised electrons, polarised positrons, polarised muons, neutrinos, neutrons and radioactive ions. New research opportunities in a wide domain of fundamental and applied physics can be opened by the Gamma Factory scientific programme based on the above primary and secondary beams.

**Ground-state hyperfine splitting of B-like ions in the high-Z region**

**99**, 062503 (2019)

**Abstract:** The hyperfine splitting of the ground state of selected B-like ions within the range of nuclear charge numbers Z=49–83 is investigated in detail. The rigorous QED approach together with the large-scale configuration-interaction Dirac-Fock-Sturm method are employed for the evaluation of the interelectronic-interaction contributions of first and higher orders in 1/Z. The screened QED corrections are evaluated to all orders in αZ by using an effective potential. The influence of nuclear magnetization distribution is taken into account within the single-particle nuclear model.

**High-precision calculations of the 1s²2s2p ¹P₁->1s²2s² ¹S₀ spin-allowed E1 transition in C iii**

**99**, 062511 (2019)

**Abstract:** Large-scale relativistic calculations are performed for the transition energy and line strength of the 1s22s2p 1P1− 1s22s2 1S0 transition in Be-like carbon. Based on the multiconfiguration Dirac-Hartree-Fock~(MCDHF) approach, different correlation models are developed to account for all major electron-electron correlation contributions. These correlation models are tested with various sets of the initial and the final state wave functions. The uncertainty of the predicted line strength due to missing correlation effects is estimated from the differences between the results obtained with those models. The finite nuclear mass effect is accurately calculated taking into account the energy, wave functions as well as operator contributions. As a result, a reliable theoretical benchmark of the E1 line strength is provided to support high precision lifetime measurement of the 1s22s2p 1P1 state in Be-like carbon.

**Formation of relativistic electromagnetic solitons in over-dense plasmas**

**26**, 063107 (2019)

**Abstract:** We report the formation of electromagnetic solitons in over-dense plasmas in the relativistic transparency regime. By using one-dimensional and two-dimensional particle-in-cell simulations, the formation and basic properties of these long-lived relativistic electromagnetic solitons are studied. The predicted mechanism of soliton formation is different from the existing investigations. The latter ones are found to exist in the wake of the high-intensity laser pulse during the interaction with a low density plasma, and such solitons are made of low-frequency, spatially localized electromagnetic fields. While for the former ones, frequency of solitons formed in the relativistic transparency regime is comparable to incident laser frequency. Moreover, a threshold of plasma density under which stable solitons can be formed is analyzed. These newly predicted solitons are expected to be observed in the present-day laser-plasma experiments.

**HILITE—A tool to investigate interactions of matter and light**

**n/a**, 1 (2019)

**Abstract:** Detailed investigations of laser–ion interactions require well‐defined ion targets and detection techniques for high‐sensitivity measurements of reaction educts and products. To this end, we have designed and built the High‐Intensity Laser‐Ion Trap Experiment Penning trap setup, which features various ion‐target preparation techniques including selection, cooling, compression, and positioning as well as destructive and non‐destructive measurement techniques to determine the number of stored ions for all charge states individually and simultaneously. We have recently performed first commissioning experiments of ion deceleration and dynamic ion capture with highly charged ion bunches from an electron beam ion source. We have characterized our single‐pass non‐destructive ion counter in detail and were able to determine the ion velocity as well as the number of ions from the signals acquired.

**The hyperfine puzzle of strong-field bound-state QED**

**240**, 51 (2019)

**Abstract:** The hyperfine splitting in heavy highly charged ions provide the means to test QED in extremely strong magnetic fields. In order to provide a meaningful test, the splitting has to be measured in H-like and Li-like ions to remove uncertainties from nuclear structure. This has been achieved at the experimental storage ring ESR but a discrepancy to the theoretical prediction of more than 7s was observed. We report on these measurements as well as on NMR measurements that were performed to solve this issue.

**Nondipole strong-field approximation for spatially structured laser fields**

**99**, 053404 (2019)

**Abstract:** The strong-field approximation (SFA) is widely used to theoretically describe the ionization of atoms and molecules in intense laser fields. We here propose an extension of the SFA to incorporate nondipole contributions in the interaction between the photoelectron and the driving laser field. To this end, we derive Volkov-type continuum wave functions of an electron propagating in a laser field of arbitrary spatial dependence. Based on previous work by L. Rosenberg and F. Zhou [Phys. Rev. A 47, 2146 (1993)], we show how to construct such Volkov-type solutions to the Schrödinger equation for an electron in a vector potential that can be written as an integral superposition of plane waves. These solutions are therefore not restricted to plane waves but are also appropriate to deal with more complex laser fields like twisted Bessel or Laguerre-Gaussian beams, where the magnetic field plays an important role. As an example, we compute photoelectron spectra in the above-threshold ionization of atoms with a single-mode plane-wave laser field of midinfrared wavelength. Especially, we demonstrate how peak offsets in the p_z direction can be extracted that result from the nondipole nature of the interaction. Here, we find good agreement with previous theoretical and experimental studies for circular polarization and discuss differences for linear polarization.

**Radiative electron capture as a tunable source of highly linearly polarized x rays**

**99**, 052702 (2019)

**Abstract:** The radiative electron capture (REC) into the K shell of bare Xe ions colliding with a hydrogen gas target has been investigated. In this study, the degree of linear polarization of the K-REC radiation was measured and compared with rigorous relativistic calculations as well as with the previous results recorded for U92+. Owing to the improved detector technology, a significant gain in precision of the present polarization measurement is achieved compared to the previously published results. The obtained data confirms that for medium-Z ions such as Xe, the REC process is a source of highly polarized x rays which can easily be tuned with respect to the degree of linear polarization and the photon energy. We argue, in particular, that for relatively low energies the photons emitted under large angles are almost fully linear polarized.

**Inverse odd-even staggering in nuclear charge radii and possible octupole collectivity in ²¹⁷,²¹⁸,²¹⁹At revealed by in-source laser spectroscopy**

**99**, 054317 (2019)

**Abstract:** Hyperfine-structure parameters and isotope shifts for the 795-nm atomic transitions in 217, 218, 219At have been measured at CERN-ISOLDE, using the in-source resonance-ionization spectroscopy technique. Magnetic dipole and electric quadrupole moments, and changes in the nuclear mean-square charge radii, have been deduced. A large inverse odd-even staggering in radii, which may be associated with the presence of octupole collectivity, has been observed. Namely, the radius of the odd-odd isotope 218At has been found to be larger than the average of its even-N neighbors, 217, 219At. The discrepancy between the additivity-rule prediction and experimental data for the magnetic moment of 218At also supports the possible presence of octupole collectivity in the considered nuclei.

**Perturbative methods for assisted nonperturbative pair production**

**99**, 096002 (2019)

**Abstract:** In the dynamically assisted Schwinger mechanism, the pair production probability is significantly enhanced by including a weak, rapidly varying field in addition to a strong, slowly varying field. In a previous paper we showed that several features of dynamical assistance can be understood by a perturbative treatment of the weak field. Here we show how to calculate the prefactors of the higher-orders terms, which is important because the dominant contribution can come from higher orders. We give a new and independent derivation of the momentum spectrum using the worldline formalism, and extend our WKB approach to calculate the amplitude to higher orders. We show that these methods are also applicable to doubly assisted pair production.

**Spin states in multiphoton pair production for circularly polarized light**

**99**, 096017 (2019)

**Abstract:** Scalar and fermionic particle pair production in rotating electric fields is investigated in the nonperturbative multiphoton regime. Angular momentum distribution functions in above-threshold pair production processes are calculated numerically within quantum kinetic theory and discussed on the basis of a photon absorption model. The particle spectra can be understood if the spin states of the particle-antiparticle pair are taken into account.

**Thermally versus dynamically assisted Schwinger pair production**

**99**, 096007 (2019)

**Abstract:** We study electron-positron pair production by the combination of a strong, constant electric field and a thermal background. We show that this process is similar to dynamically assisted Schwinger pair production, where the strong field is instead assisted by another coherent field, which is weaker but faster. We treat the interaction with the photons from the thermal background perturbatively, while the interaction with the electric field is nonperturbative (i.e., a Furry picture expansion in α). At O(α2) we have ordinary perturbative Breit-Wheeler pair production assisted nonperturbatively by the electric field. Already at this order we recover the same exponential part of the probability as previous studies, which did not expand in α. This means that we do not have to consider higher orders, so our approach allows us to calculate the preexponential part of the probability, which has not been obtained before in this regime. Although the prefactor is in general subdominant compared to the exponential part, in this case it can be important because it scales as α2≪1 and is therefore much smaller than the prefactor at O(α0) (pure Schwinger pair production). We show that, because of the exponential enhancement, O(α2) still gives the dominant contribution for temperatures above a certain threshold, but, because of the small prefactor, the threshold is higher than what the exponential alone would suggest.

**All-Loop Result for the Strong Magnetic Field Limit of the Heisenberg-Euler Effective Lagrangian**

**122**, 211602 (2019)

**Abstract:** We provide an explicit expression for the strong magnetic field limit of the Heisenberg-Euler effective Lagrangian for both scalar and spinor quantum electrodynamics. To this end, we show that the strong magnetic field behavior is fully determined by one-particle reducible contributions discovered only recently. The latter can efficiently be constructed in an essentially algebraic procedure from lower-order one-particle reducible diagrams. Remarkably, the leading strong magnetic field behavior of the all-loop Heisenberg-Euler effective Lagrangian only requires input from the one-loop Lagrangian. Our result revises previous findings based exclusively on one-particle irreducible contributions. In addition, we briefly discuss the strong electric field limit and comment on external field QED in the large N limit.

**Charge state tailoring of relativistic heavy ion beams for the Gamma Factory project at CERN**

**n/a**, 1 (2019)

**Abstract:** We present charge‐state evolution studies for Pb⁵⁴⁺ ion beams passing through stripper foils at relativistic energies of 5.9 GeV/u. The purpose of this investigation is to determine the optimum target material and non‐equilibrium thickness for the efficient production of few‐electron lead ions, that is, Pb⁸⁰⁺ and Pb⁸¹⁺, at the present European Organization for Nuclear Research, CERN, accelerator facility at energies as high as 5.9 GeV/u. Based on these predictions, an Al stripper foil has been selected for a proof‐of‐principle measurement in the frame of the Gamma Factory study group. The experimental data confirms a substantial yield of non‐bare Pb ions. In addition, a charge‐state evolution study for the production of Li‐like lead ions Pb⁷⁹⁺ is presented, which will be subject of a follow‐up experiment in the near future.

**Lifetime measurements of ultrashort-lived excited states in Be-like ions**

**n/a**, 1 (2019)

**Abstract:** We propose to measure the lifetime of short-lived excited states in highly charged ions by pump-probe experiments. Utilizing two synchronized and delayed Femtosecond pulses allows accessing these lifetimes with Femtosecond precision. Such measurements could provide sensitive tests of state-of-the art atomic structure calculations beyond the capabilities of established methods.

**Photon-Photon Scattering at the High-Intensity Frontier: Paraxial Beams**

**1206**, 012016 (2019)

**Abstract:** Our goal is to study optical signatures of quantum vacuum nonlinearities in strong macroscopic electromagnetic fields provided by high-intensity laser beams. The vacuum emission scheme is perfectly suited for this task as it naturally distinguishes between incident laser beams, described as classical electromagnetic fields driving the effect, and emitted signal photons encoding the signature of quantum vacuum nonlinearity. Using the Heisenberg-Euler effective action, our approach allows for a reliable study of photonic signatures of QED vacuum nonlinearity in the parameter regimes accessible by all-optical high-intensity laser experiments. To this end, we employ an efficient, flexible numerical algorithm, which allows for a detailed study of the signal photons emerging in the collision of focused paraxial high-intensity laser pulses. Due to the high accuracy of our numerical solutions we predict the total number of signal photons, but also have full access to the signal photons’ characteristics, including their spectrum, propagation directions and polarizations. We discuss setups offering an excellent background-to-noise ratio, thus providing an important step towards the experimental verification of quantum vacuum nonlinearities.

**The Vacuum Emission Picture Beyond Paraxial Approximation**

**1206**, 012017 (2019)

**Abstract:** Optical signatures of the effective nonlinear couplings among electromagnetic fields in the quantum vacuum can be conveniently described in terms of stimulated photon emission processes induced by strong classical, space-time dependent electromagnetic fields. Recent studies have adopted this approach to study collisions of Gaussian laser pulses in paraxial approximation. The present study extends these investigations beyond the paraxial approximation by using an efficient numerical solver for the classical input fields. This new numerical code allows for a consistent theoretical description of optical signatures of QED vacuum nonlinearities in generic electromagnetic fields governed by Maxwell’s equations in the vacuum, such as manifestly non-paraxial laser pulses. Our code is based on a locally constant field approximation of the Heisenberg-Euler effective Lagrangian. As this approximation is applicable for essentially all optical high-intensity laser experiments, our code is capable of calculating signal photon emission amplitudes in completely generic input field configurations, limited only by numerical cost.

**Plasma environment effects on K lines of astrophysical interest - I. Atomic structure, radiative rates, and Auger widths of oxygen ions**

**624**, A74 (2019)

**Abstract:** Aims. In the context of black-hole accretion disks, the main goal of the present study is to estimate the plasma environment effects on the atomic structure and radiative parameters associated with the K-vacancy states in ions of the oxygen isonuclear sequence.

Methods. We used a time-averaged Debye–Hückel potential for both the electron–nucleus and the electron–electron interactions implemented in the fully relativistic multiconfiguration Dirac–Fock (MCDF) method.

Results. Modified ionization potentials, K thresholds, Auger widths, and radiative transition wavelengths and rates are reported for O I–O VII in plasma environments with electron temperature and density ranges 105−107 K and 1018−1022 cm−3.

**Approaching the Gamow Window with Stored Ions: Direct Measurement of ¹²⁴Xe(p,γ) in the ESR Storage Ring**

**122**, 092701 (2019)

**Abstract:** We report the first measurement of low-energy proton-capture cross sections of 124Xe in a heavy-ion storage ring. 124Xe^54+ ions of five different beam energies between 5.5 and 8 AMeV were stored to collide with a windowless hydrogen target. The 125Cs reaction products were directly detected. The interaction energies are located on the high energy tail of the Gamow window for hot, explosive scenarios such as supernovae and x-ray binaries. The results serve as an important test of predicted astrophysical reaction rates in this mass range. Good agreement in the prediction of the astrophysically important proton width at low energy is found, with only a 30% difference between measurement and theory. Larger deviations are found above the neutron emission threshold, where also neutron and γ widths significantly impact the cross sections. The newly established experimental method is a very powerful tool to investigate nuclear reactions on rare ion beams at low center-of-mass energies.