# Peer-Review Publications

## 2018

**Cryogenic Current Comparators for Larger Beamlines**

**28**, 1 (2018)

**Abstract:** The non-destructive measurement of charged particle beams with intensities below 1 μA represents still a challenge in current R&D efforts. Beam peak-intensities of modern high power accelerators are in the range of milli-amperes, but for a large number of experiments, the pulse lengths have to be increased by several orders of magnitude (slow extraction process) to avoid saturation in the detectors. At the same time, the intensities of exotic ion- or antiproton-beams – depending on the production yield – might be in the range of nano-amperes or even below. The solution of this measurement problem should moreover include the possibility to calibrate the electrical current with traceability to national standards.

**An investigation on THz yield from laser-produced solid density plasmas at relativistic laser intensities**

**20**, 063019 (2018)

**Abstract:** We experimentally characterize the generation of high-power terahertz radiation (THz) at the rear surface of a target irradiated by multiple laser pulses. A detailed dependence of the THz yield as a function of laser pulse duration, energy, target material and thickness is presented. We studied the THz radiation emitted mainly in two directions from the target rear surface, namely target normal (acceptance angle 0.87 sr) and non-collinear direction (perpendicular to the target normal direction—acceptance angle 4.12 sr). Independent measurements based on electro-optic diagnostics and pyroelectric detector were employed to estimate the THz yield. Most of the energy is emitted at large angles relative to the target normal direction. THz yield increases with incident laser intensity and thinner targets are better emitters of THz radiation compared to thicker ones.

**Lifetimes of relativistic heavy-ion beams in the High Energy Storage Ring of FAIR**

**421**, 45 (2018)

**Abstract:** The High Energy Storage Ring, HESR, will be constructed at the Facility for Antiproton and Ion Research, FAIR, Darmstadt. For the first time, it will be possible to perform experiments with cooled high-intensity stable and radioactive heavy ions at highly relativistic energies. To design experiments at the HESR, realistic estimations of beam lifetimes are indispensable. Here we report calculated cross sections and lifetimes for typical U88+, U90+, U92+, Sn49+ and Sn50+ ions in the energy range E = 400 MeV/u–5 GeV/u, relevant for the HESR. Interactions with the residual gas and with internal gas-jet targets are also considered.

**Analysis of angular momentum properties of photons emitted in fundamental atomic processes**

**97**, 043808 (2018)

**Abstract:** Many atomic processes result in the emission of photons. Analysis of the properties of emitted photons, such as energy and angular distribution as well as polarization, is regarded as a powerful tool for gaining more insight into the physics of corresponding processes. Another characteristic of light is the projection of its angular momentum upon propagation direction. This property has attracted a special attention over the past decades due to studies of twisted (or vortex) light beams. Measurements being sensitive to this projection may provide valuable information about the role of angular momentum in the fundamental atomic processes. Here we describe a simple theoretical method for determination of the angular momentum properties of the photons emitted in various atomic processes. This method is based on the evaluation of expectation value of the total angular momentum projection operator. To illustrate the method, we apply it to the textbook examples of plane-wave, spherical-wave, and Bessel light. Moreover, we investigate the projection of angular momentum for the photons emitted in the process of the radiative recombination with ionic targets. It is found that the recombination photons do carry a nonzero projection of the orbital angular momentum.

**Photon-photon scattering at the high-intensity frontier**

**97**, 076002 (2018)

**Abstract:** The tremendous progress in high-intensity laser technology and the establishment of dedicated high-field laboratories in recent years have paved the way towards a first observation of quantum vacuum nonlinearities at the high-intensity frontier. We advocate a particularly prospective scenario, where three synchronized high-intensity laser pulses are brought into collision, giving rise to signal photons, whose frequency and propagation direction differ from the driving laser pulses, thus providing various means to achieve an excellent signal to background separation. Based on the theoretical concept of vacuum emission, we employ an efficient numerical algorithm which allows us to model the collision of focused high-intensity laser pulses in unprecedented detail. We provide accurate predictions for the numbers of signal photons accessible in experiment. Our study is the first to predict the precise angular spread of the signal photons, and paves the way for a first verification of quantum vacuum nonlinearity in a well-controlled laboratory experiment at one of the many high-intensity laser facilities currently coming online.

**Ring-like spatial distribution of laser accelerated protons in the ultra-high-contrast TNSA-regime**

**60**, 055010 (2018)

**Abstract:** The spatial distribution of protons accelerated from submicron-thick plastic foil targets using multi-terawatt, frequency-doubled laser pulses with ultra-high temporal contrast has been investigated experimentally. A very stable, ring-like beam profile of the accelerated protons, oriented around the target’s normal direction has been observed. The ring’s opening angle has been found to decrease with increasing foil thicknesses. Two-dimensional particle-in-cell simulations reproduce our results indicating that the ring is formed during the expansion of the proton density distribution into the vacuum as described by the mechanism of target-normal sheath acceleration. Here—in addition to the longitudinal electric fields responsible for the forward acceleration of the protons—a lateral charge separation leads to transverse field components accelerating the protons in the lateral direction.

**Photon polarization tensor in circularly polarized Hermite- and Laguerre-Gaussian beams**

**33**, 1850044 (2018)

**Abstract:** We derive analytical expressions for the photon polarization tensor in circularly polarized Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) beams, complementing the corresponding results for linearly polarized beams obtained recently. As they are based upon a locally constant field approximation of the one-loop Heisenberg–Euler effective Lagrangian for quantum electrodynamics (QED) in constant fields, our results are generically limited to slowly varying electromagnetic fields, varying on spatial (temporal) scales much larger than the Compton wavelength (time) of the electron.

**K-shell ionization of heavy hydrogenlike ions**

**97**, 032518 (2018)

**Abstract:** A theoretical study of the K-shell ionization of hydrogenlike ions, colliding with bare nuclei, is performed within the framework of the time-dependent Dirac equation. Special emphasis is placed on the ionization probability that is investigated as a function of impact parameter, collision energy, and nuclear charge. To evaluate this probability in a wide range of collisional parameters we propose a simple analytical expression for the transition amplitude. This expression contains three fitting parameters that are determined from the numerical calculations, based on the adiabatic approximation. In contrast to previous studies, our analytical expression for the transition amplitude and ionization probability accounts for the full multipole expansion of the two-center potential and allows accurate description of nonsymmetric collisions of nuclei with different atomic numbers Z1≠Z2. The calculations performed for both symmetric and asymmetric collisions indicate that the ionization probability is reduced when the difference between the atomic numbers of ions increases.

**Spatio-Temporal Characterization of Pump-Induced Wavefront Aberrations in Yb3 + -Doped Materials**

**12**, 1700211 (2018)

**Abstract:** Abstract A comprehensive spatio-temporal characterization is presented describing the pump-induced wavefront aberrations in Yb3 + -doped YAG, CaF2, and fluorophosphate glass. Time-resolved interferometric measurements were performed to reveal the profiles of the total optical path differences (OPDs), which are described by the spatio-temporal superposition of thermal as well as electronic contributions, across the free aperture of the considered diode-pumped active materials. These contributions were individually determined by a COMSOL-based thermal profile model along with a detailed characterization of the electronic changes by measuring the single-pass gain and the spatial fluorescence profile. Due to the low quantum defect, the amplitude of the electronic component becomes comparable for all three materials and, in the case of Yb:CaF2, almost completely compensates the thermal component resulting from a pump pulse during the time frame of laser pulse amplification. Finally, all relevant material constants – such as the photoelastic constant and the polarizability difference – could be determined during this investigation, allowing the accurate modeling of the total pump-induced wavefront aberrations and subsequent optimization for laser systems worldwide employing these Yb3 + -doped materials.

**Quantum interference in laser spectroscopy of highly charged lithiumlike ions**

**97**, 022510 (2018)

**Abstract:** We investigate the quantum interference induced shifts between energetically close states in highly charged ions, with the energy structure being observed by laser spectroscopy. In this work, we focus on hyperfine states of lithiumlike heavy-Z isotopes and quantify how much quantum interference changes the observed transition frequencies. The process of photon excitation and subsequent photon decay for the transition 2s→2p→2s is implemented with fully relativistic and full-multipole frameworks, which are relevant for such relativistic atomic systems. We consider the isotopes 207Pb79+ and 209Bi80+ due to experimental interest, as well as other examples of isotopes with lower Z, namely 141Pr56+ and 165Ho64+. We conclude that quantum interference can induce shifts up to 11% of the linewidth in the measurable resonances of the considered isotopes, if interference between resonances is neglected. The inclusion of relativity decreases the cross section by 35%, mainly due to the complete retardation form of the electric dipole multipole. However, the contribution of the next higher multipoles (e.g., magnetic quadrupole) to the cross section is negligible. This makes the contribution of relativity and higher-order multipoles to the quantum interference induced shifts a minor effect, even for heavy-Z elements.

**All-optical signatures of strong-field QED in the vacuum emission picture**

**97**, 036022 (2018)

**Abstract:** We study all-optical signatures of the effective nonlinear couplings among electromagnetic fields in the quantum vacuum, using the collision of two focused high-intensity laser pulses as an example. The experimental signatures of quantum vacuum nonlinearities are encoded in signal photons, whose kinematic and polarization properties differ from the photons constituting the macroscopic laser fields. We implement an efficient numerical algorithm allowing for the theoretical investigation of such signatures in realistic field configurations accessible in experiment. This algorithm is based on a vacuum emission scheme and can readily be adapted to the collision of more laser beams or further involved field configurations. We solve the case of two colliding pulses in full 3+1-dimensional spacetime and identify experimental geometries and parameter regimes with improved signal-to-noise ratios.

**A sensitive EUV Schwarzschild microscope for plasma studies with sub-micrometer resolution**

**89**, 023703 (2018)

**Abstract:** We present an extreme ultraviolet (EUV) microscope using a Schwarzschild objective which is optimized for single-shot sub-micrometer imaging of laser-plasma targets. The microscope has been designed and constructed for imaging the scattering from an EUV-heated solid-density hydrogen jet. Imaging of a cryogenic hydrogen target was demonstrated using single pulses of the free-electron laser in Hamburg (FLASH) free-electron laser at a wavelength of 13.5 nm. In a single exposure, we observe a hydrogen jet with ice fragments with a spatial resolution in the sub-micrometer range. In situ EUV imaging is expected to enable novel experimental capabilities for warm dense matter studies of micrometer-sized samples in laser-plasma experiments.

**Isolated proton bunch acceleration by a petawatt laser pulse**

**9**, 423 (2018)

**Abstract:** Often, the interpretation of experiments concerning the manipulation of the energy distribution of laser-accelerated ion bunches is complicated by the multitude of competing dynamic processes simultaneously contributing to recorded ion signals. Here we demonstrate experimentally the acceleration of a clean proton bunch. This was achieved with a microscopic and three-dimensionally confined near critical density plasma, which evolves from a 1 µm diameter plastic sphere, which is levitated and positioned with micrometer precision in the focus of a Petawatt laser pulse. The emitted proton bunch is reproducibly observed with central energies between 20 and 40 MeV and narrow energy spread (down to 25%) showing almost no low-energetic background. Together with three-dimensional particle-in-cell simulations we track the complete acceleration process, evidencing the transition from organized acceleration to Coulomb repulsion. This reveals limitations of current high power lasers and viable paths to optimize laser-driven ion sources.

**Considerations towards the possibility of the observation of parity nonconservation in highly charged ions in storage rings**

**93**, 025401 (2018)

**Abstract:** The feasibility of an experiment for the observation of parity nonconserving effects using He-like highly charged ions in storage rings is discussed theoretically. The basic idea is the observation of an asymmetry in the emission of the hyperfine quenched transition (1s2s)¹{S₀\to (1s)²¹S₀+γ } with respect to the direction of a beam of ions with polarized nuclei. It will be shown, that for such an experiment 151Eu^61+ ions with nuclear spin I=5/2 in the excited electronic state (1s2s)¹S₀ with zero total electron angular momentum and polarized nuclei are the best available candidates. The nuclei can be polarized if H-like Eu^62+ ions capture an electron from a polarized electron beam which overlays the ion beam on some part of the ring and travels with nearly the same velocity. It is suggested, to monitor steadily the degree of the nuclear polarization by the observation of the selective laser excitation and subsequent decay of the Zeeman sublevels of the excited hyperfine states of the ionic ground state. Estimates for the observation time aiming at an accuracy of PNC measurement of about 0.1 % are given.

## 2017

**Resonance-enhanced multi-octave supercontinuum generation in antiresonant hollow-core fibers**

**6**, e17124 (2017)

**Abstract:** Ultrafast supercontinuum generation in gas-filled waveguides is an enabling technology for many intriguing applications ranging from attosecond metrology towards biophotonics, with the amount of spectral broadening crucially depending on the pulse dispersion of the propagating mode. In this study, we show that structural resonances in a gas-filled antiresonant hollow core optical fiber provide an additional degree of freedom in dispersion engineering, which enables the generation of more than three octaves of broadband light that ranges from deep UV wavelengths to near infrared. Our observation relies on the introduction of a geometric-induced resonance in the spectral vicinity of the ultrafast pump laser, outperforming gas dispersion and yielding a unique dispersion profile independent of core size, which is highly relevant for scaling input powers. Using a krypton-filled fiber, we observe spectral broadening from 200 nm to 1.7 μm at an output energy of ∼ 23 μJ within a single optical mode across the entire spectral bandwidth. Simulations show that the frequency generation results from an accelerated fission process of soliton-like waveforms in a non-adiabatic dispersion regime associated with the emission of multiple phase-matched Cherenkov radiations on both sides of the resonance. This effect, along with the dispersion tuning and scaling capabilities of the fiber geometry, enables coherent ultra-broadband and high-energy sources, which range from the UV to the mid‐infrared spectral range.

**Characterization of two ultrashort laser pulses using interferometric imaging of self-diffraction**

**42**, 5246 (2017)

**Abstract:** Noncollinear pulse characterization methods can be applied to over-octave spanning waveforms, but geometrical effects in the nonlinear medium such as beam smearing and critical sensitivity to beam alignment hinder their accurate application. Here, a method is introduced for the temporal and spatial characterization of two pulses by interferometric, spectrally resolved imaging of self-diffraction. Geometrical effects are resolved by the method and, therefore, do not limit the accuracy. Two methods for quantitative pulse retrieval are presented. One method is analytical and very fast; the other method is iterative and more robust if applied to noisy data.

**Single-shot, real-time carrier-envelope phase measurement and tagging based on stereographic above-threshold ionization at short-wave infrared wavelengths**

**42**, 5150 (2017)

**Abstract:** A high-precision, single-shot, and real-time carrier-envelope phase (CEP) measurement at 1.8 μm laser wavelength based on stereographic photoelectron spectroscopy is presented. A precision of the CEP measurement of 120 mrad for each and every individual laser shot for a 1 kHz pulse train with randomly varying CEP is demonstrated. Simultaneous to the CEP measurement, the pulse lengths are characterized by evaluating the spatial asymmetry of the measured above-threshold ionization (ATI) spectra of xenon and referenced to a standard pulse-duration measurement based on frequency-resolved optical gating. The validity of the CEP measurement is confirmed by implementing phase tagging for a CEP-dependent measurement of ATI in xenon with high energy resolution.

**Ground-state hyperfine splitting for Rb, Cs, Fr, Ba⁺, and Ra⁺**

**96**, 062502 (2017)

**Abstract:** We have systematically investigated the ground-state hyperfine structure for alkali-metal atoms 87Rb, 33Cs, and 211Fr and alkali-metal-like ions 135Ba^+ and 225Ra^+, which are of particular interest for parity violation studies. The quantum electrodynamic one-loop radiative corrections have been rigorously evaluated within an extended Furry picture employing core-Hartree and Kohn-Sham atomic potentials. Moreover, the effect of the nuclear magnetization distribution on the hyperfine structure intervals has been studied in detail and its uncertainty has been estimated. Finally, the theoretical description of the hyperfine structure has been completed with full many-body calculations performed in the all-orders correlation potential method.

**Photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian beams**

**96**, 116004 (2017)

**Abstract:** In this article, we provide analytical expressions for the photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian laser beams. Our results are based on a locally constant field approximation of the one-loop Heisenberg-Euler effective Lagrangian for quantum electrodynamics. Hence, by construction they are limited to slowly varying electromagnetic fields, varying on spatial and temporal scales significantly larger than the Compton wavelength/time of the electron. The latter criterion is fulfilled by all laser beams currently available in the laboratory. Our findings will, e.g., be relevant for the study of vacuum birefringence experienced by probe photons brought into collision with a high-intensity laser pulse which can be represented as a superposition of either Hermite- or Laguerre-Gaussian modes.

**Optically transparent solid electrodes for precision Penning traps**

**88**, 123101 (2017)

**Abstract:** We have conceived, built, and operated a cryogenic Penning trap with an electrically conducting yet optically transparent solid electrode. The trap, dedicated to spectroscopy and imaging of confined particles under large solid angles, is of “half-open” design with one open endcap and one closed endcap that mainly consists of a glass window coated with a highly transparent conductive layer. This arrangement allows for the trapping of externally or internally produced particles and yields flexible access for optical excitation and efficient light collection from the trapping region. At the same time, it is electrically closed and ensures long-term ion confinement under well-defined conditions. With its superior surface quality and its high as well as homogeneous optical transmission, the window electrode is an excellent replacement for partially transmissive electrodes that use holes, slits, metallic meshes, and the like.

**Plasma channel undulator excited by high-order laser modes**

**7**, 16884 (2017)

**Abstract:** The possibility of utilizing plasma undulators and plasma accelerators to produce compact ultraviolet and X-ray sources, has attracted considerable interest for a few decades. This interest has been driven by the great potential to decrease the threshold for accessing such sources, which are mainly provided by a few dedicated large-scale synchrotron or free-electron laser (FEL) facilities. However, the broad radiation bandwidth of such plasma devices limits the source brightness and makes it difficult for the FEL instability to develop. Here, using multi-dimensional particle-in-cell (PIC) simulations, we demonstrate that a plasma undulator generated by the beating of a mixture of high-order laser modes propagating inside a plasma channel, leads to a few percent radiation bandwidth. The strength of the undulator can reach unity, the period can be less than a millimeter, and the number of undulator periods can be significantly increased by a phase locking technique based on the longitudinal tapering. Polarization control of such an undulator can be achieved by appropriately choosing the phase of the modes. According to our results, in the fully beam loaded regime, the electron current in the plasma undulator can reach 0.3\^aEUR%0kA level, making such an undulator a potential candidate towards a table-top FEL.

**Enhanced absorption and cavity effects of three-photon pumped ZnO nanowires**

**111**, 213106 (2017)

**Abstract:** Semiconductor nanowire (NW) lasers attract a lot of attention as potential elements of nanophotonic circuits and lab-on-a chip devices. Here, we report on the experimental investigation of stimulated near ultraviolet (NUV) emission, pumped by three-photon absorption from near infrared femtosecond laser pulses, from ZnO NW arrays of different morphologies and compare it to the bulk. The spectrally and temporally resolved measurements of the NUV emission show both strong enhancements in the absorption and emission properties of the nanowire arrays compared to bulk samples. Thus, we determine a many times higher three-photon absorption in the nanostructure morphology compared to the bulk material. Furthermore, the threshold pumping intensity for stimulated emission in a vertically oriented nanowire array is twice lower and the emission onset time is shorter than in randomly oriented arrays, revealing strong influence of the macroscopic nanowire arrangement.

**Using the focal phase to control attosecond processes**

**19**, 124007 (2017)

**Abstract:** The spatial evolution of the electric field of focused broadband light is crucial for many emerging attosecond technologies. Here the effects of the input beam parameters on the evolution of few-cycle laser pulses in the focus are discussed. Specifically, we detail how the frequency-dependent input beam geometry, chirp and chromatic aberration can affect the spatial dependence of the carrier-envelope phase (CEP), central frequency and pulse duration in the focus. These effects are confirmed by a direct, three-dimensional measurement of the CEP-evolution in the focus of a typical few-cycle pulse laser using electron rescattering at metal nanotips in combination with a CEP-metre. Moreover, we demonstrate a simple measurement technique to estimate the focal CEP evolution by input-beam parameters. These parameters can be used in novel ways in order to control attosecond dynamics and tailor highly nonlinear light–matter interactions.

**Velocity map imaging of scattering dynamics in orthogonal two-color fields**

**51**, 015001 (2017)

**Abstract:** In strong-field ionization processes, two-color laser fields are frequently used for controlling sub-cycle electron dynamics via the relative phase of the laser fields. Here we apply this technique to velocity map imaging spectroscopy using an unconventional orientation with the polarization of the ionizing laser field perpendicular to the detector surface and the steering field parallel to it. This geometry allows not only to image the phase-dependent photoelectron momentum distribution (PMD) of low-energy electrons that interact only weakly with the ion (direct electrons), but also to investigate the low yield of higher-energy rescattered electrons. Phase-dependent measurements of the PMD of neon and xenon demonstrate control over direct and rescattered electrons. The results are compared with semi-classical calculations in three dimensions including elastic scattering at different orders of return and with solutions of the three-dimensional time-dependent Schrödinger equation.

**First determination of ground state electromagnetic moments of ⁵³Fe**

**96**, 054314 (2017)

**Abstract:** The hyperfine coupling constants of neutron deficient 53Fe were deduced from the atomic hyperfine spectrum of the 3d^6 4s^2 ^5D_4 <-> 3d^6 4s 4p ^5F_5 transition, measured using the bunched-beam collinear laser spectroscopy technique. The low-energy 53Fe beam was produced by projectile-fragmentation reactions followed by gas stopping, and used for the first time for laser spectroscopy. Ground state magnetic-dipole and electric-quadrupole moments were determined as μ = -0.65(1)μ_N and Q = +35(15)e^2 fm^2, respectively. The multiconfiguration Dirac-Fock method was used to calculate the electric field gradient to deduce Q from the quadrupole hyperfine coupling constant, since the quadrupole coupling constant has not been determined for any Fe isotopes. Both experimental values agree well with nuclear shell model calculations using the GXPF1A effective interaction performed in a full fp shell model space, which support the soft nature of the 56Ni nucleus.

**In-gas laser ionization and spectroscopy of actinium isotopes near the N=126 closed shell**

**96**, 054331 (2017)

**Abstract:** The in-gas laser ionization and spectroscopy (IGLIS) technique was applied on the 212-215Ac isotopes, produced at the Leuven Isotope Separator On-Line (LISOL) facility by using the in-gas-cell and the in-gas-jet methods. The first application under on-line conditions of the in-gas-jet laser spectroscopy method showed a superior performance in terms of selectivity, spectral resolution, and efficiency in comparison with the in-gas-cell method. Following the analysis of both experiments, the magnetic-dipole moments for the 212-215Ac isotopes, electric-quadrupole moments and nuclear spins for the 214,215Ac isotopes are presented and discussed. A good agreement is obtained with large-scale nuclear shell-model calculations by using a 208Pb core.

**Three dimensional magnetic solutions in massive gravity with (non)linear field**

**775**, 251 (2017)

**Abstract:** The Noble Prize in physics 2016 motivates one to study different aspects of topological properties and topological defects as their related objects. Considering the significant role of the topological defects (especially magnetic strings) in cosmology, here, we will investigate three dimensional horizonless magnetic solutions in the presence of two generalizations: massive gravity and nonlinear electromagnetic field. The effects of these two generalizations on properties of the solutions and their geometrical structure are investigated. The differences between de Sitter and anti de Sitter solutions are highlighted and conditions regarding the existence of phase transition in geometrical structure of the solutions are studied.

**Impact of generalized Yukawa interactions on the lower Higgs-mass bound**

**77**, 743 (2017)

**Abstract:** We investigate the impact of operators of higher canonical dimension on the lower Higgs-mass consistency bound by means of generalized Higgs--Yukawa interactions. Analogously to higher-order operators in the bare Higgs potential in an effective field theory approach, the inclusion of higher-order Yukawa interactions, e.g., ϕ^3ψ^¯ψ, leads to a diminishing of the lower Higgs-mass bound and thus to a shift of the scale of new physics towards larger scales by a few orders of magnitude without introducing a metastability in the effective Higgs potential. We observe that similar renormalization group mechanisms near the weak-coupling fixed point are at work in both generalizations of the microscopic action. Thus, a combination of higher-dimensional operators with generalized Higgs as well as Yukawa interactions does not lead to an additive shift of the lower mass bound, but it relaxes the consistency bounds found recently only slightly. On the method side, we clarify the convergence properties of different projection and expansion schemes for the Yukawa potential used in the functional renormalization group literature so far.

**Tadpole diagrams in constant electromagnetic fields**

**2017**, 75 (2017)

**Abstract:** We show how all possible one-particle reducible tadpole diagrams in constant electromagnetic fields can be constructed from one-particle irreducible constant-field diagrams. The construction procedure is essentially algebraic and involves differentiations of the latter class of diagrams with respect to the field strength tensor and contractions with derivatives of the one-particle irreducible part of the Heisenberg-Euler effective Lagrangian in constant fields. Specific examples include the two-loop addendum to the Heisenberg-Euler effective action as well as a novel one-loop correction to the charged particle propagator in constant electromagnetic fields discovered recently. As an additional example, the approach devised in the present article is adopted to derive the tadpole contribution to the two-loop photon polarization tensor in constant fields for the first time.

**Pair production in low-energy collisions of uranium nuclei beyond the monopole approximation**

**408**, 97 (2017)

**Abstract:** A method for calculation of electron-positron pair production in low-energy heavy-ion collisions beyond the monopole approximation is presented. The method is based on the numerical solving of the time-dependent Dirac equation with the full two-center potential. The one-electron wave functions are expanded in the finite basis set constructed on the two-dimensional spatial grid. Employing the developed approach the probabilities of bound-free pair production are calculated for collisions of bare uranium nuclei at the energy near the Coulomb barrier. The obtained results are compared with the corresponding values calculated in the monopole approximation.

**Intensities of K-X-ray satellite and hypersatellite target radiation in Bi83+-Xe @70MeV/u collisions**

**408**, 31 (2017)

**Abstract:** Non-perturbative calculations of the relativistic quantum dynamics of electrons in the Bi83+-Xe collisions at 70 AMeV are performed. A method of calculation employs an independent particle model with effective single-electron Dirac-Kohn-Sham operator. Solving of the single-electron equations is based on the coupled-channel approach with atomic-like Dirac-Sturm-Fock orbitals, localized at the ions (atoms). Special attention is paid to the inner-shell processes. Intensities of the K satellite and hypersatellite target radiation are evaluated. The role of the relativistic effects is studied.

**Impact parameter sensitive study of inner-shell atomic processes in the experimental storage ring**

**408**, 27 (2017)

**Abstract:** In this work, we present a pilot experiment in the experimental storage ring (ESR) at GSI devoted to impact parameter sensitive studies of inner shell atomic processes for low-energy (heavy-) ion-atom collisions. The experiment was performed with bare and He-like xenon ions (Xe54+, Xe52+) colliding with neutral xenon gas atoms, resulting in a symmetric collision system. This choice of the projectile charge states was made in order to compare the effect of a filled K-shell with the empty one. The projectile and target X-rays have been measured at different observation angles for all impact parameters as well as for the impact parameter range of ∼35–70 fm.

**Higher-order perturbative relativistic calculations for few-electron atoms and ions**

**408**, 46 (2017)

**Abstract:** An effective computational method is developed for electronic-structure calculations in few-electron atoms and ions on the basis of the Dirac-Coulomb-Breit Hamiltonian. The recursive formulation of the perturbation theory provides an efficient access to the higher-order contributions of the interelectronic interaction. Application of the presented approach to the binding energies of lithiumlike and boronlike systems is demonstrated. The results obtained are in agreement with the large-scale configuration interaction Dirac-Fock-Sturm method and other all-order calculations.

**Quadratic Zeeman effect in boronlike argon**

**408**, 70 (2017)

**Abstract:** Abstract A theoretical investigation of the second-order Zeeman effect in boronlike ions is presented. Rigorous calculations of the one-photon-exchange and one-loop QED corrections allow for predictions of the corresponding theoretical values for boronlike argon with an accuracy of about 2%. The obtained results are important in view of the forthcoming measurements of the Zeeman splitting in 40Ar13+ at GSI (ARTEMIS experiment).

**Third-order Zeeman effect in highly charged ions**

**408**, 80 (2017)

**Abstract:** The contribution of the third order in magnetic field to the Zeeman splitting of the ground state of hydrogenlike, lithiumlike, and boronlike ions in the range Z=6-82 is investigated within the relativistic approach. Both perturbative and non-perturbative methods of calculation are employed and found to be in agreement. For lithiumlike and boronlike ions the interelectronic-interaction effects are taken into account within the approximation of the local screening potential. The contribution of the third-order effect in low- and medium-Z boronlike ions is found to be important for anticipated high-precision measurements.

**Theoretical analysis of the electron bridge process in 229Th3+**

**408**, 84 (2017)

**Abstract:** We investigate the deexcitation of the 229Th nucleus via the excitation of an electron. Detailed calculations are performed for the enhancement of the nuclear decay width due to the so called electron bridge (EB) compared to the direct photoemission from the nucleus. The results are obtained for triply ionized thorium by using a B-spline pseudo basis approach to solve the Dirac equation for a local xα potential. This approach allows for an approximation of the full electron propagator including the positive and negative continuum. We show that the contribution of continua slightly increases the enhancement compared to a propagator calculated by a direct summation over bound states. Moreover we put special emphasis on the interference between the direct and exchange Feynman diagrams that can have a strong influence on the enhancement.

**Nuclear magnetic shielding in boronlike ions**

**408**, 89 (2017)

**Abstract:** The relativistic treatment of the nuclear magnetic shielding effect in boronlike ions is presented. The leading-order contribution of the magnetic-dipole hyperfine interaction is calculated. Along with the standard second-order perturbation theory expression, the solutions of the Dirac equation in the presence of magnetic field are employed. All methods are found to be in agreement with each other and with the previous calculations for hydrogenlike and lithiumlike ions. The effective screening potential is used to account approximately for the interelectronic interaction.

**Binding energies of the 1s2 2s2 2pj states in boronlike argon**

**408**, 103 (2017)

**Abstract:** The binding energies of the ground 1s2 2s2 2p1/2 and first excited 1s2 2s2 2p3/2 states in boronlike argon are rigorously evaluated. The calculations are performed by the QED perturbation theory in the framework of the extended Furry picture taking into account all the relevant first- and second-order radiative and correlation corrections. The third- and higher-order interelectronic-interaction effects are considered within the Breit approximation. The relativistic nuclear recoil effect is taken into account. In comparison with the previous calculations of the binding energies in boronlike argon the accuracy of the theoretical predictions has been significantly improved.

**Relativistic effects in the non-resonant two-photon K-shell ionization of neutral atoms**

**408**, 125 (2017)

**Abstract:** Relativistic effects in the non-resonant two-photon K-shell ionization of neutral atoms are studied theoretically within the framework of second-order perturbation theory. The non-relativistic results are compared with the relativistic calculations in the dipole and no-pair approximations as well as with the complete relativistic approach. The calculations are performed in both velocity and length gauges. Our results show a significant decrease of the total cross section for heavy atoms as compared to the non-relativistic treatment, which is mainly due to the relativistic wavefunction contraction. The effects of higher multipoles and negative continuum energy states counteract the relativistic contraction contribution, but are generally much weaker. While the effects beyond the dipole approximation are equally important in both gauges, the inclusion of negative continuum energy states visibly contributes to the total cross section only in the velocity gauge.

**Dielectronic recombination of highly charged ions with spin-polarized electrons**

**408**, 130 (2017)

**Abstract:** Angular distribution and linear polarization of photon emission following dielectronic recombination of initially lithium-like ions with spin-polarized electrons are studied. In particular, a general expression is derived for the alignment parameter of the doubly excited states produced via the resonant capture of spin-polarized electrons. By means of the alignment parameter, moreover, the angular distribution and linear polarization of the subsequently emitted photons are further obtained. Detailed computations are performed for the 1s2 2s J0=1/2+εe-→1s2s2 2p1/2 J=1→1s2 2s2 Jf=0+γ resonant electron capture and subsequent radiative decay of iodine ions. It is found that the spin polarization of the incident electrons changes only the q=±1 components of the alignment parameter A2q. As a consequence, the electron spin polarization contributes weakly to the γ photon angular distribution and linear polarization that are dominantly determined by the A20 parameter.

**Hyperfine induced effects on the angular distribution of the dielectronic hypersatellite line**

**408**, 93 (2017)

**Abstract:** Abstract We investigate the dielectronic recombination (DR) of an electron and a highly-charged ion with non-zero nuclear spin. We assume that the incident electron is captured into doubly-excited 1s2κκ′J=0,1,2 levels of Be-like ions just above of its autoionization threshold. The angular distribution of the subsequent radiative emission is investigated especially for its dependence upon the nuclear spin and the nuclear magnetic moment. While the hyperfine and even the fine-structure of the ions cannot be resolved in typical DR experiments, we found the photon angular distribution, following the decay of the 1s2 2p3/2nsJ=1,2 DR resonance very sensitive to the nuclear parameters.

**Nonlinear pulse compression to 43 W GW-class few-cycle pulses at 2 μm wavelength**

**42**, 4179 (2017)

**Abstract:** High-average power laser sources delivering intense few-cycle pulses in wavelength regions beyond the near infrared are promising tools for driving the next generation of high-flux strong-field experiments. In this work, we report on nonlinear pulse compression to 34.4 μJ-, 2.1-cycle pulses with 1.4 GW peak power at a central wavelength of 1.82 μm and an average power of 43 W. This performance level was enabled by the combination of a high-repetition-rate ultrafast thulium-doped fiber laser system and a gas-filled antiresonant hollow-core fiber.

**Temporal contrast enhancement of energetic laser pulses by filtered self-phase-modulation-broadened spectra**

**42**, 3761 (2017)

**Abstract:** We present a novel approach for temporal contrast enhancement of energetic laser pulses by filtered self-phase-modulation-broadened spectra. A measured temporal contrast enhancement by at least seven orders of magnitude in a simple setup has been achieved. This technique is applicable to a wide range of laser parameters and poses a highly efficient alternative to existing contrast-enhancement methods.

**Attosecond streaking with twisted X waves and intense infrared pulses**

**96**, 043423 (2017)

**Abstract:** We investigate the photoionization of atoms by attosecond X waves carrying orbital angular momentum in the presence of a strong, linearly polarized, near infrared (NIR) laser pulse. In the plane-wave case, the streaking of photoelectrons by the NIR pulse has been used to characterize the ionizing pulse. In contrast to plane-wave pulses, X waves have a spatially dependent temporal profile, which modifies the ionization process. Here we explore theoretically the influence of this complex pulse structure on the streaking of photoelectrons for both localized and macroscopically extended targets. On the basis of the strong-field approximation, we find that the streaking spectra of localized targets sensitively depend on the opening angle of the X wave and the position of the atomic target relative to the beam axis. For macroscopically extended targets, we find that the streaking spectra do not depend on the parameters characterizing the twist of the X wave.

**Streak Camera for Strong-Field Ionization**

**119**, 183201 (2017)

**Abstract:** Ionization of an atom or molecule by a strong laser field produces suboptical cycle wave packets whose control has given rise to attosecond science. The final states of the wave packets depend on ionization and deflection by the laser field, which are convoluted in conventional experiments. Here, we demonstrate a technique enabling efficient electron deflection, separate from the field driving strong-field ionization. Using a midinfrared deflection field permits one to distinguish electron wave packets generated at different field maxima of an intense few-cycle visible laser pulse. We utilize this capability to trace the scattering of low-energy electrons driven by the midinfrared field. Our approach represents a general technique for studying and controlling strong-field ionization dynamics on the attosecond time scale.

**Spectral and spatial characterisation of laser-driven positron beams**

**59**, 014015 (2017)

**Abstract:** The generation of high-quality relativistic positron beams is a central area of research in experimental physics, due to their potential relevance in a wide range of scientific and engineering areas, ranging from fundamental science to practical applications. There is now growing interest in developing hybrid machines that will combine plasma-based acceleration techniques with more conventional radio-frequency accelerators, in order to minimise the size and cost of these machines. Here we report on recent experiments on laser-driven generation of high-quality positron beams using a relatively low energy and potentially table-top laser system. The results obtained indicate that current technology allows to create, in a compact setup, positron beams suitable for injection in radio-frequency accelerators.

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

**849**, 5 (2017)

**Abstract:** Absolute cross-sections for m -fold photoionization (m=1, ... , 6 ) of Fe+ by a single photon were measured employing the photon–ion merged-beams setup PIPE at the PETRA III synchrotron light source, operated by DESY in Hamburg, Germany. Photon energies were in the range 680–920 eV, which covers the photoionization resonances associated with 2p and 2s excitation to higher atomic shells as well as the thresholds for 2p and 2s ionization. The corresponding resonance positions were measured with an uncertainty of ±0.2 eV. The cross-section for Fe+ photoabsorption is derived as the sum of the individually measured cross-sections for m -fold ionization. Calculations of the Fe+ absorption cross-sections were carried out using two different theoretical approaches, Hartree–Fock including relativistic extensions and fully relativistic multiconfiguration Dirac–Fock. Apart from overall energy shifts of up to about 3 eV, the theoretical cross-sections are in good agreement with each other and with the experimental results. In addition, the complex de-excitation cascades after the creation of inner-shell holes in the Fe+ ion were tracked on the atomic fine-structure level. The corresponding theoretical results for the product charge-state distributions are in much better agreement with the experimental data than previously published configuration-average results. The present experimental and theoretical results are valuable for opacity calculations and are expected to pave the way to a more accurate determination of the iron abundance in the interstellar medium.

**MCDF calculations of Auger cascade processes**

**71**, 253 (2017)

**Abstract:** We model the multiple ionization of near-neutral core-excited atoms where a cascade of Auger processes leads to the emission of several electrons. We utilize the multiconfiguration Dirac-Fock (MCDF) method to generate approximate wave functions for all fine-structure levels and to account for all decays between them. This approach allows to compute electron spectra, the population of final-states and ion yields, that are accessible in many experiments. Furthermore, our approach is based on the configuration interaction method. A careful treatment of correlation between electronic configurations enables one to model three-electron processes such as an Auger decay that is accompanied by an additional shake-up transition. Here, this model is applied to the triple ionization of atomic cadmium, where we show that the decay of inner-shell 4p holes to triply-charged final states is purely due to the shake-up transition of valence 5s electrons.

**Influence of plasma environment on K-line emission in highly ionized iron atoms evaluated using a Debye–Hückel model**

**95**, 858 (2017)

**Abstract:** The influence of plasma environment on the atomic parameters associated with the K-vacancy states has been investigated theoretically for several iron ions. To do this, a time-averaged Debye–Hückel potential for both the electron–nucleus and electron–electron interactions has been considered in the framework of relativistic multiconfiguration Dirac–Fock computations. More particularly, the plasma screening effects on ionization potentials, K-thresholds, transition energies, and radiative rates have been estimated in the astrophysical context of accretion disks around black holes. In the present paper, we describe the behaviour of those atomic parameters for Ne-, Na-, Ar-, and K-like iron ions.

**Angular momentum–induced delays in solid-state photoemission enhanced by intra-atomic interactions**

**357**, 1274 (2017)

**Abstract:** Attosecond time-resolved photoemission spectroscopy reveals that photoemission from solids is not yet fully understood. The relative emission delays between four photoemission channels measured for the van der Waals crystal tungsten diselenide (WSe2) can only be explained by accounting for both propagation and intra-atomic delays. The intra-atomic delay depends on the angular momentum of the initial localized state and is determined by intra-atomic interactions. For the studied case of WSe2, the photoemission events are time ordered with rising initial-state angular momentum. Including intra-atomic electron-electron interaction and angular momentum of the initial localized state yields excellent agreement between theory and experiment. This has required a revision of existing models for solid-state photoemission, and thus, attosecond time-resolved photoemission from solids provides important benchmarks for improved future photoemission models.