# Publikationen von

Prof. Dr. Stephan Fritzsche

Alle Publikationen des HI Jena

## 2020

**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.

**Polarization-dependent high-intensity Kapitza-Dirac effect in strong laser fields**

**101**, 031401 (2020)

**Abstract:** We study the deflection of photoelectrons in intense elliptically polarized standing light waves, known as the high-intensity Kapitza-Dirac effect. In order to compute the longitudinal momentum transfer to the photoelectron in above-threshold ionization, we utilize a complete description of the quantum dynamics in the spatially dependent field of the standing light wave. We propose experimental conditions under which low-energy photoelectrons can be generated with remarkably high longitudinal momenta that can be controlled via the polarization of the standing wave. We expect that future experimental realizations will provide additional insights into the momentum transfer in intense laser-atom interactions.

**Breakdown of the electric dipole approximation at Cooper minima in direct two-photon ionisation**

**10**, 3617 (2020)

**Abstract:** We predict breakdown of the electric dipole approximation at nonlinear Cooper minimum in direct two-photon K–shell atomic ionisation by circularly polarised light. According to predictions based on the electric dipole approximation, we expect that tuning the incident photon energy to the Cooper minimum in two-photon ionisation results in pure depletion of one spin projection of the initially bound 1s electrons, and hence, leaves the ionised atom in a fully oriented state. We show that by inclusion of electric quadrupole interaction, dramatic drop of orientation purity is obtained. The low degree of the remaining ion orientation provides a direct access to contributions of the electron-photon interaction beyond the electric dipole approximation in the two-photon ionisation of atoms and molecules. The orientation of the photoions can be experimentally detected either directly by a Stern-Gerlach analyzer, or by means of subsequent Kα fluorescence emission, which has the information about the ion orientation imprinted in the polarisation of the emitted photons.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**Particle-in-cell simulation of transport and energy deposition of intense proton beams in solid-state materials**

**100**, 013208 (2019)

**Abstract:** A particle-in-cell (PIC) simulation code is used to investigate the transport and energy deposition of an intense proton beam in solid-state material. This code is able to simulate close particle interactions by using a Monte Carlo binary collision model. Such a model takes into account all related interactions between the incident protons and material particles, e.g., proton-nucleus, proton–bound-electron, and proton–free-electron collisions. This code also includes a Monte Carlo model for the collisional ionization and electron-ion recombination as well as the depression of the ionization potential by shielding of surrounding particles. Moreover, for intense proton beams, in order to include collective electromagnetic effects, significantly speed up the simulation, and simultaneously avoid numerical instabilities, an approach that combines the PIC method with a reduced model of high-density plasma based on Ohm's law is used. Simulation results indicate that the collective electromagnetic effects have a significant influence on the transport and energy deposition of proton beams. The Ohmic electric field would increase the stopping power and leads to a shortened range of proton beams in solid. The magnetic field would localize the energy deposition by collimating proton beams, which would otherwise be deflected by the collisions with nuclei.

**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.

**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.

**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.

**Electron- and proton-impact excitation of heliumlike uranium in relativistic collisions**

**99**, 032706 (2019)

**Abstract:** We have studied the K-shell excitation of He-like uranium (U90+) in relativistic collisions with hydrogen and argon atoms. Performing measurements with different targets, as well as with different collision energies, enabled us to explore the proton- (nucleus-) impact excitation as well as the electron-impact excitation process for the heaviest He-like ion. The large fine-structure splitting in uranium allowed us to partially resolve excitation into different L-shell levels. State-of-the-art relativistic calculations which include excitation mechanisms due to the interaction with both protons (nucleus) and electrons are in good agreement with the experimental findings. Moreover, our experimental data clearly demonstrate the importance of including the generalized Breit interaction in the treatment of the electron-impact excitation process.

**Dichroism in two-color above-threshold ionization with twisted XUV beams and intense infrared laser fields**

**99**, 023403 (2019)

**Abstract:** We theoretically investigate the two-color above-threshold ionization of atoms and ions by twisted XUV Bessel and Laguerre-Gaussian (LG) beams in the presence of a strong circularly polarized near-infrared (NIR) laser field. The presence of the NIR field modifies the continuum states accessible to the photoelectron. Based on the strong-field approximation, we explore the resulting energy and angular distributions of photoelectron as a function of the beam parameters. In particular, we analyze dichroism signals that arise due to the twisted nature of the XUV beam and the helicity of the NIR field. We focus on the comparison between LG beams and Bessel beams in the paraxial approximation. Here, we find that both beams yield similar results when the paraxial regime is valid. For localized targets, the dichroism signals strongly depend on the size and position of the atoms relative to the beam axis. Moreover, the dichroism signal tends to zero when the XUV LG beam is linear polarized. Detailed computations of the dichroism are performed and discussed for the 4s valence-shell photoionization of Ca⁺ ions.

## 2018

**Characteristics of X/γ-ray radiations by intense laser interactions with high-Z solids: The role of bremsstrahlung and radiation reactions**

**3**, 293 (2018)

**Abstract:** In this work, characteristics of X/γ-ray radiations by intense laser interactions with high-Z solids are investigated by means of a newly developed particle-in-cell (PIC) simulation code. The PIC code takes advantage of the recently developed ionization and collision dynamics models, which make it possible to model different types of materials based on their intrinsic atomic properties. Within the simulations, both bremsstrahlung and nonlinear Compton scatterings have been included. Different target materials and laser intensities are considered for studying the parameter-dependent features of X/γ-ray radiations. The relative strength and angular distributions of X/γ ray productions from bremsstrahlung and nonlinear Compton scatterings are compared to each other. The threshold under which the nonlinear Compton scatterings become dominant over bremsstrahlung is also outlined.

**Diagnostics of polarization purity of x rays by means of Rayleigh scattering**

**98**, 053403 (2018)

**Abstract:** Synchrotron radiation is commonly known to be completely linearly polarized when observed in the orbital plane of the synchrotron motion. Under actual experimental conditions, however, the degree of polarization of the synchrotron radiation may be lower than the ideal 100%. We demonstrate that even tiny impurities of polarization of the incident radiation can drastically affect the polarization of the elastically scattered light. We propose to use this effect as a precision tool for the diagnostics of the polarization purity of the synchrotron radiation. Two variants of the diagnostics method are proposed. The first one is based on the polarization measurements of the scattered radiation and relies on theoretical calculations of the transition amplitudes. The second one involves simultaneous measurements of the polarization and the cross sections of the scattered radiation and is independent of theoretical amplitudes.

**First Ionization Potentials of Fm, Md, No, and Lr: Verification of Filling-Up of 5f Electrons and Confirmation of the Actinide Series**

**140**, 14609 (2018)

**Abstract:** We report the first ionization potentials (IP1) of the heavy actinides, fermium (Fm, atomic number Z = 100), mendelevium (Md, Z = 101), nobelium (No, Z = 102), and lawrencium (Lr, Z = 103), determined using a method based on a surface ionization process coupled to an online mass separation technique in an atom-at-a-time regime. The measured IP1 values agree well with those predicted by state-of-the-art relativistic calculations performed alongside the present measurements. Similar to the well-established behavior for the lanthanides, the IP1 values of the heavy actinides up to No increase with filling up the 5f orbital, while that of Lr is the lowest among the actinides. These results clearly demonstrate that the 5f orbital is fully filled at No with the [Rn]5f147s2 configuration and that Lr has a weakly bound electron outside the No core. In analogy to the lanthanide series, the present results unequivocally verify that the actinide series ends with Lr.

**Elastic scattering of twisted electrons by diatomic molecules**

**98**, 042701 (2018)

**Abstract:** The elastic scattering of twisted electrons by diatomic molecules is studied within the framework of the nonrelativistic first Born approximation. In this process, the coherent interaction of incident electrons with two molecular centers may cause interference patterns in the angular distributions of outgoing particles. We investigate how this Young-type interference is influenced by the complex internal structure of twisted beams. In particular, we show that the corkscrewlike phase front and the inhomogeneous intensity profile of the incident beam can strongly modify the angular distribution of electrons, scattered off a single well-localized molecule. For the collision with a macroscopic target, composed of randomly distributed but aligned molecules, the angular-differential cross section may reveal valuable information about the transverse and longitudinal momenta of twisted states. To illustrate the difference between the scattering of twisted and plane-wave beams for both single-molecule and macroscopic-target scenarios, detailed calculations have been performed for a H2 target.

**Selectivity of the Br 3d⁻1 Auger decays in HBr**

**98**, 043406 (2018)

**Abstract:** The Auger decay of the spin-orbit and molecular-field split Br 3d−1 core holes in HBr is investigated, both by a photoelectron–Auger-electron coincidence experiment and by ab initio calculations based on the one-center approximation. The branching ratios for the Auger decay of the five different core-hole states to the 4p(σ,π)−2 dicationic final states are determined. Experimental and theoretical data are in good agreement and conform to results for the 4pπ−2 final states from a previous analysis of the high-resolution conventional Auger-electron spectrum. The branching ratios for the Br 3d−1 Auger decay to the 4p(σ,π)−2 with Σ symmetry follow the propensity rule of L2,3VV Auger decay stating that the oriented core holes decay preferentially by involving a valence electron from an orbital with the same spatial orientation. For the M4,5VV decay in HBr this propensity rule has to be supplemented by the requirement that the Auger-electron channel and the other valence orbital have the same preferential orientation. We also probe the influence of the Auger kinetic energy on the distortion of the photoline caused by the postcollision interaction effect. For small kinetic energies, differences between experimental results and theoretical predictions are identified.

**Particle-in-cell simulations of laser–plasma interactions at solid densities and relativistic intensities: the role of atomic processes**

**6**, e50 (2018)

**Abstract:** Direct numerical simulation of intense laser–solid interactions is still of great challenges, because of the many coupled atomic and plasma processes, such as ionization dynamics, collision among charged particles and collective electromagnetic fields, to name just a few. Here, we develop a new particle-in-cell (PIC) simulation code, which enables us to calculate laser–solid interactions in a more realistic way. This code is able to cover almost ‘all’ the coupled physical processes. As an application of the new code, the generation and transport of energetic electrons in front of and within the solid target when irradiated by intense laser beams are studied. For the considered case, in which laser intensity is 10^20 W/cm2 and pre-plasma scale length in front of the solid is 10 μm, several quantitative conclusions are drawn: (i) the collisional damping (although it is very weak) can significantly affect the energetic electrons generation in front of the target, (ii) the Bremsstrahlung radiation will be enhanced by 2–3 times when the solid is dramatically heated and ionized, (iii) the ‘cut-off’ electron energy is lowered by an amount of 25% when both collision damping and Bremsstrahlung radiations are included, and (iv) the resistive electromagnetic fields due to Ohmic heating play nonignorable roles and must be taken into account in such interactions.

**Controlling quantum random walk with a step-dependent coin**

**20**, 083028 (2018)

**Abstract:** We report on the possibility of controlling quantum random walks (QWs) with a step-dependent coin (SDC). The coin is characterized by a (single) rotation angle. Considering different rotation angles, one can find diverse probability distributions for this walk including: complete localization, Gaussian and asymmetric likes. In addition, we explore the entropy of walk in two contexts; for probability density distributions over position space and walker's internal degrees of freedom space (coin space). We show that entropy of position space can decrease for a SDC with the step-number, quite in contrast to a walk with step-independent coin (SIC). For entropy of coin space, a damped oscillation is found for walk with SIC while for a SDC case, the behavior of entropy depends on rotation angle. In general, we demonstrate that quantum walks with simple initiatives may exhibit a quite complex and varying behavior if SDCs are applied. This provides the possibility of controlling QW with a SDC.

**Above-threshold ionization by few-cycle Bessel pulses carrying orbital angular momentum**

**98**, 023407 (2018)

**Abstract:** We investigate theoretically the above-threshold ionization (ATI) of localized atomic targets by intense few-cycle Bessel pulses that carry orbital angular momentum (OAM), known also as twisted light. More specifically, we use the strong-field approximation (SFA) to compute the photoelectron energy spectra. While for plane-wave laser pulses the outgoing photoelectron is typically described by Volkov states within the SFA, no equivalent is known for an electron in a twisted laser field. Here, we therefore introduce a local dipole approximation for the (continuum) state of the photoelectron that is justified for few-cycle pulses. Based on this approximation, we demonstrate that the photoelectrons can also be emitted into the propagation direction of the pulse. When measured in propagation direction, moreover, we show that the magnitude of the ATI peaks depend on the opening angle and the (projection of) total angular momentum of the Bessel pulse.

**Hyperfine interaction with the ²²⁹Th nucleus and its low-lying isomeric state**

**98**, 020503 (2018)

**Abstract:** The thorium nucleus with a mass number A=229 has attracted much interest because its extremely low-lying first excited isomeric state at about 8 eV opens the possibility for the development of a nuclear clock. Both the energy of this state as well as the nuclear magnetic dipole and electric quadrupole moment of the 229mTh isomer are subjects of intense research. The latter can be determined by investigating the hyperfine structure of thorium atoms or ions. Due to its electronic structure and the long lifetime of the nuclear isomeric state, Th2+ is especially suitable for such kinds of studies. In this Rapid Communication, we present a combined experimental and theoretical investigation of the hyperfine structure of the 229Th^(2+) ion in the nuclear ground state, where a good agreement between theory and experiment is found. For the nuclear excited state we use our calculations in combination with recent measurements to obtain the nuclear dipole moment of the isomeric state μ_iso=−0.35 μN, which is in contradiction to the theoretically predicted value of μ_iso=−0.076 μN.

**Tailored orbital angular momentum in high-order harmonic generation with bicircular Laguerre-Gaussian beams**

**98**, 011401 (2018)

**Abstract:** We report on a method to generate extreme ultraviolet vortices from high-order harmonic generation with two-color counter-rotating Laguerre-Gaussian (LG) beams that carry a well-defined orbital angular momentum (OAM). Our calculations show that the OAM of each harmonic can be directly controlled by the OAM of the incident LG modes. Furthermore, we show how the incoming LG modes have to be tailored, in order to generate every possible value of OAM in the emitted harmonics. In addition, we analyze the emitted harmonics with respect to their divergence and find that it decreases with the harmonic order and increases with the OAM of the emitted harmonic.

**Maximum Elliptical Dichroism in Atomic Two-Photon Ionization**

**121**, 053401 (2018)

**Abstract:** Elliptical dichroism is known in atomic photoionization as the difference in the photoelectron angular distributions produced in nonlinear ionization of atoms by left- and right-handed elliptically polarized light. We theoretically demonstrate that the maximum dichroism |ΔED|=1 always appears in two-photon ionization of any atom if the photon energy is tuned in so that the electron emission is dominantly determined by two intermediate resonances. We propose the two-photon ionization of atomic helium in order to demonstrate this remarkable phenomenon. The maximum elliptical dichroism could be used as a sensitive tool for analyzing the polarization state of photon beams produced by free-electron lasers.

**Dispersive refraction of different light to heavy materials at MeV γ-ray energies**

**97**, 063843 (2018)

**Abstract:** The dispersive behavior of materials with atomic charge numbers varying from Z=4 (beryllium, Be) to Z=82 (lead, Pb) was investigated experimentally and theoretically at gamma-ray energies up to 2 MeV. The experiment was performed at the double-crystal gamma spectrometer GAMS6 of the Institut Laue-Langevin in Grenoble. The experimental results were compared with theoretical calculations which account for all major elastic processes involved. Overall, we found a good agreement between theory and experiment. We find that, for the development of refractive optics at $\gamma$-ray energies beyond those currently in use, high-Z materials become increasingly attractive compared to the beryllium lens-stacks used at x-ray energies.

**Probing Sizes and Shapes of Nobelium Isotopes by Laser Spectroscopy**

**120**, 232503 (2018)

**Abstract:** Until recently, ground-state nuclear moments of the heaviest nuclei could only be inferred from nuclear spectroscopy, where model assumptions are required. Laser spectroscopy in combination with modern atomic structure calculations is now able to probe these moments directly, in a comprehensive and nuclear-model-independent way. Here we report on unique access to the differential mean-square charge radii of 252,253,254No, and therefore to changes in nuclear size and shape. State-of-the-art nuclear density functional calculations describe well the changes in nuclear charge radii in the region of the heavy actinides, indicating an appreciable central depression in the deformed proton density distribution in 252,254No isotopes. Finally, the hyperfine splitting of 253No was evaluated, enabling a complementary measure of its (quadrupole) deformation, as well as an insight into the neutron single-particle wave function via the nuclear spin and magnetic moment.

**Influence of a stray magnetic field on the measurement of long-range spin-spin interaction**

**2**, 055025 (2018)

**Abstract:** We study the influence of an additional uncontrolled (stray) magnetic field upon the measurement of long-range spin-spin interaction strength of two spin-1/2 valence electrons bound in two separate ions at well-defined distances from each other. This stray field, which is neither perpendicular nor parallel to the line connecting two ions, could appear due to the Earth magnetic field, or, due to the slight angular misalignment between the applied magnetic field and the line connecting two ions. It is found that the presence of the stray magnetic field plays an important role in the dynamics of the spin-states of two electrons. If neglected in the analysis, moreover, such a stray field may affect the measurement of the spin-spin interaction strength, especially at smaller inter-spin distances.

**Line strengths of QED-sensitive forbidden transitions in B-, Al-, F- and Cl-like ions**

**97**, 052506 (2018)

**Abstract:** The magnetic dipole (M1) line strength between the fine-structure levels of the ground configurations in B-, F-, Al-, and Cl-like ions are calculated for the four elements argon, iron, molybdenum, and tungsten. Systematically enlarged multiconfiguration Dirac-Hartree-Fock (MCDHF) wave functions are employed to account for the interelectronic interaction with the Breit interaction included in first-order perturbation theory. The QED corrections are evaluated to all orders in αZ utilizing an effective potential approach. The calculated line strengths are compared with the results of other theories. The M1 transition rates are reported using accurate energies from the literature. Moreover, the lifetimes in the range of millisecond to picosecond are predicted including the contributions from the transition rate due to the E2 transition channel. The discrepancies of the predicted rates from those available from the literature are discussed and a benchmark data set of theoretical lifetimes is provided to support future experiments.

**Charge radii and electromagnetic moments of ¹⁹⁵⁻²¹¹At**

**97**, 054327 (2018)

**Abstract:** Hyperfine-structure parameters and isotope shifts of 195–211At have been measured for the first time at CERN-ISOLDE, using the in-source resonance-ionization spectroscopy method. The hyperfine structures of isotopes were recorded using a triad of experimental techniques for monitoring the photo-ion current. The Multi-Reflection Time-of-Flight Mass Spectrometer, in connection with a high-resolution electron multiplier, was used as an ion-counting setup for isotopes that either were affected by strong isobaric contamination or possessed a long half-life; the ISOLDE Faraday cups were used for cases with high-intensity beams; and the Windmill decay station was used for short-lived, predominantly α-decaying nuclei. The electromagnetic moments and changes in the mean-square charge radii of the astatine nuclei have been extracted from the measured hyperfine-structure constants and isotope shifts. This was only made possible by dedicated state-of-the-art large-scale atomic computations of the electronic factors and the specific mass shift of atomic transitions in astatine that are needed for these extractions. By comparison with systematics, it was possible to assess the reliability of the results of these calculations and their ascribed uncertainties. A strong deviation in the ground-state mean-square charge radii of the lightest astatine isotopes, from the trend of the (spherical) lead isotopes, is interpreted as the result of an onset of deformation. This behavior bears a resemblance to the deviation observed in the isotonic polonium isotopes. Cases for shape coexistence have been identified in 197,199At, for which a significant difference in the charge radii for ground (9/2−) and isomeric (1/2+) states has been observed.

**Isotope shifts from collinear laser spectroscopy of doubly charged yttrium isotopes**

**97**, 042504 (2018)

**Abstract:** Collinear laser spectroscopy has been performed on doubly charged ions of radioactive yttrium in order to study the isotope shifts of the 294.6-nm 5s2S1/2→5p2P1/2 line. The potential of such an alkali-metal-like transition to improve the reliability of atomic-field-shift and mass-shift factor calculations, and hence the extraction of nuclear mean-square radii, is discussed. Production of yttrium ion beams for such studies is available at the IGISOL IV Accelerator Laboratory, Jyväskylä, Finland. This newly recommissioned facility is described here in relation to the on-line study of accelerator-produced short-lived isotopes using collinear laser spectroscopy and application of the technique to doubly charged ions.

**Strong-field ionization with twisted laser pulses**

**97**, 043418 (2018)

**Abstract:** We apply quantum trajectory Monte Carlo computations in order to model strong-field ionization of atoms by twisted Bessel pulses and calculate photoelectron momentum distributions (PEMD). Since Bessel beams can be considered as an infinite superposition of circularly polarized plane waves with the same helicity, whose wave vectors lie on a cone, we compared the PEMD of such Bessel pulses to those of a circularly polarized pulse. We focus on the momentum distributions in propagation direction of the pulse and show how these momentum distributions are affected by experimental accessible parameters, such as the opening angle of the beam or the impact parameter of the atom with regard to the beam axis. In particular, we show that we can find higher momenta of the photoelectrons, if the opening angle is increased.

**Neon in ultrashort and intense x-rays from free electron lasers**

**51**, 055602 (2018)

**Abstract:** We theoretically examine neon atoms in ultrashort and intense x-rays from free electron lasers and compare our results with data from experiments conducted at the Linac Coherent Light Source. For this purpose, we treat in detail the electronic structure in all possible nonrelativistic cationic configurations using a relativistic multiconfiguration approach. The interaction with the x-rays is described in rate-equation approximation. To understand the mechanisms of the interaction, a path analysis is devised which allows us to investigate what sequences of photoionization and decay processes lead to a specific configuration and with what probability. Thereby, we uncover a connection to the mathematics of graph theory and formal languages. In detail, we study the ion yields and find that plain rate equations do not provide a satisfactory description. We need to extend the rate equations for neon to incorporate double Auger decay of a K-shell vacancy and photoionization shake off for neutral neon. Shake off is included for valence and core ionization; the former has hitherto been overlooked but has important consequences for the ion yields from an x-ray energy below the core ionization threshold. Furthermore, we predict the photon yields from xuv and x-ray fluorescence; these allow one insights into the configurations populated by the interaction with the x-rays. Finally, we discover that inaccuracies in those Auger decay widths employed in previous studies have only a minor influence on ion and photon yields.

**Ultrafast quantum control of ionization dynamics in krypton**

**9**, 719 (2018)

**Abstract:** Ultrafast spectroscopy with attosecond resolution has enabled the real time observation of ultrafast electron dynamics in atoms, molecules and solids. These experiments employ attosecond pulses or pulse trains and explore dynamical processes in a pump–probe scheme that is selectively sensitive to electronic state of matter via photoelectron or XUV absorption spectroscopy or that includes changes of the ionic state detected via photo-ion mass spectrometry. Here, we demonstrate how the implementation of combined photo-ion and absorption spectroscopy with attosecond resolution enables tracking the complex multidimensional excitation and decay cascade of an Auger auto-ionization process of a few femtoseconds in highly excited krypton. In tandem with theory, our study reveals the role of intermediate electronic states in the formation of multiply charged ions. Amplitude tuning of a dressing laser field addresses different groups of decay channels and allows exerting temporal and quantitative control over the ionization dynamics in rare gas atoms.

**Rayleigh scattering of twisted light by hydrogenlike ions**

**97**, 023802 (2018)

**Abstract:** The elastic Rayleigh scattering of twisted light and, in particular, the polarization (transfer) of the scattered photons have been analyzed within the framework of second-order perturbation theory and Dirac's relativistic equation. Special attention was paid hereby to the scattering on three different atomic targets: single atoms, a mesoscopic (small) target, and a macroscopic (large) target, which are all centered with regard to the beam axis. Detailed calculations of the polarization Stokes parameters were performed for C5+ ions and for twisted Bessel beams. It is shown that the polarization of scattered photons is sensitive to the size of an atomic target and to the helicity, the opening angle, and the projection of the total angular momentum of the incident Bessel beam. These computations indicate more that the Stokes parameters of the (Rayleigh) scattered twisted light may significantly differ from their behavior for an incident plane-wave radiation.

**LCLS in-photon out: fluorescence measurement of neon using soft x-rays**

**51**, 034003 (2018)

**Abstract:** We measured the fluorescence photon yield of neon upon soft x-ray ionization (∼1200 eV) from the x-ray free-electron laser at Linac Coherent Light Source, and demonstrated the usage of a grazing incidence spectrometer with a variable line spacing grating to perform x-ray fluorescence spectroscopy on a gas phase system. Our measurements also allowed us to estimate the focal size of the beam from the theoretical description developed, in terms of the rate equation approximation accounting for photoionization shake off of neutral neon and double auger decay of single core holes.

## 2017

**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.

**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.

**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.

**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.

**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.

**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.

**Ab initio calculations of energy levels, transition rates and lifetimes in Ni xii**

**469**, 4620 (2017)

**Abstract:** We report large-scale multi-configuration Dirac–Hartree–Fock calculations and relativistic configuration interaction calculations for allowed E1 and forbidden transitions (M1, E2, M2) among the fine structure levels of the 3s^2 3p^5, 3s 3p^6 and 3s^2 3p^4 3d configurations for Ni xii. In our systematically enlarged wave functions, we incorporated the effects of relativity, all important electron correlations and rearrangement of the bound electron density within two different computational models. We compare our calculated energies for the fine structure levels with previous calculations and experiments. We validate all the tentative experimental lines recently identified by Del Zanna & Badnell with one exception. We discuss the consistency of our transition rates in comparison to semi-empirical predictions. We present ab initio lifetime values by taking into account all allowed E1 and forbidden transitions (M1, E2, M2) rates among lowest 31 levels. Our results for lifetime values are better than previously reported ab initio and semi-empirical values as compared to available experiments, thus, providing reliable predictions in the prospects of future experiments.

**Photoexcitation of atoms by Laguerre-Gaussian beams**

**96**, 023407 (2017)

**Abstract:** In a recent experiment, Schmiegelow et al. [Nat. Commun. 7, 12998 (2016)] investigated the magnetic sublevel population of Ca^+ ions in a Laguerre-Gaussian light beam if the target atoms were just centered along the beam axis. They demonstrated in this experiment that the sublevel population of the excited atoms is uniquely defined by the projection of the orbital angular momentum of the incident light. However, little attention has been paid so far to the question of how the magnetic sublevels are populated when atoms are displaced from the beam axis by some impact parameter b. Here, we analyze this sublevel population for different atomic impact parameters in first-order perturbation theory and by making use of the density-matrix formalism. Detailed calculations are performed especially for the 4s ^2S_1/2 -> 3d ^2D_5/2 transition in Ca^+ ions and for the vector potential of a Laguerre-Gaussian beam in Coulomb gauge. It is shown that the magnetic sublevel population of the excited ^2D_5/2 level varies significantly with the impact parameter and is sensitive to the polarization, the radial index, as well as the orbital angular momentum of the incident light beam.

**Angle-resolved x-ray spectroscopic scheme to determine overlapping hyperfine splittings in highly charged heliumlike ions**

**96**, 012503 (2017)

**Abstract:** An angle-resolved x-ray spectroscopic scheme is presented for determining the hyperfine splitting of highly charged ions. For heliumlike ions, in particular, we propose to measure either the angular distribution or polarization of the 1s2p ^3P_{1,F} -> 1s^2 ^1S_{0,F_f} emission following the stimulated decay of the initial 1s 2s ^1S_{0,F_i} level. It is found that both the angular and polarization characteristics of the emitted x-ray photons strongly depend on the (relative) splitting of the partially overlapping hyperfine 1s 2p ^3P_{1,F} resonances and may thus help resolve their hyperfine structure. The proposed scheme is feasible with present-day photon detectors and allows a measurement of the hyperfine splitting of heliumlike ions with a relative accuracy of about 10^{-4}.

**Auger decay of 4d inner-shell holes in atomic Hg leading to triple ionization**

**96**, 012505 (2017)

**Abstract:** Formation of triply ionized states upon the creation of 4d inner-shell holes in atomic Hg is investigated by using synchrotron radiation of 730 eV photon energy and a versatile multielectron coincidence detection technique in combination with multiconfiguration Dirac-Fock calculations. By carefully selecting Coster-Kronig electrons detected only in coincidence with a 4d photoelectron, the Coster-Kronig spectrum has been extracted and the corresponding branching ratios of the 4d hole have been determined. The results are found to differ from previously established experimental ratios based on electron impact ionization but to agree now better with theory. We also present an Auger cascade analysis of pathways leading to triply ionized states of atomic Hg upon removal of a 4d inner-shell electron.

**Photoelectron distribution of nonresonant two-photon ionization of neutral atoms**

**96**, 013409 (2017)

**Abstract:** Photoelectron angular distributions following the nonresonant two-photon K-shell ionization of neutral atoms are studied theoretically. Using the independent particle approximation and relativistic second-order perturbation theory, the contributions of screening and relativistic effects to the photoelectron angular distribution are evaluated. A simple nonrelativistic expression is presented for the angle-differential cross section in dipole approximation for two-photon ionization by elliptically polarized photons, and its limitations are analyzed numerically. Moreover, we show that screening effects of the inactive electrons can significantly affect the photoelectron distributions and can also lead to a strong elliptical dichroism. Numerical results are presented for the case of two-photon K-shell ionization of neutral Ne, Ge, Xe, and U atoms.

**Spin-dependent quantum theory of high-order above-threshold ionization**

**95**, 063408 (2017)

**Abstract:** The strong-field-approximation theory of high-order above-threshold ionization of atoms is generalized to include the electron spin. The obtained rescattering amplitude consists of a direct and exchange part. On the examples of excited He atoms as well as Li^+ and Be^2+ ions, it is shown that the interference of these two amplitudes leads to an observable difference between the photoelectron momentum distributions corresponding to different initial spin states: Pronounced minima appear for singlet states, which are absent for triplet states.

**Electron impact scattering and calculated ionization cross sections for SFx (x=1–5) radicals**

**417**, 8 (2017)

**Abstract:** Abstract The spherical complex optical potential (SCOP) formalism is employed to solve the e−-SFx (x=1–5) scattering system. In this article, the total cross sections by electron impact from 50 to 5000eV are calculated. The complex scattering potential ionization contribution (CSP-ic) method is used to compute the electron-induced total ionization cross sections from the inelastic cross section in the energy range from ionization threshold to 5000eV. For most of the reported radicals, the magnitude and shape of cross section compares well with previous measurements and calculations, wherever available. However, for many targets results are predicted for the first time in this work. From the electron-impact scattering cross sections for the SFx (x=1–5) radicals, we also estimate the gas-kinetic radius and the van der Waals coefficient.

**Auger cascades in resonantly excited neon**

**95**, 053407 (2017)

**Abstract:** The Auger cascades following the resonant 1s → np (n = 3, 4) excitation of neutral neon are studied theoretically. In contrast to previous investigations, we here model the complete cascade from the initially core-excited 1s⁻¹3p ¹P₁ and 1s⁻¹4p ¹P₁ levels of Ne up to the doubly-ionized Ne²⁺ ions. Extensive multiconfiguration Dirac-Fock (MCDF) calculations are carried out, combined with a proper cascades model, to incorporate as many decay branches as possible, including all major single-electron shake-up and shake-down processes. We simulate the electron spectra and predict shake probabilities, ion yields, as well as the relative population of the intermediate and final states. Experimentally known level energies for neutral, singly- and doubly-ionized neon are utilized whenever possible in order to improve the predictions. Most features from experiment can be reproduced with quite good agreement if a sufficiently large basis is taken into account. These simulations therefore demonstrate not only the required computational effort, but also that it is nowadays possible to predict whole Auger spectra of decay cascades, a central feature for further exploring electron coincidence maps as obtained at synchrotrons and free-electron lasers.

**Plasma effects on atomic data for the K-vacancy states of highly charged iron ions**

**1811**, 040002 (2017)

**Abstract:** The main goal of the present work is to estimate the effects of plasma environment 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. In order to do this, multiconfiguration Dirac-Fock computations have been carried out by considering a time averaged Debye-Hückel potential for both the electron-nucleus and electron-electron interactions. In the present paper, a first sample of results related to the ionization potentials, the K-thresholds, the transition energies and the radiative emission rates is reported for the ions Fe23+ and Fe24+.

**Spin-dependent rescattering in strong-field ionization of helium**

**50**, 065001 (2017)

**Abstract:** We investigate the influence of singlet and triplet spin states on rescattered photoelectrons in strong-field ionization of excited helium. Choosing either a symmetric or antisymmetric spatial wave function as the initial state results in different scattering cross sections for the 1s2s¹S and ³S states. These cross sections are used in the semi-classical model of strong-field ionization. Our investigations show that the photoelectron momentum distributions of rescattered electrons exhibit a significant dependence on the relative spin state of the projectile and the bound electron which should be observable in experiments. The proposed experimental approach can be understood as a testbed for probing the spin dynamics of electrons during strong-field ionization and the presented results as a baseline for their identification.

**Towards high-resolution laser ionization spectroscopy of the heaviest elements in supersonic gas jet expansion**

**8**, 14520 (2017)

**Abstract:** Resonant laser ionization and spectroscopy are widely used techniques at radioactive ion beam facilities to produce pure beams of exotic nuclei and measure the shape, size, spin and electromagnetic multipole moments of these nuclei. However, in such measurements it is difficult to combine a high efficiency with a high spectral resolution. Here we demonstrate the on-line application of atomic laser ionization spectroscopy in a supersonic gas jet, a technique suited for high-precision studies of the ground- and isomeric-state properties of nuclei located at the extremes of stability. The technique is characterized in a measurement on actinium isotopes around the N=126 neutron shell closure. A significant improvement in the spectral resolution by more than one order of magnitude is achieved in these experiments without loss in efficiency.

**Monte Carlo approach to calculate proton stopping in warm dense matter within particle-in-cell simulations**

**95**, 023207 (2017)

**Abstract:** A Monte Carlo approach to proton stopping in warm dense matter is implemented into an existing particle-in-cell code. This approach is based on multiple electron-electron, electron-ion, and ion-ion binary collision and accounts for both the free and the bound electrons in the plasmas. This approach enables one to calculate the stopping of particles in a more natural manner than existing theoretical treatment. In the low-temperature limit, when “all” electrons are bound to the nucleus, the stopping power coincides with the predictions from the Bethe-Bloch formula and is consistent with the data from the National Institute of Standard and Technology database. At higher temperatures, some of the bound electrons are ionized, and this increases the stopping power in the plasmas, as demonstrated by A. B. Zylstra et al. [Phys. Rev. Lett. 114, 215002 (2015)]. At even higher temperatures, the degree of ionization reaches a maximum and thus decreases the stopping power due to the suppression of collision frequency between projected proton beam and hot plasmas in the target.

**Monte Carlo approach to calculate ionization dynamics of hot solid-density plasmas within particle-in-cell simulations**

**95**, 023208 (2017)

**Abstract:** A physical model based on a Monte Carlo approach is proposed to calculate the ionization dynamics of hot-solid-density plasmas within particle-in-cell (PIC) simulations, and where the impact (collision) ionization (CI), electron-ion recombination (RE), and ionization potential depression (IPD) by surrounding plasmas are taken into consideration self-consistently. When compared with other models, which are applied in the literature for plasmas near thermal equilibrium, the temporal relaxation of ionization dynamics can also be simulated by the proposed model. Besides, this model is general and can be applied for both single elements and alloys with quite different compositions. The proposed model is implemented into a PIC code, with (final) ionization equilibriums sustained by competitions between CI and its inverse process (i.e., RE). Comparisons between the full model and model without IPD or RE are performed. Our results indicate that for bulk aluminium at temperature of 1 to 1000 eV, (i) the averaged ionization degree increases by including IPD; while (ii) the averaged ionization degree is significantly over estimated when the RE is neglected. A direct comparison from the PIC code is made with the existing models for the dependence of averaged ionization degree on thermal equilibrium temperatures and shows good agreements with that generated from Saha-Boltzmann model and/or FLYCHK code.

## 2016

**Multiconfiguration calculations of electronic isotope shift factors in Al I**

**94**, 062508 (2016)

**Abstract:** The present work reports results from systematic multiconfiguration Dirac–Hartree–Fock calculations of electronic isotope shift factors for a set of transitions between low-lying levels of neutral aluminium. These electronic quantities together with observed isotope shifts between different pairs of isotopes provide the changes in mean-square charge radii of the atomic nuclei. Two computational approaches are adopted for the estimation of the mass- and field-shift factors. Within these approaches, different models for electron correlation are explored in a systematic way to determine a reliable computational strategy and to estimate theoretical error bars of the isotope shift factors.

**Relativistic calculations of the nonresonant two-photon ionization of neutral atoms**

**94**, 063412 (2016)

**Abstract:** The nonresonant, two-photon, one-electron ionization of neutral atoms is studied theoretically in the framework of relativistic second-order perturbation theory and independent particle approximation. In particular, the importance of relativistic and screening effects in the total two-photon ionization cross section is investigated. Detailed computations have been carried out for the K-shell ionization of neutral Ne, Ge, Xe, and U atoms. The relativistic effects significantly decrease the total cross section; for the case of U, for example, they reduce the total cross section by a factor of two. Moreover, we have found that the account for the screening effects of the remaining electrons leads to occurrence of an unexpected minimum in the total cross section at the total photon energies equal to the ionization threshold; for the case of Ne, for example, the cross section drops there by a factor of three.

**Charge Radii of Neutron Deficient ⁵²,⁵³Fe Produced by Projectile Fragmentation**

**117**, 252501 (2016)

**Abstract:** Bunched-beam collinear laser spectroscopy is performed on neutron deficient Fe52,53 prepared through in-flight separation followed by a gas stopping. This novel scheme is a major step to reach nuclides far from the stability line in laser spectroscopy. Differential mean-square charge radii δ⟨r2⟩ of Fe52,53 are determined relative to stable Fe56 as δ⟨r2⟩56,52=−0.034(13) fm2 and δ⟨r2⟩56,53=−0.218(13) fm2, respectively, from the isotope shift of atomic hyperfine structures. The multiconfiguration Dirac-Fock method is used to calculate atomic factors to deduce δ⟨r2⟩. The values of δ⟨r2⟩ exhibit a minimum at the N=28 neutron shell closure. The nuclear density functional theory with Fayans and Skyrme energy density functionals is used to interpret the data. The trend of δ⟨r2⟩ along the Fe isotopic chain results from an interplay between single-particle shell structure, pairing, and polarization effects and provides important data for understanding the intricate trend in the δ⟨r2⟩ of closed-shell Ca isotopes.

**Nuclear Excitation by Two-Photon Electron Transition**

**117**, 243001 (2016)

**Abstract:** A new mechanism of nuclear excitation via two-photon electron transitions (NETP) is proposed and studied theoretically. As a generic example, detailed calculations are performed for the E1E1 1s2sS01→1s2S01 two-photon decay of a He-like Ac87+225 ion with a resonant excitation of the 3/2+ nuclear state with an energy of 40.09(5) keV. The probability for such a two-photon decay via the nuclear excitation is found to be PNETP=3.5×10−9 and, thus, is comparable with other mechanisms, such as nuclear excitation by electron transition and by electron capture. The possibility for the experimental observation of the proposed mechanism is thoroughly discussed.

**Polarization transfer in Rayleigh scattering of hard x-rays**

**18**, 103034 (2016)

**Abstract:** We report on the first elastic hard x-ray scattering experiment where the linear polarization characteristics of both the incident and the scattered radiation were observed. Rayleigh scattering was investigated in a relativistic regime by using a high- Z target material, namely gold, and a photon energy of 175 keV. Although the incident synchrotron radiation was nearly 100% linearly polarized, at a scattering angle of θ=90° we observed a strong depolarization for the scattered photons with a degree of linear polarization of +27% ± 12% only. This finding agrees with second-order quantum electrodynamics calculations of Rayleigh scattering, when taking into account a small polarization impurity of the incident photon beam which was determined to be close to 98%. The latter value was obtained independently from the elastic scattering by analyzing photons that were Compton-scattered in the target. Moreover, our results indicate that when relying on state-of-the-art theory, Rayleigh scattering could provide a very accurate method to diagnose polarization impurities in a broad region of hard x-ray energies.

**Two-color above-threshold ionization of atoms and ions in XUV Bessel beams and intense laser light**

**94**, 053420 (2016)

**Abstract:** The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultraviolet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target atoms with regard to the beam axis. In addition, analog to the circular dichroism in typical two-color ATI experiments with circularly polarized light, we define and discuss seven different dichroism signals for such vortex Bessel beams that arise from the various combinations of the orbital and spin angular momenta of the two light fields. For localized targets, it is found that these dichroism signals strongly depend on the size and position of the atoms relative to the beam. For macroscopically extended targets, in contrast, three of these dichroism signals tend to zero, while the other four just coincide with the standard circular dichroism, similar as for Bessel beams with a small opening angle. Detailed computations of the dichroism are performed and discussed for the 4s valence-shell photoionization of Ca+ ions.

**Changes in nuclear structure along the Mn isotopic chain studied via charge radii**

**94**, 054321 (2016)

**Abstract:** The hyperfine spectra of Mn51,53−64 were measured in two experimental runs using collinear laser spectroscopy at ISOLDE, CERN. Laser spectroscopy was performed on the atomic 3d54s2S5/26→3d54s4pP3/26 and ionic 3d54s5S2→3d54p5P3 transitions, yielding two sets of isotope shifts. The mass and field shift factors for both transitions have been calculated in the multiconfiguration Dirac-Fock framework and were combined with a King plot analysis in order to obtain a consistent set of mean-square charge radii which, together with earlier work on neutron-deficient Mn, allow the study of nuclear structure changes from N=25 across N=28 up to N=39. A clear development of deformation is observed towards N=40, confirming the conclusions of the nuclear moments studies. From a Monte Carlo shell-model study of the shape in the Mn isotopic chain, it is suggested that the observed development of deformation is not only due to an increase in static prolate deformation but also due to shape fluctuations and triaxiality. The changes in mean-square charge radii are well reproduced using the Duflo-Zuker formula except in the case of large deformation.

**Photoionization of neutral atoms by X waves carrying orbital angular momentum**

**94**, 041402 (2016)

**Abstract:** In contrast to plane waves, twisted or vortex beams have a complex spatial structure. Both their intensity and energy flow vary within the wave front. Beyond that, polychromatic vortex beams, such as X waves, have a spatially dependent energy distribution. We propose a method to measure this (local) energy spectrum. The method is based on the measurement of the energy distribution of photoelectrons from alkali-metal atoms. On the basis of our fully relativistic calculations, we argue that even ensembles of atoms can be used to probe the local energy spectrum of short twisted pulses.

**Prominent role of multielectron processes in K-shell double and triple photodetachment of oxygen anions**

**94**, 041401 (2016)

**Abstract:** The photon-ion merged-beam technique was used at a synchrotron light source for measuring the absolute cross sections of the double and triple photodetachment of O− ions. The experimental photon energy range of 524–543 eV comprised the threshold for K-shell ionization. Using resolving powers of up to 13 000, the position, strength, and width of the below-threshold 1s2s22p6 S2 resonance as well as the positions of the 1s2s22p5 P3 and 1s2s22p5 P1 thresholds for K-shell ionization were determined with high precision. In addition, systematically enlarged multiconfiguration Dirac-Fock calculations have been performed for the resonant detachment cross sections. Results from these ab initio computations agree very well with the measurements for the widths and branching fractions for double and triple detachment, if double shakeup (and shakedown) of the valence electrons and the rearrangement of the electron density is taken into account. For the absolute cross sections, however, a previously found discrepancy between measurements and theory is confirmed.

**Elastic scattering of vortex electrons provides direct access to the Coulomb phase**

**94**, 076001 (2016)

**Abstract:** Vortex electron beams are freely propagating electron waves carrying adjustable orbital angular momentum with respect to the propagation direction. Such beams were experimentally realized just a few years ago and are now used to probe various electromagnetic processes. So far, these experiments used the single vortex electron beams, either propagating in external fields or impacting a target. Here, we investigate the elastic scattering of two such aligned vortex electron beams and demonstrate that this process allows one to experimentally measure features which are impossible to detect in the usual plane-wave scattering. The scattering amplitude of this process is well approximated by two plane-wave scattering amplitudes with different momentum transfers, which interfere and give direct experimental access to the Coulomb phase. This phase (shift) affects the scattering of all charged particles and has thus received significant theoretical attention but was never probed experimentally. We show that a properly defined azimuthal asymmetry, which has no counterpart in plane-wave scattering, allows one to directly measure the Coulomb phase as function of the scattering angle.

**Physics book: CRYRING@ESR**

**225**, 797 (2016)

**Abstract:** The exploration of the unique properties of stored and cooled beams of highly-charged ions as provided by heavy-ion storage rings has opened novel and fascinating research opportunities in the realm of atomic and nuclear physics research. Since the late 1980s, pioneering work has been performed at the CRYRING at Stockholm and at the Test Storage Ring (TSR) at Heidelberg. For the heaviest ions in the highest charge-states, a real quantum jump was achieved in the early 1990s by the commissioning of the Experimental Storage Ring (ESR) at GSI Helmholtzzentrum für Schwerionenforschung (GSI) in Darmstadt where challenging experiments on the electron dynamics in the strong field regime as well as nuclear physics studies on exotic nuclei and at the borderline to atomic physics were performed. Meanwhile also at Lanzhou a heavy-ion storage ring has been taken in operation, exploiting the unique research opportunities in particular for medium-heavy ions and exotic nuclei.

**Double-slit experiment in momentum space**

**115**, 41001 (2016)

**Abstract:** Young's classic double-slit experiment demonstrates the reality of interference when waves and particles travel simultaneously along two different spatial paths. Here, we propose a double-slit experiment in momentum space, realized in the free-space elastic scattering of vortex electrons. We show that this process proceeds along two paths in momentum space, which are well localized and well separated from each other. For such vortex beams, the (plane-wave) amplitudes along the two paths acquire adjustable phase shifts and produce interference fringes in the final angular distribution. We argue that this experiment can be realized with the present-day technology. We show that it gives experimental access to the Coulomb phase, a quantity which plays an important role in all charged particle scattering but which usual scattering experiments are insensitive to.

**Electric dipole polarizabilities of Rydberg states of alkali-metal atoms**

**94**, 032503 (2016)

**Abstract:** Calculations of the static electric-dipole scalar and tensor polarizabilities are presented for two alkali-metal atoms, Rb and Cs, for the nS, nP½,3/2, and nD3/2,5/2 states with large principal quantum numbers up to n=50. The calculations are performed within an effective one-electron approximation, based on the Dirac-Fock Hamiltonian with a semiempirical core-polarization potential. The obtained results are compared with those from a simpler semiempirical approach and with available experimental data.

**Probing the energy flow in Bessel light beams using atomic photoionization**

**94**, 033420 (2016)

**Abstract:** The growing interest in twisted light beams also requires a better understanding of their complex internal structure. Particular attention is currently being given to the energy circulation in these beams as usually described by the Poynting vector field. In the present study we propose to use the photoionization of alkali-metal atoms as a probe process to measure (and visualize) the energy flow in twisted light fields. Such measurements are possible since the angular distribution of photoelectrons, emitted from a small atomic target, appears sensitive to and is determined by the local direction of the Poynting vector. To illustrate the feasibility of the proposed method, detailed calculations were performed for the ionization of sodium atoms by nondiffractive Bessel beams.

**Erratum: Electron-ion collision spectroscopy: Lithium-like xenon ions [Phys. Rev. A 91, 012710 (2015)]**

**94**, 029903 (2016)

**Abstract:** *

**Electromagnetic wave propagation in spatially homogeneous yet smoothly time-varying dielectric media**

**178**, 158 (2016)

**Abstract:** We explore the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics. By modelling the smooth transition, occurring during a finite period t, as a phenomenologically realistic and sigmoidal change of the dielectric permittivity, an analytically exact solution to Maxwell’s equations is derived for the electric displacement in terms of hypergeometric functions. Using this solution, we show the possibility of amplification and attenuation of waves and associate this with the decrease and increase of the time-dependent permittivity. We demonstrate, moreover, that such an energy exchange between waves and non-stationary media leads to the transformation (or conversion) of frequencies. Our results may pave the way towards controllable light–matter interaction in time-varying structures.

**Suppression of spin-exchange relaxation in tilted magnetic fields within the geophysical range**

**94**, 013403 (2016)

**Abstract:** We present a detailed experimental and theoretical study on the relaxation of spin coherence due to the spin-exchange mechanism arising in the electronic ground states of alkali-metal vapor atoms. As opposed to the well-explored formation of a stretched state in a longitudinal geometry (magnetic field parallel to the laser propagation direction) we employ adapted hyperfine-selective optical pumping in order to suppress spin-exchange relaxation. By comparing measurements of the intrinsic relaxation rate of the spin coherence in the ground state of cesium atoms with detailed density-matrix simulations we show that the relaxation due to spin-exchange collisions can be reduced substantially even in a tilted magnetic field of geomagnetic strength, the major application case of scalar magnetic surveying. This explains the observed striking improvement in sensitivity and further deepens the understanding of the light-narrowed Mx magnetometer, which was presented recently. Additionally, new avenues for investigating the dynamics in alkali-metal atoms governed by the spin-exchange interaction and interacting with arbitrary external fields open up.

**Angular correlation function of the hypersatellite-satellite x-ray cascade following K-shell electron capture of ⁵⁵Fe**

**94**, 014611 (2016)

**Abstract:** The first measurement of the hypersatellite-satellite two-photon angular correlation function following the electron capture decay of Fe55 was carried out. In particular, two hybrid active pixel detectors were employed to measure the anisotropy parameter β_eff2(exp)=0.097±0.053, which closely agreed with the theoretical value β_eff2(theor)=0.09735, calculated in the electric-dipole approximation. In addition, we also determined the double K-shell vacancy creation probability in this specific electron capture decay with improved accuracy. We found PKK=(1.388±0.037)×10−4, with a systematic error ΔPKK,syst=0.042×10−4.

**Photoelectron angular distributions and correlations in sequential double and triple atomic ionization by free electron lasers**

**63**, 334 (2016)

**Abstract:** We present a review of theoretical studies of the simplest nonlinear photoprocesses detected in the XUV range with the use of free electron lasers: sequential double and triple ionization of atoms by two and three XUV photons. Photoelectron angular distributions and angular correlations between emitted electrons are considered. A comparison of the calculated results with recent angle-resolved photoelectron spectroscopy experiments is discussed.

**Level sequence and splitting identification of closely spaced energy levels by angle-resolved analysis of fluorescence light**

**93**, 063413 (2016)

**Abstract:** The angular distribution and linear polarization of the fluorescence light following the resonant photoexcitation is investigated within the framework of density matrix and second-order perturbation theory. Emphasis has been placed on “signatures” for determining the level sequence and splitting of intermediate (partially) overlapping resonances, if analyzed as a function of photon energy of incident light. Detailed computations within the multiconfiguration Dirac–Fock method have been performed, especially for the 1s^2 2s^2 2p^6 3s,Ji=1/2+γ1 → (1s^2 2s 2p^6 3s)_1 3p3/2,J=1/2,3/2 → 1s^2 2s^2 2p^6 3s,Jf=1/2+γ2 photoexcitation and subsequent fluorescence emission of atomic sodium. A remarkably strong dependence of the angular distribution and linear polarization of the γ2 fluorescence emission is found upon the level sequence and splitting of the intermediate (1s^2 2s 2p^6 3s)_1 3p3/2,J=1/2,3/2 overlapping resonances owing to their finite lifetime (linewidth). We therefore suggest that accurate measurements of the angular distribution and linear polarization might help identify the sequence and small splittings of closely spaced energy levels, even if they cannot be spectroscopically resolved.

**Cu charge radii reveal a weak sub-shell effect at N=40**

**93**, 064318 (2016)

**Abstract:** Collinear laser spectroscopy on Cu58–75 isotopes was performed at the CERN-ISOLDE radioactive ion beam facility. In this paper we report on the isotope shifts obtained from these measurements. State-of-the-art atomic physics calculations have been undertaken in order to determine the changes in mean-square charge radii δ⟨r2⟩A,A′ from the observed isotope shifts. A local minimum is observed in these radii differences at N=40, providing evidence for a weak N=40 sub-shell effect. However, comparison of δ⟨r2⟩A,A′ with a droplet model prediction including static deformation deduced from the spectroscopic quadrupole moments, points to the persistence of correlations at N=40.

**Strong higher-order resonant contributions to x-ray line polarization in hot plasmas**

**93**, 061201 (2016)

**Abstract:** We studied angular distributions of x rays emitted in resonant recombination of highly charged iron and krypton ions, resolving dielectronic, trielectronic, and quadruelectronic channels. A tunable electron beam drove these processes, inducing x rays registered by two detectors mounted along and perpendicular to the beam axis. The measured emission asymmetries comprehensively benchmarked full-order atomic calculations. We conclude that accurate polarization diagnostics of hot plasmas can only be obtained under the premise of inclusion of higher-order processes that were neglected in earlier work.

**Absorption of twisted light by a mesoscopic atomic target**

**91**, 064001 (2016)

**Abstract:** The excitation of a hydrogen-atom target by a twisted Bessel light beam is investigated. The atoms are assumed to have a Gaussian spatial distribution in the target. Theoretical analysis is performed within a nonrelativistic framework using a first-order perturbation approach and density matrix formalism. By using this theory, we derive the expressions for excitation cross sections and for alignment parameters of the excited atomic state. In particular, we make calculations for the 1s -> 2p transition caused by the interaction of Bessel beams with the atomic target. For this transition, we analyze the population of magnetic sublevels for the excited 2p state and study how it is affected by the projection of the total angular momentum of incident light. The calculations indicate that the projection of the total angular momentum of the incident Bessel beam affects the alignment of atoms for sufficiently small targets with size less than 200 nm. This can be observed experimentally by measuring the linear polarization of the subsequent fluorescent light.

**Analytical results for nonlinear Compton scattering in short intense laser pulses**

**82**, 655820203 (2016)

**Abstract:** We study in detail the strong-field QED process of nonlinear Compton scattering in short intense plane wave laser pulses of circular polarization. Our main focus is placed on how the spectrum of the backscattered laser light depends on the shape and duration of the initial short intense pulse. Although this pulse shape dependence is very complicated and highly nonlinear, and has never been addressed explicitly, our analysis reveals that all the dependence on the laser pulse shape is contained in a class of three-parameter master integrals. Here we present completely analytical expressions for the nonlinear Compton spectrum in terms of these master integrals. Moreover, we analyse the universal behaviour of the shape of the spectrum for very high harmonic lines.

**Linear polarization of the characteristic x-ray lines following inner-shell photoionization of tungsten**

**93**, 033409 (2016)

**Abstract:** The linear polarization of the characteristic lines Lα1 (3d5/2→2p3/2) and Lα2 (3d3/2→2p3/2), following inner-shell photoionization of neutral tungsten, is analyzed both experimentally and theoretically. In the experiment, a tungsten target is photoionized by the primary emission of an x-ray tube with incident photon energies in the range of 10.2–30 keV. The σ and π components of the emitted fluorescence are measured by using a spectropolarimeter, based on x-ray diffraction at Bragg angles close to 45∘. The degree of linear polarization of the Lα1 and Lα2 lines is determined to be +(1.6±0.5)% and −(7±2)%, respectively. In addition, this degree of polarization is calculated within the framework of the density-matrix theory as a function of the incident photon energy. These calculations are in good agreement with the experimental results and show only a weak dependence of the degree of polarization on the energy of the incident photoionizing photon.

**Caustic structures in x-ray Compton scattering off electrons driven by a short intense laser pulse**

**18**, 023044 (2016)

**Abstract:** We study the Compton scattering of x-rays off electrons that are driven by a relativistically intense short optical laser pulse. The frequency spectrum of the laser-assisted Compton radiation shows a broad plateau in the vicinity of the laser-free Compton line due to a nonlinear mixing between x-ray and laser photons. Special emphasis is placed on how the shape of the short assisting laser pulse affects the spectrum of the scattered x-rays. In particular, we observe sharp peak structures in the plateau region, whose number and locations are highly sensitive to the laser pulse shape. These structures are interpreted as spectral caustics by using a semiclassical analysis of the laser-assisted QED matrix element, relating the caustic peak locations to the laser-driven electron motion.

**Many-electron effects on x-ray Rayleigh scattering by highly charged He-like ions**

**93**, 023418 (2016)

**Abstract:** The Rayleigh scattering of x rays by many-electron highly charged ions is studied theoretically. The many-electron perturbation theory, based on a rigorous quantum electrodynamics approach, is developed and implemented for the case of the elastic scattering of (high-energetic) photons by heliumlike ions. Using this elaborate approach, we here investigate the many-electron effects beyond the independent-particle approximation (IPA) as conventionally employed for describing the Rayleigh scattering. The total and angle-differential cross sections are evaluated for the x-ray scattering by heliumlike Ni^26+, Xe^52+, and Au^77+ ions in their ground state. The obtained results show that, for high-energetic photons, the effects beyond the IPA do not exceed 2% for the scattering by a closed K shell.

## 2015

**Relativistically prolonged lifetime of the 2s2p 3P0 level of zero nuclear-spin beryllium-like ions**

**17**, 103009 (2015)

**Abstract:** The E1M1 transition rate of the 2s2p{\ ³P₀\to 2s²\ ¹S₀} line in beryllium-like ions has been calculated within the framework of relativistic second-order perturbation theory. Both multiconfiguration and quantum-electrodynamical computations have been carried out independently to better understand and test for all major electron–electron correlation contributions in the representation of the initial, intermediate and final states. By comparing the results from these methods, which agree well for all ions along the beryllium isoelectronic sequence, the lifetime of the metastable 2s2p 3P0 level is found to be longer by about 2–3 orders of magnitude for all medium and heavy elements than was estimated previously. This makes the 3P0 level of beryllium-like ions to one of the longest living (low-lying) electronic excitations of a tightly bound system with potential applications for atomic clocks and in astro physics and plasma physics.

**Electronic structure theory of the superheavy elements**

**944**, 518 (2015)

**Abstract:** High-accuracy calculations of atomic properties of the superheavy elements (SHE) up to element 122 are reviewed. The properties discussed include ionization potentials, electron affinities and excitation energies, which are associated with the spectroscopic and chemical behavior of these elements, and are therefore of considerable interest. Accurate predictions of these quantities require high-order inclusion of relativity and electron correlation, as well as large, converged basis sets. The Dirac–Coulomb–Breit Hamiltonian, which includes all terms up to second order in the fine-structure constant a, serves as the framework for the treatment; higher-order Lamb shift terms are considered in some selected cases. Electron correlation is treated by either the multiconfiguration self-consistent-field approach or by Fock-space coupled cluster theory. The latter is enhanced by the intermediate Hamiltonian scheme, allowing the use of larger model (P) spaces. The quality of the calculations is assessed by applying the same methods to lighter homologs of the SHEs and comparing with available experimental information. Very good agreement is obtained, within a few hundredths of an eV, and similar accuracy is expected for the SHEs. Many of the properties predicted for the SHEs differ significantly from what may be expected by straightforward extrapolation of lighter homologs, demonstrating that the structure and chemistry of SHEs are strongly affected by relativity. The major scientific challenge of the calculations is to find the electronic structure and basic atomic properties of the SHE and assign its proper place in the periodic table. Significant recent developments include joint experimental–computational studies of the excitation spectrum of Fm and the ionization energy of Lr, with excellent agreement of experiment and theory, auguring well for the future of research in the field.

**Coherent population of magnetic sublevels of 2p₃/₂ state in hydrogenlike uranium by radiative recombination**

**2015**, 014027 (2015)

**Abstract:** The x-rays emitted in the process of radiative recombination (RR) of quasi-free electrons into 2p₃/₂ excited state of hydrogenlike uranium ion were studied experimentally. Both the RR x-ray and the subsequently emitted Lyα₁ x-ray were detected in time-coincidences. The angular distribution of the Lyα₁ x-rays varied as a function of the RR x-ray emission direction. This observation revealed the coherent population of magnetic sublevels of the 2p₃/₂ state in the hydrogenlike uranium ion.

**Experimental study of the dielectronic recombination into Li-like uranium**

**2015**, 014024 (2015)

**Abstract:** We have measured the x-rays following 116.15 MeV/u U⁸⁹⁺ collisions with H 2 at 35°, 90°, 120° and 150° observation angles with regard to the ion beam direction. From our experimental spectra combined with radiative electron capture calculations, we obtain angular distribution of characteristic x-rays L to K following the resonance transfer and excitation. Our result shows a good qualitative agreement with theoretical predictions.

**Nuclear magnetic dipole moment effect on the angular distribution of the K-alpha lines**

**166**, 014029 (2015)

**Abstract:** We present a theoretical analysis of the fine-structure transitions for helium-like heavy ions with non-zero nuclear spin. The angular distribution of these transitions is studied for its sensitivity with regard to the nuclear magnetic dipole moment. Detailed calculations, performed for the helium-like Sn48+, Xe52+ and Tl79+ ions with nuclear spin I=1/2, indicate that the emission pattern of the fine-structure resolved photons is significantly affected by the nuclear magnetic dipole moment and that this effect can be addressed experimentally at present storage ring facilities.

**Effect of bound-state dressing in laser-assisted radiative recombination**

**92**, 053426 (2015)

**Abstract:** We present a theoretical study on the recombination of a free electron into the ground state of a hydrogenlike ion in the presence of an external laser field. Emphasis is placed on the effects caused by the laser dressing of the residual ionic bound state. To investigate how this dressing affects the total and angle-differential cross section of laser-assisted radiative recombination (LARR) we apply first-order perturbation theory and the separable Coulomb-Volkov continuum ansatz. Using this approach, detailed calculations are performed for low-Z hydrogenlike ions and laser intensities in the range from I_L=10^12 to 10^13W/cm2. It is seen that the total cross section as a function of the laser intensity is remarkably affected by the bound-state dressing. Moreover, the laser dressing becomes manifest as asymmetries in the angular distribution and the (energy) spectrum of the emitted recombination photons.

**Ionization of H₂⁺ molecular ions by twisted Bessel light**

**92**, 043415 (2015)

**Abstract:** The photoionization of H+2 molecular ions is investigated for Bessel beams of twisted light. In particular, the angle-differential photoionization cross sections are evaluated for a macroscopic target of randomly distributed but initially aligned ions by using the nonrelativistic first-order perturbation theory. Detailed calculations of these cross sections and angular distributions are performed for different setups of the electron detectors and for selected opening angles of the Bessel beams and are compared with those for incident plane-wave radiation. It is shown that the modification in the angular distributions of the photoelectrons can be understood quite easily from the variations in the intensity pattern of the Bessel beams, relative to the size of the H+2 molecular ions.

**Polarization measurement of dielectronic recombination transitions in highly charged krypton ions**

**92**, 042702 (2015)

**Abstract:** We report linear polarization measurements of x rays emitted due to dielectronic recombination into highly charged krypton ions. The ions in the He-like through O-like charge states were populated in an electron-beam ion trap with the electron-beam energy adjusted to recombination resonances in order to produce Ka x rays. The x rays were detected with a newly developed Compton polarimeter using a beryllium scattering target and 12 silicon x-ray detector diodes sampling the azimuthal distribution of the scattered x rays. The extracted degrees of linear polarization of several dielectronic recombination transitions agree with results of relativistic distorted-wave calculations. We also demonstrate a high sensitivity of the polarization to the Breit interaction, which is remarkable for a medium-Z element like krypton. The experimental results can be used for polarization diagnostics of hot astrophysical and laboratory fusion plasmas.

**Target effects in negative-continuum-assisted dielectronic recombination**

**92**, 042708 (2015)

**Abstract:** The process of recombination of a quasifree electron into a bound state of an initially bare nucleus with the simultaneous creation of a bound-electron–free-positron pair is investigated. This process is called negative-continuum-assisted dielectronic recombination (NCDR). In a typical experimental setup, the initial electron is not free but bound in a light atomic target. In the present work, we study the effects of the atomic target on the single- and double-differential cross sections of positron production in the NCDR process. Calculations are performed within the relativistic framework based on QED theory, accounting for the electron-electron interaction to first order in perturbation theory. We demonstrate how the momentum distribution of the target electrons removes the nonphysical singularity of the differential cross section which occurs for the initially free and monochromatic electrons.

**Corrigendum: Rayleigh x-ray scattering from many-electron atoms and ions**

**48**, 189501 (2015)

**Abstract:** A theoretical analysis is presented for the elastic Rayleigh scattering of x-rays by many-electron atoms and ions. Special emphasis is placed on the angular distribution and linear polarization of the scattered photons for the case when the incident light is completely (linearly) polarized. Based on second-order perturbation theory and the independent particle approximation, we found that the Rayleigh angular distribution is strongly affected by the charge state and shell structure of the target ions or atoms. This effect can be observed experimentally at modern synchrotron facilities and might provide further insight into the structure of heavy atomic systems.

**Linear polarization of x-rays emitted in the decay of highly-charged ions via overlapping resonances**

**635**, 012020 (2015)

**Abstract:** The linear polarization of x-rays, emitted from highly-charged ions, has been studied within the framework of the density matrix theory and the multiconfiguration Dirac-Fock method. Emphasis was placed especially on two-photon cascades that proceed via intermediate overlapping resonances. For such two-step cascades, we here explore how the level-splitting of the resonances affects the linear polarization of the x-rays, and whether modifications in the degree of polarization may help determine small level-splittings in multiply- and highly-charged ions, if carefully analyzed along isoelectronic sequences. Detailed calculations are carried out for the 1s 2p2 J_i = 3/2 → 1s 2s 2p J = 1/2, 3/2 + γ1 → 1s2 2s J_f = 1/2 + γ1 + γ2 radiative cascade of lithium-like W^71+ ions. For this cascade, a quite remarkable increase of the (degree of) linear polarization is found for the second-step γ2 photons, if the level-splitting becomes smaller than Δω ≲ 0.2 a.u. ≈ 5.4 eV. Accurate polarization measurements of x-rays may therefore be also utilized in the future to ascertain small level-splittings in multiply- and highly-charged ions.

**Subshell-selective x-ray studies of radiative recombination of U⁹²⁺ ions with electrons for very low relative energies**

**92**, 032710 (2015)

**Abstract:** Radiative recombination (RR) into the K shell and L subshells of U92+ ions interacting with cooling electrons has been studied in an x-ray RR experiment at the electron cooler of the Experimental Storage Ring at GSI. The measured radiative recombination rate coefficients for electron-ion relative energies in the range 0–1000 meV demonstrate the importance of relativistic effects. The observed asymmetry of the measured K-RR x-ray emission with respect to the cooling energy, i.e., zero average relative velocity (〈vrel〉=0), are explained by fully relativistic RR calculations. With our new approach, we show that the study of the angular distribution of RR photons for different relative energies opens new perspectives for detailed understanding of the RR of ions with cooling electrons in cold magnetized plasma.

**High-Resolution Spectroscopy on the Laser-Cooling Candidate La⁻**

**115**, 113001 (2015)

**Abstract:** The bound-bound transition from the 5d²6s² ³F₂e ground state to the 5d6s²6p ³D₁o excited state in negative lanthanum has been proposed as a candidate for laser cooling, which has not yet been achieved for negative ions. Anion laser cooling holds the potential to allow the production of ultracold ensembles of any negatively charged species. We have studied the aforementioned transition in a beam of negative La ions by high-resolution laser spectroscopy. The center-of-gravity frequency was measured to be 96.592 80(10) THz. Seven of the nine expected hyperfine structure transitions were resolved. The observed peaks were unambiguously assigned to the predicted hyperfine transitions by a fit, confirmed by multiconfigurational self-consistent field calculations. From the determined hyperfine structure we conclude that La⁻ is a promising laser cooling candidate. Using this transition, only three laser beams would be required to repump all hyperfine levels of the ground state.

**Triple ionization of atomic Cd involving 4p⁻1 and 4s⁻1 inner-shell holes**

**92**, 023414 (2015)

**Abstract:** The triple ionization spectrum of atomic Cd formed upon the removal of a 4p or a 4s inner-shell electron and subsequent Auger decays has been obtained at 200 eV photon energy. By using a versatile multielectron coincidence detection technique based on a magnetic bottle spectrometer in combination with multiconfiguration Dirac-Fock calculations, Auger cascades leading to tricationic final states have been analyzed and final-state configurations have been identified. The most prominent Auger cascades leading to the ground state of Cd³⁺ have been identified in good agreement with theory.

**Compton scattering of twisted light: Angular distribution and polarization of scattered photons**

**92**, 013401 (2015)

**Abstract:** Compton scattering of twisted photons is investigated within a nonrelativistic framework using first-order perturbation theory. We formulate the problem in the density-matrix theory, which enables one to gain new insights into scattering processes of twisted particles by exploiting the symmetries of the system. In particular, we analyze how the angular distribution and polarization of the scattered photons are affected by the parameters of the initial beam such as the opening angle and the projection of orbital angular momentum. We present analytical and numerical results for the angular distribution and the polarization of Compton scattered photons for initially twisted light and compare them with the standard case of plane-wave light.

**Scattering of twisted relativistic electrons by atoms**

**92**, 012705 (2015)

**Abstract:** The Mott scattering of high-energetic twisted electrons by atoms is investigated within the framework of the first Born approximation and Dirac's relativistic equation. Special emphasis is placed on the angular distribution and longitudinal polarization of the scattered electrons. In order to evaluate these angular and polarization properties we consider two experimental setups in which the twisted electron beam collides with either a single well-localized atom or macroscopic atomic target. Detailed relativistic calculations have been performed for both setups and for the electrons with kinetic energy from 10 to 1000 keV. The results of these calculations indicate that the emission pattern and polarization of outgoing electrons differ significantly from the scattering of plane-wave electrons and can be very sensitive to the parameters of the incident twisted beam. In particular, it is shown that the angular- and polarization-sensitive Mott measurements may reveal valuable information about both the transverse and longitudinal components of the linear momentum and the projection of the total angular momentum of twisted electron states. Thus, the Mott scattering emerges as a diagnostic tool for the relativistic vortex beams.

**Collinear laser spectroscopy of atomic cadmium: Extraction of nuclear magnetic dipole and electric quadrupole moments**

**69**, 164 (2015)

**Abstract:** Hyperfine structure A and B factors of the atomic 5s5p ³P₂ -> 5s6s ³S₁ transition are determined from collinear laser spectroscopy data of ¹⁰⁷−¹²³Cd and ¹¹¹m−¹²³mCd. Nuclear magnetic moments and electric quadrupole moments are extracted using reference dipole moments and calculated electric field gradients, respectively. The hyperfine structure anomaly for isotopes with s₁/₂ and d₅/₂ nuclear ground states and isomeric h11/2 states is evaluated and a linear relationship is observed for all nuclear states except s₁/₂. This corresponds to the Moskowitz-Lombardi rule that was established in the mercury region of the nuclear chart but in the case of cadmium the slope is distinctively smaller than for mercury. In total four atomic and ionic levels were analyzed and all of them exhibit a similar behaviour. The electric field gradient for the atomic 5s5p ³P₂ level is derived from multi-configuration Dirac-Hartree-Fock calculations in order to evaluate the spectroscopic nuclear quadrupole moments. The results are consistent with those obtained in an ionic transition and based on a similar calculation.

**Combined linear polarization and angular distribution measurements of x-rays for precise determination of multipole-mixing in characteristic transitions of high- Z systems**

**48**, 144031 (2015)

**Abstract:** By applying novel-type position sensitive x-ray detectors as Compton polarimeters we recently performed a study of the linear polarization of Lyman-α₁ radiation following radiative electron capture into initially bare uranium ions. It was found that a model-independent determination of the ratio of the E1 and M2 transition amplitudes, and consequently of the corresponding transition rates, is feasible by combining the linear polarization data with a measurement of the angular distribution of the emitted radiation. In this work a detailed description of the underlying experimental technique for combined measurements of the linear polarization and the angular distribution of characteristic transitions in high-Z ions is presented. Special emphasis is given to the application of two, two-dimensional position-sensitive x-ray detectors for Compton polarimetry of hard x-rays. Moreover, we demonstrate the polarimeter efficiency of such detector systems can be significantly improved if events, where the charge is spread over neighboring segments, are reconstructed to be used in the polarization analysis.

**Ground-state excitation of heavy highly-charged ions**

**48**, 144006 (2015)

**Abstract:** We have studied the excitation of H-like and He-like uranium (U^91+ and U^90+ ) in relativistic collisions with gaseous targets by observing the subsequent x-ray emission. The experiment was conducted at the ESR storage ring of the GSI accelerator facility in Darmstadt, Germany. The measurements were performed with a newly developed multi-phase target at different collision energies. This enabled us to explore the proton (nucleus) impact excitation as well as the electron impact excitation processes in the relativistic collisions. The large fine-structure splitting in uranium allowed us to unambiguously resolve excitation to different L-shell levels. Moreover, information about the population of different magnetic sublevels has been obtained via an angular differential study of the decay photons associated with the subsequent de-excitation process. The experimental results are compared with calculations performed within the relativistic framework including excitation mechanisms due to both protons (nucleus) and electrons.

**Dielectronic recombination rate coefficients of initially rubidium-like tungsten**

**69**, 140 (2015)

**Abstract:** Ab initio calculations of dielectronic recombination (DR) rate coefficients of initially rubidium-like W³⁷⁺ ions have been performed for the electron temperatures from 1 eV to 5×10⁴ eV, by using the Flexible Atomic Code based on the relativistic configuration-interaction method. Special attention has been paid to the partial contributions to total DR rate coefficients as associated with the excitation of individual subshells. A detailed comparison of the calculations shows that the excitation from 4p subshell dominates total DR rate coefficients followed by the excitations from 4s and 4d subshells, while the contribution of excitations from 3l(l=s, p, d) subshells becomes important only at high temperatures. Besides, it is found that the electron excitations associated with Δ n=0,1 dominate at low-temperature plasmas, however, the excitations associated with Δ n≥2 become non-negligible at high-temperature ones.

**Spectroscopy of berylliumlike xenon ions using dielectronic recombination**

**48**, 144008 (2015)

**Abstract:** Be-like ¹³⁶Xe⁵⁰⁺ ions have been investigated employing the resonant electron-ion collision process of dielectronic recombination (DR) as a spectroscopic tool. The experiments were performed at the experimental storage ring in Darmstadt, Germany, using its electron cooler as a target for free electrons. DR Rydberg resonance series 2s²+e⁻ \to 2s 2pj n lj for the associated intra-L-shell transitions 2s² ¹S₀ - 2s 2p₁/₂ ³P₁, 2s² ¹S₀ - 2s 2p₃/₂ ³P₂ and 2s² ¹S₀ - 2s 2p₃/₂ ¹P₁ were observed with high resolution. In addition to these excitations from the ground state we determined resonances associated with excitations 2s 2p₁/₂ ³P₀ to 2p₁/₂ 2p₃/₂ ³P₁ of ions initially in the metastable 2s 2p₁/₂ ³P₀ state. The corresponding excitation energies were determined to be E(¹S₀ \to ³P₁)=127.269(46) eV, E(¹S₀ \to ³P₂)=469.474(81) eV and E(¹S₀ to ¹P₁)=532.801(16) eV and E(³P₀ to 2p₁/₂ 2p₃/₂ ³P₁)=533.733(22) eV. These excitation energies are compared with previous measurements and with recent state-of-the-art atomic structure calculations.

**Stepwise contraction of the n f Rydberg shells in the 3d photoionization of multiply-charged xenon ions**

**48**, 144003 (2015)

**Abstract:** Triple photoionization of Xe³⁺, Xe⁴⁺ and Xe⁵⁺ ions has been studied in the energy range 670-750 eV, including the 3d ionization threshold. The photon-ion merged-beam technique was used at a synchrotron light source to measure the absolute photoionization cross sections. These cross sections exhibit a progressively larger number of sharp resonances as the ion charge state is increased. This clearly visualizes the re-ordering of the ε f continuum into a regular series of (bound) Rydberg orbitals as the ionic core becomes more attractive. The energies and strengths of the resonances are extracted from the experimental data and are further analysed by relativistic atomic-structure calculations.

**Rayleigh x-ray scattering from many-electron atoms and ions**

**48**, 144015 (2015)

**Abstract:** A theoretical analysis is presented for the elastic Rayleigh scattering of x-rays by many-electron atoms and ions. Special emphasis is placed on the angular distribution and linear polarization of the scattered photons for the case when the incident light is completely (linearly) polarized. Based on second-order perturbation theory and the independent particle approximation, we found that the Rayleigh angular distribution is strongly affected by the charge state and shell structure of the target ions or atoms. This effect can be observed experimentally at modern synchrotron facilities and might provide further insight into the structure of heavy atomic systems.

**Reply to Comment on `Hyperfine-induced modifications to the angular distribution of the Kα₁ x-ray emission' **

**91**, 056502 (2015)

**Abstract:** In a recent work, the Kα₁ (1s 2p₃/₂ ¹,³P₁,₂ → 1s² ¹S₀) x-ray emission following the radiative electron capture into initially hydrogen-like ions has been explored for ions with nonzero nuclear spin (I ≠ 0). A rather strong influence upon the angular distribution of the (hyperfine- and fine-structure averaged) Kα₁ radiation was found, especially for isotopes with nuclear spin I=1/2, while this effect are less important for isotopes with nuclear spin I>1/2. Two comments were made by Inal and Benmouna about this work with regard to (i) the incoherent summation of the individual hyperfine components of the 1s2p3/2 1P1→1s21S0 transition and (ii) the treatment of the hyperfine-induced E1-M2 multipole mixing in the 1s 2p3/2 ³P₂ → 1s², ¹S₀ fine-structure component. While we agree with the first comment and here provide updated anisotropy parameters, the hyperfine-induced modification of the Kα₁ emission remains valid and may help in the future to determine the nuclear parameters of radioactive isotopes. We also explain that the hyperfine-induced E1-M2 mixing has already been fully taken into account in our previous work.

**Ab initio MCDHF calculations of electronnucleus interactions**

**90**, 054011 (2015)

**Abstract:** We present recent advances in the development of atomic ab initio multiconfiguration Dirac-Hartree-Fock theory, implemented in the GRASP relativistic atomic structure code. For neutral atoms, the deviations of properties calculated within the Dirac-Hartree-Fock (DHF) method (based on independent particle model of an atomic cloud) are usually dominated by electron correlation effects, i.e. the non-central interactions of individual electrons. We present the recent advances in accurate calculations of electron correlation effects in small, medium, and heavy neutral atoms. We describe methods of systematic development of multiconfiguration expansions leading to systematic, controlled improvement of the accuracy of the ab initio calculations. These methods originate from the concept of the complete active space (CAS) model within the DHF theory, which, at least in principle, permits fully relativistic calculations with full account of electron correlation effects. The calculations within the CAS model on currently available computer systems are feasible only for very light systems. For heavier atoms or ions with more than a few electrons, restrictions have to be imposed on the multiconfiguration expansions. We present methods and tools, which are designed to extend the numerical calculations in a controlled manner, where multiconfiguration expansions account for all leading electron correlation effects. We show examples of applications of the GRASP code to calculations of hyperfine structure constants, but the code may be used for calculations of arbitrary bound-state atomic properties. In recent years it has been applied to calculations of atomic and ionic spectra (transition energies and rates), to determinations of nuclear electromagnetic moments, as well as to calculations related to interactions of bound electrons with nuclear electromagnetic moments leading to violations of discrete symmetries.

**Relativistic configuration-interaction calculation of Kα transition energies in beryllium-like argon**

**90**, 054003 (2015)

**Abstract:** Relativistic configuration-interaction calculations have been performed for energy levels of the low-lying and core-excited states of beryllium-like argon, Ar14+. These calculations include the one-loop quantum electrodynamics (QED) effects as obtained by two different methods: the screening-potential approach and the model QED operator approach. The calculations are supplemented by a systematic estimation of the uncertainties of the theoretical predictions.

**Linear polarization of x-ray transitions due to dielectronic recombination in highly charged ions**

**91**, 042705 (2015)

**Abstract:** The linear polarization of x rays produced by dielectronic recombination into highly charged xenon ions was measured at an electron beam ion trap using the Compton polarimetry technique. This opens numerous possibilities for diagnostics of anisotropies of hot plasmas. Moreover, it was observed that the polarization of x rays, following the dielectronic capture populating the [1s 2s2 2p1/2]_1 state, is highly sensitive to the Breit interaction. The experimental results for this transition rule out by 5σ calculations not taking the Breit interaction into account.

**Narrowband inverse Compton scattering x-ray sources at high laser intensities**

**91**, 033402 (2015)

**Abstract:** Narrowband x- and γ-ray sources based on the inverse Compton scattering of laser pulses suffer from a limitation of the allowed laser intensity due to the onset of nonlinear effects that increase their bandwidth. It has been suggested that laser pulses with a suitable frequency modulation could compensate this ponderomotive broadening and reduce the bandwidth of the spectral lines, which would allow one to operate narrowband Compton sources in the high-intensity regime. In this paper we therefore present the theory of nonlinear Compton scattering in a frequency-modulated intense laser pulse. We systematically derive the optimal frequency modulation of the laser pulse from the scattering matrix element of nonlinear Compton scattering, taking into account the electron spin and recoil. We show that, for some particular scattering angle, an optimized frequency modulation completely cancels the ponderomotive broadening for all harmonics of the backscattered light. We also explore how sensitively this compensation depends on the electron-beam energy spread and emittance, as well as the laser focusing.

**Compton polarimetry using double-sided segmented x-ray detectors**

**583**, 012041 (2015)

**Abstract:** Hard x-ray polarimetry of radiation emitted in collisions of heavy ions, electrons or photons with matter provides detailed information on the collision dynamics as well as of the atomic structure in the presence of extreme field strengths. Moreover, it also opens a route for polarization diagnosis of spin-polarized ion and electron beams which, for example, might be useful in future parity non-conservation studies. Owing to recent progress in the development of highly segmented solid-state detectors, a novel type of polarimeter for the hard x-ray regime has become available. Applied as Compton polarimeters, two-dimensional position-sensitive x-ray detectors now allow for precise and efficient measurements of x-ray linear polarization properties. In this report recent polarimetry studies using such detector systems are reviewed.

**Electron-ion collision spectroscopy: Lithium-like xenon ions**

**91**, 012710 (2015)

**Abstract:** The resonant process of dielectronic recombination (DR) has been applied as a spectroscopic tool to investigate intra-L-shell excitations 2s−2pj in Li-like 136Xe51+. The experiments were carried out at the electron cooler of the Experimental Storage Ring of the GSI-Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany. The observed center-of-mass energy range (0–505 eV) covers all resonances associated with the 2s+e−→(2p1/2nlj)J and (2p3/2nlj)J DR processes. Energies and strengths of isolated 2p1/2n and 2p3/2n DR-resonance groups were obtained for principal quantum numbers n up to 43 and 36, respectively. The 2s−2p1/2 and 2s−2p3/2 excitation energies were deduced to be 119.816(42) eV and 492.174(52) eV. The excitation energies are compared with previous measurements of other groups and with recent QED calculations. In addition, the experimental spectra and extracted resonance strengths are compared with multiconfiguration Dirac-Fock calculations. Measurements and theory are found to be in good agreement with each other.

**Interaction of twisted light with many-electron atoms and ions**

**91**, 013403 (2015)

**Abstract:** The excitation of many-electron atoms and ions by twisted light has been studied within the framework of the density-matrix theory and Dirac's relativistic equation. Special attention is paid to the magnetic sublevel population of excited atomic states as described by means of the alignment parameters. General expressions for the alignment of the excited states are obtained under the assumption that the photon beam, prepared as a coherent superposition of two twisted Bessel states, irradiates a macroscopic target. We demonstrate that for this case the population of excited atoms can be sensitive to both the transverse momentum and the (projection of the) total angular momentum of the incident radiation. While the expressions are general and can be employed to describe the photoexcitation of any atom, independent on its shell structure and number of electrons, we performed calculations for the 3s→3p transition in sodium. These calculations indicate that the “twistedness” of incoming radiation can lead to a measurable change in the alignment of the excited P3/22 state as well as the angular distribution of the subsequent fluorescence emission.

## 2014

**Relativistic calculations of double K-shell-photoionization cross sections for neutral medium-Z atoms**

**90**, 063422 (2014)

**Abstract:** Fully relativistic calculations are presented for the double K-shell photoionization cross section for several neutral medium-Z atoms, from magnesium (Z=10) up to silver (Z=47). The calculations take into account all multipoles of the absorbed photon as well as the retardation of the electron-electron interaction. The approach is based on the partial-wave representation of the Dirac continuum states and uses the Green's-function technique to represent the full Dirac spectrum of intermediate states. The method is strictly gauge invariant, which is used as an independent cross-check of the computational procedure. The calculated ratios of the double-to-single K-shell ionization cross sections are compared with the experimental data and with previous computations.

**Determination of small level splittings in highly charged ions via angle-resolved measurements of characteristic x rays**

**90**, 052515 (2014)

**Abstract:** The angular distribution and the photon-photon angular correlation have been investigated for the x-ray emission from two-step radiative cascades that proceed via overlapping intermediate resonances. In particular, density matrix theory is applied in order to explore how the splitting of these intermediate levels affects the subsequent x-ray emission and whether measurements of photon angular distributions may help reveal level crossings in highly charged ions, if analyzed along isoelectronic sequences. Detailed computations within the multiconfiguration Dirac-Fock method were performed especially for the two-step 1s2p2J_i=1/2,3/2→1s2s2pJ=1/2,3/2+γ1→1s22sJ_f=1/2+γ1+γ2 cascade of lithiumlike ions, for which a level crossing of the two 1s2s2pJ=1/2,3/2 intermediate resonances occurs in the range 74≤Z≤79. For this cascade, a remarkably strong depolarization effect, associated with the finite lifetime of these intermediate levels, is found for the angular distribution and the photon-photon correlation function for all level splittings Δω≲0.2a.u.≈5.4 eV. We therefore suggest that accurate angle-resolved measurements of the x-ray emission may serve also as a tool for determining small level splittings in excited highly charged ions.

**Observation of Coherence in the Time-Reversed Relativistic Photoelectric Effect**

**113**, 113001 (2014)

**Abstract:** The photoelectric effect has been studied in the regime of hard x rays and strong Coulomb fields via its time-reversed process of radiative recombination (RR). In the experiment, the relativistic electrons recombined into the 2p3/2 excited state of hydrogenlike uranium ions, and both the RR x rays and the subsequently emitted characteristic x rays were detected in coincidence. This allowed us to observe the coherence between the magnetic substates in a highly charged ion and to identify the contribution of the spin-orbit interaction to the RR process.

**Relativistic configuration-interaction calculation of Kα transition energies in berylliumlike iron**

**90**, 022509 (2014)

**Abstract:** We perform relativistic configuration-interaction calculations of the energy levels of the low-lying and core-excited states of berylliumlike iron, Fe^(22+). The results include the QED contributions calculated by two different methods, the model QED operator approach and the screening-potential approach. The uncertainties of theoretical energies are estimated systematically. The predicted wavelengths of the Kα transitions in berylliumlike iron improve previous theoretical results and compare favorably with the experimental data.

**Absorption of twisted light by hydrogenlike atoms**

**90**, 013425 (2014)

**Abstract:** Theoretical analysis of the excitation of low-Z hydrogenlike atoms by incident twisted light is presented. Emphasis is placed on the cross sections that describe transitions between particular atomic substates. Simple expressions for these partial cross sections are derived using the nonrelativistic first-order perturbation theory and the momentum representation of the photon wave functions. Based on the developed approach, calculations have been performed for the 1s→2p and 2p→3d transitions induced in the course of interaction of twisted (Bessel) light with a macroscopic hydrogen target. Results of these calculations, supported by an analytical analysis, clearly indicate that the sublevel population of residual atoms following absorption of twisted photons differs much from what is expected for the standard plane-wave case; this effect can be easily observed experimentally by measuring the linear polarization of the subsequent fluorescent emission.

**Structured x-ray beams from twisted electrons by inverse Compton scattering of laser light**

**90**, 012118 (2014)

**Abstract:** The inverse Compton scattering of laser light on high-energetic twisted electrons is investigated with the aim to construct spatially structured x-ray beams. In particular, we analyze how the properties of the twisted electrons, such as the topological charge and aperture angle of the electron Bessel beam, affect the energy and angular distribution of scattered x rays. We show that with suitably chosen initial twisted electron states one can synthesize tailor-made x-ray beam profiles with a well-defined spatial structure, in a way not possible with ordinary plane-wave electron beams.

**Enhancing the Macroscopic Yield of Narrow-Band High-Order Harmonic Generation by Fano Resonances**

**112**, 233002 (2014)

**Abstract:** Resonances in the photoabsorption spectrum of the generating medium can modify the spectrum of high-order harmonics. In particular, window-type Fano resonances can reduce photoabsorption within a narrow spectral region and, consequently, lead to an enhanced emission of high-order harmonics in absorption-limited generation conditions. For high harmonic generation in argon it is shown that the 3s3p6np1P1 window resonances (n=4, 5, 6) give rise to enhanced photon yield. In particular, the 3s3p64p1P1 resonance at 26.6 eV allows a relative enhancement up to a factor of 30 in a 100 meV bandwidth compared to the characteristic photon emission of the neighboring harmonic order. This enhanced, spectrally isolated, and coherent photon emission line has a relative energy bandwidth of only ΔE/E=3×10^−3. Therefore, it might be very useful for applications such as precision spectroscopy or coherent diffractive imaging. The presented mechanism can be employed for tailoring and controlling the high harmonic emission of manifold target materials.

**Radiative capture of twisted electrons by bare ions**

**16**, 053024 (2014)

**Abstract:** Recent advances in the production of twisted electron beams with a subnanometer spot size offer unique opportunities to explore the role of orbital angular momentum in basic atomic processes. In the present work, we address one of these processes: radiative recombination of twisted electrons with bare ions. On the basis of the density matrix formalism and the non-relativistic Schrödinger theory, analytical expressions are derived for the angular distribution and the linear polarization of photons emitted due to the capture of twisted electrons into the ground state of (hydrogen-like) ions. We show that these angular and polarization distributions are sensitive to both the transverse momentum and the topological charge of the electron beam. To observe in particular the value of this charge, we propose an experiment that makes use of the coherent superposition of two twisted beams.

**Mapping spin-orbit activated interchannel coupling**

**106**, 13001 (2014)

**Abstract:** Recent advances in the generation of femtosecond extreme ultraviolet pulses have opened up the possibility to study final-state wave functions in photoemission experiments. Here, we investigate, for the first time using femtosecond time-resolved core-level spectroscopy, the feasibility of observing the buildup of a state correlation in a direct time domain. Giant changes in the ratio of photoemission cross-sections of spin-orbit split core states, the branching ratio, are identified. Multi-configuration Dirac-Fock calculations show that the origin of the branching ratio deviation is due to strong core-valence interactions. The possibility to tune this interaction by charge transfer offers intriguing opportunities to study correlation effects in solid and molecular systems in the future.

**Inelastic Raman scattering of light by hydrogenlike ions**

**89**, 042501 (2014)

**Abstract:** The inelastic Raman scattering of light by hydrogenlike ions has been studied by means of second-order perturbation theory and the relativistic Coulomb Green's-function approach. In particular, we investigate the total and angle-differential Raman cross sections as well as the magnetic sublevel population of the residual (excited) ions. Detailed calculations are performed for the inelastic scattering of photons by neutral hydrogen as well as hydrogenlike xenon and uranium ions, accompanied by the 1s1/2→2s1/2, 1s1/2→2p1/2, and 1s1/2→2p3/2 transitions. Moreover, we discuss how the Raman scattering is affected by relativistic and resonance effects as well as the higher-multipole contributions to the electron-photon interaction.

**Interaction of Relativistic Electron-Vortex Beams with Few-Cycle Laser Pulses**

**112**, 134801 (2014)

**Abstract:** We study the interaction of relativistic electron-vortex beams (EVBs) with laser light. Exact analytical solutions for this problem are obtained by employing the Dirac-Volkov wave functions to describe the (monoenergetic) distribution of the electrons in vortex beams with well-defined orbital angular momentum. Our new solutions explicitly show that the orbital angular momentum components of the laser field couple to the total angular momentum of the electrons. When the field is switched off, it is shown that the laser-driven EVB coincides with the field-free EVB as reported by Bliokh et al. [Phys. Rev. Lett. 107, 174802 (2011)]. Moreover, we calculate the probability density for finding an electron in the beam profile and demonstrate that the center of the beam is shifted with respect to the center of the field-free EVB.

**The Feynman tools for quantum information processing: Design and implementation**

**185**, 1697 (2014)

**Abstract:** The Feynman tools have been re-designed with the goal to establish and implement a high-level (computer) language that is capable to deal with the physics of finite, n

-qubit systems, from frequently required computations to mathematically advanced tasks in quantum information processing. In particular, emphasis has been placed to introduce a small but powerful set of keystring-driven commands in order to support both, symbolic and numerical computations. Though the current design is implemented again within the framework of Maple, it is general and flexible enough to be utilized and combined with other languages and computational environments. The present implementation facilitates a large number of computational tasks, including the definition, manipulation and parametrization of quantum states, the evaluation of quantum measures and quantum operations, the evolution of quantum noise in discrete models, quantum measurements and state estimation, and several others. The design is based on a few high-level commands, with a syntax close to the mathematical notation and its use in the literature, and which can be generalized quite readily in order to solve computational tasks at even higher degree of complexity.

In this work, I present and discuss the (re-design of the) Feynman tools and make major parts of the code available for public use. Moreover, a few selected examples are shown and demonstrate possible application of this toolbox. The Feynman tools are provided as Maple library and can hence be used on all platforms on which this computer-algebra system is accessible.

**Hyperfine-induced modifications to the angular distribution of the Kα1x-ray emission**

**89**, 022513 (2014)

**Abstract:** The angular distribution of the Kα_{1} (1s2p_{3/2}^{1,3}P_{1,2}→1s^{21}S_{0}) x-ray emission following the radiative electron capture into initially hydrogenlike ions with nonzero nuclear spin has been studied within the density matrix theory and the multiconfiguration Dirac-Fock method. Emphasis is placed especially upon the hyperfine interaction and how this interaction of the magnetic moment of the nucleus with those of the electrons affects the angular properties of the Kα_{1} radiation. Calculations were performed for selected isotopes of heliumlike Sn48+, Xe52+, and Tl79+ ions. A quite sizable contribution of the hyperfine interaction upon the Kα_{1} angular emission is found for isotopes with nuclear spin I = 1/2, while its effect is suppressed for (most) isotopes with nuclear spin I > 1/2. We therefore suggest that accurate measurements of the Kα_{1} angular distribution at ion storage rings can be utilized as a tool for determining the nuclear parameters of rare stable and radioactive isotopes with I ≥ 1/2.

**Core-valence double photoionization of atomic mercury**

**89**, 013411 (2014)

**Abstract:** Multielectron coincidence spectroscopy has been used to study core 4f valence 5d, 6s double photoionization of atomic mercury. Multiconfiguration Dirac–Fock calculations were performed to calculate the energies and to estimate the single-photon intensities of the 4f^{13}(5d^{9}6s^{2} + 5d^{10}6s^{1}) double-ionized states of atomic mercury. Reasonable agreement between the measured and simulated spectra is found if the relaxation effects of the bound-state density is taken into account in the computation of the photoionization amplitudes.

## 2013

**Polarization correlations in the elastic Rayleigh scattering of photons by hydrogenlike ions**

**88**, 062515 (2013)

**Abstract:** The (elastic) Rayleigh scattering of hard x rays by hydrogenlike ions has been investigated within the framework of second-order perturbation theory and Dirac's relativistic equation. The focus of this study was, in particular, on two questions: (i) How is the polarization of scattered photons affected if the incident light is itself (linearly) polarized, and (ii) how do the nondipole contributions to the electron-photon interaction and the relativistic contraction of the wave functions influence such a polarization transfer? Detailed calculations were performed for Ne9+, Xe53+, and U91+ targets and for photon energies up to ten times the 1s ionization threshold of the ions. From the comparison of these fully relativistic computations with the (nonrelativistic) dipole approximation we conclude that relativistic and higher-multipole effects often lead to a significant or even complete depolarization for heavy targets and at high photon energies.

**Atomic ionization of hydrogen-like ions by twisted photons: angular distribution of emitted electrons**

**46**, 205002 (2013)

**Abstract:** We investigate the angular distribution of electrons that are emitted in the ionization of hydrogen-like ions by twisted photons. Analysis is performed based on the first-order perturbation theory and the non-relativistic Schrödinger equation. Special attention is paid to the dependence of the electron emission pattern on the impact parameter b of the ion with respect to the centre of the twisted wave front. In order to explore such a dependence, detailed calculations were carried out for the photoionization of the 1s ground and 2 p_y excited states of neutral hydrogen atoms. Based on these calculations, we argue that for relatively small impact parameters, the electron angular distributions may be strongly affected by altering the position of the atom within the wave front. In contrast, if the atom is placed far from the front centre, the emission pattern of the electrons is independent of the impact parameter b and resembles that observed in the photoionization by plane wave photons.

**Two-photon decay of inner-shell vacancies in heavy atoms**

**88**, 042512 (2013)

**Abstract:** Based on the second-order perturbation theory, we investigate the two-photon decay of K-shell vacancies in heavy atoms. The many-electron transition amplitude that occurs in the theory is evaluated by means of the independent particle approximation (IPA). By using this approach, computations are performed for the decay of neutral gold and are directly compared with recent experimental data, not relying on any scaling assumptions. The obtained results confirm previously identified discrepancies between the IPA theory and the experiment for the 2s→1s transition, and an apparent “resonance” region of the 3s→1s transition, but they show a moderate agreement with the measured data for the 3d→1s and 4s+4d→1s cases. Moreover, with the help of the IPA we discuss the validity of the nonrelativistic scaling that was employed in the past to estimate the relative two-photon transition probabilities P in heavy atoms based on calculations done for lighter elements and different decay geometries. We find, in particular, that the electric-dipole angular distribution of emitted photons holds rather well even in the high-Z domain, while the assumption that the relative probability P is independent of nuclear charge may result in 10–30% inaccuracy of theoretical predictions.

**Bessel beams of laser-driven two-level atoms**

**2013**, 014067 (2013)

**Abstract:** We study Bessel beams of two-level atoms that are coupled to a linearly polarized laser field. For such atom beams, we construct exact Bessel-type solutions of the Schrödinger equation beyond the paraxial approximation for beam propagation. In particular, we examine the probability density for Bessel beams of neutral two-level atoms driven by a laser field but without the level damping being taken into account. We show how the radial dependence of the probability density (from the beam axis) can be affected by tuning the parameters of the atom–laser system, such as the resonant frequency and amplitude of the laser field and/or the nuclear charge and velocity of the atomic beam.

**Parity violation in beryllium-like heavy ions**

**2013**, 014027 (2013)

**Abstract:** A novel scheme is proposed for studying the parity-violating (PV) effects in beryllium-like heavy ions. It is based on the application of circularly polarized ultraviolet light for inducing a single-photon transition between the metastable 1s^(2)2s2p^(3)P_0 and the short-lived 1s^(2)2s2p^(3)P_1 states. We argue that the cross section of such a photoabsorption process is sensitive to the mixing between the allowed magnetic dipole (M1) and the PV electric dipole (E1) excitation channels. Based on relativistic calculations, we find that the PV-mixing may influence the cross section at the level of 10^(−5) % for beryllium-like uranium, U^(88+).

**Ab initio calculations of the 2p_{3/2}-2p_{1/2} fine-structure splitting in boronlike ions**

**88**, 032518 (2013)

**Abstract:** We have performed ab initio QED calculations of the (1s)^{2}(2s)^{2}2p_{3/2}-(1s)^{2}(2s)^{2}2p_{1/2} fine-structure splitting along the boron isoelectronic sequence for all ions with 17 ≤ Z ≤ 100. This level splitting was evaluated within the extended Furry picture and by making use of four different screening potentials in order to estimate the effects of interelectronic correlations. The accuracy of the predicted transition energies has been improved significantly when compared with previous computations.

**Photoelectron angular distributions for the two-photon sequential double ionization of xenon by ultrashort extreme ultraviolet free electron laser pulses**

**46**, 164022 (2013)

**Abstract:** Xenon atoms are double-ionized by sequential two-photon absorption by ultrashort extreme ultraviolet free-electron laser pulses with a photon energy of 23.0 and 24.3 eV, produced by the SPring-8 Compact SASE Source test accelerator. The angular distributions of photoelectrons generated by two-photon double ionization are obtained using velocity map imaging. The results are reproduced reasonably well by the present theoretical calculations within the multi-configurational Dirac–Fock approach.

**Bessel beams of two-level atoms driven by a linearly polarized laser field**

**67**, 167 (2013)

**Abstract:** We study Bessel beams of two-level atoms that are driven by a linearly polarized laser field. Starting from the Schrödinger equation, we determine the states of two-level atoms in a plane-wave field respecting propagation directions both of the atom and the field. For such laser-driven two-level atoms, we construct Bessel beams beyond the typical paraxial approximation. We show that the probability density of these atomic beams obtains a non-trivial, Bessel-squared-type behavior and can be tuned under the special choice of the atom and laser parameters, such as the nuclear charge, atom velocity, laser frequency, and propagation geometry of the atom and laser beams. Moreover, we spatially and temporally characterize the beam of hydrogen and selected (neutral) alkali-metal atoms that carry non-zero orbital angular momentum (OAM). The proposed spatiotemporal Bessel states (i) are able to describe, in principle, twisted states of any two-level system which is driven by the radiation field and (ii) have potential applications in atomic and nuclear processes as well as in quantum communication.

**Polarization of M2 Line Emitted Following Electron-Impact Excitation of Beryllium-Like Ions**

**30**, 063401 (2013)

**Abstract:** Detailed calculations are carried out for the electron-impact excitation cross sections from the ground state to the individual magnetic sublevels of the 1s2s^(2) 2p_(3/2)J = 2 excited state of highly-charged beryllium-like ions by using a fully relativistic distorted-wave (RDW) method. The contributions of the Breit interaction to the linear polarization of the 1s2s^(2) 2p_(3/2)J = 2 → 1s^(2) 2s^(2)J = 0 magnetic quadrupole (M2) line are investigated systematically for the beryllium isoelectronic sequence with 42 ≤ Z ≤ 92. It is found that the Breit interaction depolarizes significantly the linear polarization of the M2 fluorescence radiation and that these depolarization effects increase as the incident electron energy and/or the atomic number is enlarged.

**Two-photon energy distribution from the decay of the 2 ¹S₀ state in He-like uranium**

**87**, 062510 (2013)

**Abstract:** We have performed a measurement of the spectral shape from the two-photon decay of the 1s2s 1S0 state in He-like uranium. The two-photon emission followed the ionization of initially Li-like uranium ions in collisions with a N2 gas-jet target. The measured shape of the two-photon energy distribution shows good agreement with results of the relativistic calculations that take into account the electron-electron interaction rigorously up to the first order in quantum electrodynamic perturbation expansion. From the full width at half maximum of the measured two-photon energy distribution, we confirm the theoretically predicted modification of the shape due to the relativistic effects.

**Hyperfine-induced effects on the linear polarization of Kα₁ emission from heliumlike ions**

**87**, 052507 (2013)

**Abstract:** The linear polarization of the characteristic photon emission from few-electron ions is studied for its sensitivity with regard to the nuclear spin and magnetic moment of the ions. Special attention is paid, in particular, to the Kα1 (1s2p3/2 1,3P1,2→1s2 1S0) decay of selected heliumlike ions following the radiative electron capture into initially hydrogenlike species. Based on the density matrix theory, a unified description is developed that includes both the many-electron and hyperfine interactions as well as the multipole-mixing effects arising from the expansion of the radiation field. It is shown that the polarization of the Kα1 line can be significantly affected by the mutipole mixing between the leading M2 and hyperfine-induced E1 components of 1s2p 3P2,Fi→1s2 1S0,Ff transitions. This E1-M2 mixing strongly depends on the nuclear properties of the considered isotopes and can be addressed experimentally at existing heavy-ion storage rings.

**Electron- and Proton-Impact Excitation of Hydrogenlike Uranium in Relativistic Collisions**

**110**, 213201 (2013)

**Abstract:** The K shell excitation of H-like uranium (U91+) in relativistic collisions with different gaseous targets has been studied at the experimental storage ring at GSI Darmstadt. By performing measurements with different targets as well as with different collision energies, we were able to observe for the first time the effect of electron-impact excitation (EIE) process in the heaviest hydrogenlike ion. The large fine-structure splitting in H-like uranium allowed us to unambiguously resolve excitation into different L shell levels. State-of-the-art calculations performed within the relativistic framework which include excitation mechanisms due to both protons (nucleus) and electrons are in good agreement with the experimental findings. Moreover, our experimental data clearly demonstrate the importance of including the generalized Breit interaction in the treatment of the EIE process.

**Single-photon multiple ionization forming double vacancies in the 2p subshell of argon**

**87**, 043409 (2013)

**Abstract:** Single-photon ionization leading to two vacancies in the 2p subshell of argon is investigated experimentally using the photoelectron time-of-flight magnetic bottle coincidence technique. Three peaks corresponding to the 3P, 1D, and 1S states of the dication are found in the ionization energy range 535 to 562 eV. Multiconfigurational Dirac-Fock calculations were performed to estimate the single-photon double-ionization cross sections. Reasonable agreement between the measured and simulated spectra is found if single and double excitations are taken into account in the wave-function expansion.

**Propagation of sound waves through a spatially homogeneous but smoothly time-dependent medium**

**333**, 47 (2013)

**Abstract:** The propagation of sound through a spatially homogeneous but non-stationary medium is investigated within the framework of fluid dynamics. For a non-vortical fluid, especially, a generalized wave equation is derived for the (scalar) potential of the fluid velocity distribution in dependence of the equilibrium mass density of the fluid and the sound wave velocity. A solution of this equation for a finite transition period ττ is determined in terms of the hypergeometric function for a phenomenologically realistic, sigmoidal change of the mass density and sound wave velocity. Using this solution, it is shown that the energy flux of the sound wave is not conserved but increases always for the propagation through a non-stationary medium, independent of whether the equilibrium mass density is increased or decreased. It is found, moreover, that this amplification of the transmitted wave arises from an energy exchange with the medium and that its flux is equal to the (total) flux of the incident and the reflected wave. An interpretation of the reflected wave as a propagation of sound backward in time is given in close analogy to Feynman and Stueckelberg for the propagation of anti-particles. The reflection and transmission coefficients of sound propagating through a non-stationary medium is analyzed in more detail for hypersonic waves with transition periods ττ between 15 and 200 ps as well as the transformation of infrasound waves in non-stationary oceans.

**Parity-nonconservation effects on the radiative recombination of heavy hydrogenlike ions**

**87**, 032714 (2013)

**Abstract:** Based on the theoretical analysis of the radiative recombination of heavy hydrogen-like ions with unpolarized electrons, a scheme is proposed for observing atomic parity nonconservation (PNC). The scheme employs the sensitivity of the polarization properties of recombination photons on the PNC-induced mixing of opposite-parity ionic levels. For the electron capture into the 1s2p(3)^P_(0) state of helium-like ions, in particular, the PNC leads to a rotation of the photon linear polarization on the angle, directly proportional to the 1s2p (3)^P_(0)–1s2s (1)^S_(0) mixing parameter. Owing to the recent advances in the development of x-ray polarimeters, the observation of such a rotation angle and, hence, the corresponding parity mixing is likely to become feasible in the future.

## 2012

**Electron emission from highly charged ions - signatures of magnetic interactions and retardation in strong fields**

**14**, 083018 (2012)

**Abstract:** The electron emission of highly charged ions has been reanalyzed with the goal of separating the magnetic and retardation contributions to the electron-electron (e-e) interaction from the static Coulomb repulsion in strong fields. A remarkable change in the electron angular distribution due to the relativistic terms in the e-e interaction is found, especially for the autoionization of beryllium-like projectiles, following a 1s → 2p_(3/2) Coulomb excitation in collision with some target nuclei. For low-energetic, high-Z projectiles with Tp ≤ 10 MeV u^(−1), a diminished (electron) emission in the forward direction as well as oscillations in the electron angular distribution due to the magnetic and retarded interactions are predicted for the autoionization of the 1s 2s^(2) 2p_(3/2) 3^P_2 resonance into the 1s^2 2s^2 S_(1/2) ground and the 1s^2 2p^2P_(1/2) excited levels of the finally lithium-like ions, and in contrast to a pure Coulomb repulsion between the bound and emitted electrons. The proposed excitation-autoionization process can be observed at existing storage rings and will provide a novel insight into the dynamics of electrons in strong fields.

**Compton polarimeters for the study of hard X-rays arising from energetic collisions of electrons and ions with matter**

**1438**, 73 (2012)

**Abstract:** Novel position-sensitive x-ray detectors are presented that, when applied as Compton polarimeters, enable precise and efficient linear polarization studies of hard x-rays up to several 100 keV. We give an analytical formula which yields a rough estimate of the polarimeter efficiencies of such detector systems. Moreover, we briefly summarize a recent linear polarization measurement of the Lyman-α1 radiation in a H-like high-Z system, namely U91+.

## 2011

**Magnetic-sublevel population and alignment for the excitation of H- and He-like uranium in relativistic collisions**

**84**, 042710 (2011)

**Abstract:** We have measured the alignment of the L-shell magnetic substates following the K-shell excitation of hydrogen- and helium-like uranium in relativistic collisions with a low-Z gaseous target. Within this experiment, the population distribution for the L-shell magnetic sublevels has been obtained via an angular differential study of the decay photons associated with the subsequent deexcitation process. The results show a very distinctive behavior for the H- and He-like heavy systems. In particular, for K → L excitation of He-like uranium, a considerable alignment of the L-shell levels was observed. A comparison of our experimental findings with recent rigorous relativistic predictions provides a good qualitative and a reasonable quantitative agreement, emphasizing the importance of the magnetic-interaction and many-body effects in the strong-field domain of high-Z ions.

**Polarization and anisotropic emission of K-shell radiation from heavy few electron ions**

**89**, 513 (2011)

**Abstract:** The population of magnetic sublevels in hydrogen-like uranium ions has been investigated in relativistic ion–atom collisions by observing the subsequent X-ray emission. Using the gas target at the experimental storage ring facility we observed the angular emission of Lyman-α radiation from hydrogen-like uranium ions. The alignment parameter for three different interaction energies was measured and found to agree well with theory. In addition, the use of different gas targets allowed for the electron-impact excitation process to be observed.

**Spectral distribution of the 2S → 1S two-photon transition in atoms and few-electron ions**

**76**, 331 (2011)

**Abstract:** The two-photon decay of the 2S state to the ground state in dressed atoms and one- or two-electron ions has been studied for several decades. Relativistic calculations have shown an Z-dependence of the spectral shape of this two-photon transition in one- or two-electron ions. We have measured the spectral distribution of the 1s2s 1^S_0 → 1s2 1^S_0 two-photon transition in He-like tin at the ESR storage ring using a new approach for such experiments. In this method, relativistic collisions of initially Li-like projectiles with a gaseous target were used to populate exclusively the first excited state, 1s2s, of He-like tin, which provided a clean two-photon spectrum. The measured two-photon spectral distribution was compared with fully relativistic calculations. The obtained results show very good agreement with the calculations for He-like tin.

## 2010

**Direct Determination of the Magnetic Quadrupole Contribution to the Lyman-alpha(1) Transition in a Hydrogenlike Ion**

**105**, 243002 (2010)

**Abstract:** We report the observation of an interference between the electric dipole (E1) and the magnetic quadrupole (M2) amplitudes for the linear polarization of the Ly-alpha(1) (2p(3/2) -> 1s(1/2)) radiation of hydrogenlike uranium. This multipole mixing arises from the coupling of the ion to different multipole components of the radiation field. Our observation indicates a significant depolarization of the Ly-alpha(1) radiation due to the E1-M2 amplitude mixing. It proves that a combined measurement of the linear polarization and of the angular distribution enables a very precise determination of the ratio of the E1 and the M2 transition amplitudes and the corresponding transition rates without any assumptions concerning the population mechanism for the 2p(3/2) state.

**Spectral Shape of the Two-Photon Decay of the 2 1S0 State in He-Like Tin**

**104**, 033001 (2010)

**Abstract:** The spectral distribution of the 1s2s 1S0→1s2 1S0 two-photon decay of He-like tin was measured using a novel approach at the gas-jet target of the ESR storage ring. Relativistic collisions of Li-like projectiles with low-density gaseous matter have been exploited to selectively populate the desired 1s2s state. Compared to conventional techniques, this approach results in a substantial gain in statistical and systematic accuracy, which allowed us to achieve for the first time a sensitivity to relativistic effects on the two-photon decay spectral shape as well as to discriminate the measured spectrum for Sn from theoretical shapes for different elements along the He-isoelectronic sequence.

## 2009

**Polarization and angular correlation studies of X-rays emitted in relativistic ion-atom collisions**

**169**, 5 (2009)

**Abstract:** Particle and photon polarization phenomena occurring in collisions of relativistic ions with matter have recently attracted particular interest. Investigations of the emitted characteristic x-ray and radiative electron capture radiation has been found to be a versatile tool for probing our present understanding of the dynamics of particles in extreme electromagnetic fields. Owing to the progress in x-ray detector technology, in addition, accurate measurements of the linear polarization for hard x-ray photons as well as the determination of the polarization plane became possible. This new diagnostic tool enables one today to derive information about the polarization of the ion beams from the photon polarization features of the radiative electron capture process.

## 2007

**Investigation of the Decay Properties of the 1s(2s) 2 State in Li-Like Uranium**

**58**, 141 (2007)

**Abstract:** We report on an experiment aiming for a study of the radiative decay modes of the 1s (2s)2 level in Li-like uranium. The experiment was performed of initially Be-like uranium colliding with N2 molecules at an energy of 90 MeV/u. By measuring the x-ray production associated with K-shell ionization of the projectile, a high selectivity for the production of the 1s (2s)2 level is observed.

**Radiative processes studied for bare uranium ions in collisions with H_2**

**58**, 243 (2007)

**Abstract:** Radiative processes occurring in collision of decelerated bare uranium ions and molecular hydrogen are studied at the heavy-ion storage ring ESR. The combination of the deceleration technique and the narrow Compton profile of molecular hydrogen allowed us to resolve a multitude of REC transitions into the bound states of the projectile and to resolve unambiguously the tip region of primary bremsstahlung. For this purpose, a supersonic molecular hydrogen jet-target, precooled with liquid nitrogen and optimized for long-term stability, was applied.