# Publikationen von

Dr. Andrey Surzhykov

Alle Publikationen des HI Jena

## 2022

**Expanding Nuclear Physics Horizons with the Gamma Factory**

**534 (3)**, 2100284 (2022)

**Abstract:** Abstract The Gamma Factory (GF) is an ambitious proposal, currently explored within the CERN Physics Beyond Colliders program, for a source of photons with energies up to ≈400 MeV and photon fluxes (up to ≈1017 photons s-1) exceeding those of the currently available gamma sources by orders of magnitude. The high-energy (secondary) photons are produced via resonant scattering of the primary laser photons by highly relativistic partially-stripped ions circulating in the accelerator. The secondary photons are emitted in a narrow cone and the energy of the beam can be monochromatized, down to 10-3...10-6 level, via collimation, at the expense of the photon flux. This paper surveys the new opportunities that may be afforded by the GF in nuclear physics and related fields.

**Polarization of Photons Scattered by Ultra-Relativistic Ion Beams**

**534**, 2100252 (2022)

**Abstract:** A theoretical investigation of the elastic resonant scattering of photons by ultra-relativistic and partially stripped ions is presented. Particular attention in the study is given to the angular distribution and polarization of scattered photons as \textasciigrave \textasciigrave seen'' in both the ion-rest and laboratory reference frames. In order to evaluate these angular and polarization properties, the irreducible polarization tensor approach is combined with the density matrix theory. If, furthermore, the ion-photon coupling is treated within the electric dipole approximation, this framework enables one to obtain simple analytical expressions for both the emission pattern and the polarization Stokes parameters of the outgoing radiation. These (analytical) expressions for the nS0 -> n \textasciigrave P1 -> nS0\textbackslash \textdollar n S\_0 \textbackslash rightarrow n<\^>\textbackslash \textbackslash prime \textbackslash P\_1 \textbackslash rightarrow n S\_0\textbackslash \textdollar , nS1/2 -> n \textasciigrave P1/2 -> nS1/2\textbackslash \textdollar n S\_\textbackslash 1/2\textbackslash \textbackslash rightarrow n<\^>\textbackslash \textbackslash prime \textbackslash P\_\textbackslash 1/2\textbackslash \textbackslash rightarrow n S\_\textbackslash 1/2\textbackslash \textbackslash \textdollar , and nS1/2 -> n \textasciigrave P3/2 -> nS1/2\textbackslash \textdollar n S\_\textbackslash 1/2\textbackslash \textbackslash rightarrow n<\^>\textbackslash \textbackslash prime \textbackslash P\_\textbackslash 3/2\textbackslash \textbackslash rightarrow n S\_\textbackslash 1/2\textbackslash \textbackslash \textdollar transitions are displayed and analyzed , that are of interest for the Gamma Factory project and whose realization is currently under discussion at CERN. Based on the performed analysis, it is demonstrated that the resonantly scattered photons can be strongly (linearly or circularly) polarized, and that this polarization can be well controlled by adjusting either the emission angle and/or the polarization state of the incident radiation. Moreover, the potential of the photon scattering for measuring the spin-polarization of ion beams is also discussed in detail.

## 2021

**Possible Polarization Measurements in Elastic Scattering at the Gamma Factory Utilizing a 2D Sensitive Strip Detector as Dedicated Compton Polarimeter**

**2100285**, 2100285 (2021)

**Angular Distribution of Characteristic Radiation Following the Excitation of He-Like Uranium in Relativistic Collisions**

**9**, 20 (2021)

**Abstract:** In this paper, we present an experimental and theoretical study of excitation processes for the heaviest stable helium-like ion, that is, He-like uranium occurring in relativistic collisions with hydrogen and argon targets. In particular, we concentrate on angular distributions of the characteristic K alpha radiation following the K -> L excitation of He-like uranium. We pay special attention to the magnetic sub-level population of the excited 1s2l(j) states, which is directly related to the angular distribution of the characteristic K alpha radiation. We show that the experimental data can be well described by calculations taking into account the excitation by the target nucleus as well as by the target electrons. Moreover, we demonstrate for the first time an important influence of the electron-impact excitation process on the angular distributions of the K alpha radiation produced by excitation of He-like uranium in collisions with different targets.

**Approximate Atomic Green Functions**

**26**, 2660 (2021)

**Abstract:** In atomic and many-particle physics, Green functions often occur as propagators to formally represent the (integration over the) complete spectrum of the underlying Hamiltonian. However, while these functions are very crucial to describing many second- and higher-order perturbation processes, they have hardly been considered and classified for complex atoms. Here, we show how relativistic (many-electron) Green functions can be approximated and systematically improved for few- and many-electron atoms and ions. The representation of these functions is based on classes of virtual excitations, or so-called excitation schemes, with regard to given bound-state reference configurations, and by applying a multi-configuration Dirac-Hartree-Fock expansion of all atomic states involved. A first implementation of these approximate Green functions has been realized in the framework of Jac, the Jena Atomic Calculator, and will facilitate the study of various multi-photon and/or multiple electron (emission) processes.

**Polarization-dependent disappearance of a resonance signal: Indication for optical pumping in a storage ring?**

**24**, 024701 (2021)

**Abstract:** We report on laser spectroscopic measurements on Li+ ions in the experimental storage ring ESR at the GSI Helmholtz Centre for Heavy Ion Research. Driving the 2s 3S1(F=3/2)↔2p 3P2(F=5/2)↔2s 3S1(F=5/2) Λ-transition in 7Li+ with two superimposed laser beams it was found that the use of circularly polarized light leads to a disappearance of the resonance structure in the fluorescence signal. This can be explained by optical pumping into a dark state of polarized ions. We present a detailed theoretical analysis of this process that supports the interpretation of optical pumping and demonstrates that the polarization induced by the laser light must then be at least partially maintained during the round trip of the ions in the storage ring. Such polarized ion beams in storage rings will provide opportunities for new experiments, especially on parity violation.

**Polarization studies on Rayleigh scattering of hard x rays by closed-shell atoms**

**103**, 012801 (2021)

**Abstract:** We present a theoretical study on the elastic Rayleigh scattering of x-ray photons by closed-shell atoms. Special attention is paid to the transfer of linear polarization from the incident to the outgoing photons. To study this process, we apply the density-matrix formalism combined with the relativistic perturbation theory. This formalism enables us to find general relations between the Stokes parameters of the incident and scattered photons. By using these expressions, we revisit the recent proposal to use Rayleigh scattering for the analysis of the polarization purity of synchrotron radiation. We show that this analysis can be performed without any need for the theoretically calculated scattering amplitudes, if the linear polarization of the scattered light is measured simultaneously at the azimuthal angles 0 degrees and 45 degrees with respect to the plane of the synchrotron. To illustrate our approach, we present detailed calculations for scattering of 145 keV photons by lead atoms.

## 2020

**The Gamma Factory Project at CERN: a New Generation of Research Tools Made of Light**

**13**, 645 (2020)

**Atomic processes with twisted electrons**

**1412**, 052013 (2020)

**Abstract:** The present status of the fully-relativistic nonperturbative calculations of the fundamental atomic processes with twisted electrons is presented. In particular, the elastic (Mott) scattering, the radiative recombination, and for the very first time, the Bremsstrahlung processes are considered. The electron-ion interaction is accounted for in a nonperturbative manner, that allows obtaining reliable results for heavy systems. We investigate the influence of the "twistedness" of the incoming electron on the angular and polarization properties of the emitted electrons and photons for the elastic and inelastic scattering, respectively. It is found that these properties exhibit a strong dependence on the opening angle of the vortex electron beam in all processes considered.

**Resonant two-photon ionization of atoms by twisted and plane-wave light**

**102**, 063115 (2020)

**Abstract:** We study the resonant two-photon ionization of neutral atoms by a combination of twisted and plane-wave light within a fully relativistic framework. In particular, the ionization of an isotropic ensemble of neutral sodium atoms (Z = 11) from their ground 3 S-2(1/2) state via the 3 P-2(3/2) level is considered. We investigate in details the influence of the kinematic parameters of incoming twisted radiation on the photoelectron angular distribution and the circular dichroism. Moreover, we study the influence of the geometry of the process on these quantities. This is done by changing the propagation directions of the incoming twisted and plane-wave light. It is found that the dependence on the kinematic parameters of the twisted photon is the strongest if the plane-wave and twisted light beams are perpendicular to each other.

**High-Precision Determination of Oxygen Kα Transition Energy Excludes Incongruent Motion of Interstellar Oxygen**

**125**, 243001 (2020)

**Abstract:** We demonstrate a widely applicable technique to absolutely calibrate the energy scale of x-ray spectra with experimentally well-known and accurately calculable transitions of highly charged ions, allowing us to measure the K-shell Rydberg spectrum of molecular O2 with 8 meV uncertainty. We reveal a systematic ∼450 meV shift from previous literature values, and settle an extraordinary discrepancy between astrophysical and laboratory measurements of neutral atomic oxygen, the latter being calibrated against the aforementioned O2 literature values. Because of the widespread use of such, now deprecated, references, our method impacts on many branches of x-ray absorption spectroscopy. Moreover, it potentially reduces absolute uncertainties there to below the meV level.

**Rayleigh scattering of linearly polarized light: Scenario of the complete experiment**

**102**, 042814 (2020)

**Vacuum polarization and finite-nuclear-size effects in the two-photon decay of hydrogenlike ions**

**102**, 042811 (2020)

**High Resolution Photoexcitation Measurements Exacerbate the Long-Standing Fe XVII Oscillator Strength Problem**

**124**, 225001 (2020)

**Abstract:** For more than 40 years, most astrophysical observations and laboratory studies of two key soft x-ray diagnostic 2p-3d transitions, 3C and 3D, in Fe XVII ions found oscillator strength ratios f(3C)/f(3D) disagreeing with theory, but uncertainties had precluded definitive statements on this much studied conundrum. Here, we resonantly excite these lines using synchrotron radiation at PETRA III, and reach, at a millionfold lower photon intensities, a 10 times higher spectral resolution, and 3 times smaller uncertainty than earlier work. Our final result of f(3C)/f(3D)=3.09(8)(6) supports many of the earlier clean astrophysical and laboratory observations, while departing by five sigmas from our own newest large-scale ab initio calculations, and excluding all proposed explanations, including those invoking nonlinear effects and population transfers.

**Towards a determination of absolute cross sections for projectile excitation of hydrogen‐like uranium in collisions with neutral atoms**

**49**, 239 (2020)

**Abstract:** Recently, the contribution of the generalized Breit interaction to electron impact ionization was identified for the first time in a high‐Z system, namely, hydrogen‐like uranium. This study employed a measurement of the relative population of the j = 1/2 and j = 3/2 states of the L shell by projectile excitation in collision of U91+ with hydrogen and nitrogen targets. However, for a rigorous test of ion–atom collision theory, also the absolute excitation cross sections are of great importance. In the present work, we report on our efforts to extend the previous study to a determination of the absolute projectile excitation cross sections by normalization to the well‐known radiative electron capture process.

## 2019

**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.

**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.

**Excitation of the ²²⁹Th nucleus via a two-photon electronic transition**

**99**, 042517 (2019)

**Abstract:** We investigate the process of nuclear excitation via a two-photon electron transition (NETP) for the case of the doubly charged thorium. The theory of the NETP process was originally devised for heavy-helium-like ions. In this work, we study this process in the nuclear clock isotope 229Th in the 2+ charge state. For this purpose we employ a combination of configuration interaction and many-body perturbation theory to calculate the probability of NETP in resonance approximation. The experimental scenario we propose for the excitation of the low-lying isomeric state in 229Th is a circular process starting with a two-step pumping stage followed by NETP. The ideal intermediate steps in this process depends on the supposed energy ℏωN of the nuclear isomeric state. For each of these energies, the best initial state for NETP is calculated. Special focus is put on the most recent experimental results for ℏωN.

**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.

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

**122**, 092701 (2019)

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

## 2018

**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.

**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.

**Elastic scattering of twisted electrons by an atomic target: Going beyond the Born approximation**

**98**, 022706 (2018)

**Abstract:** The elastic scattering of twisted electrons by neutral atoms is studied within the fully relativistic framework. The electron-atom interaction is taken into account in all orders, thus allowing us to explore high-order effects beyond the first Born approximation. To illustrate these effects, detailed calculations of the total and differential cross sections as well as the degree of polarization of scattered electrons are performed. Together with the analysis of the effects beyond the first Born approximation, we discuss the influence of the kinematic parameters of the incident twisted electrons on the angular and polarization properties of the scattered electrons.

**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.

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

**97**, 032518 (2018)

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

**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.

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

**93**, 025401 (2018)

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

## 2017

**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.

**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.

**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}.

## 2016

**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.

**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.

**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.

**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.

**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.

**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.

**Sum rules for the polarization correlations in photoionization and bremsstrahlung**

**93**, 053421 (2016)

**Abstract:** The polarization correlations in doubly differential cross sections are investigated for photoionization and ordinary bremsstrahlung. These correlations describe the polarization transfer between incident light and ejected photoelectrons as well as between an incoming electron beam and bremsstrahlung light, respectively. They are characterized by a set of seven real parameters Cij. We show that the squares of these parameters are connected by simple “sum rules.” These sum rules can be applied for both one-electron systems and also for atoms, if the latter are described within the independent particle approximation. In particular, they are exact in their simplest form (i) for the photoionization of K-, LI,II-, and MI,II-atomic shells, as well as (ii) for bremsstrahlung in which the electron is scattered into s1/2 or p1/2 states, as in the tip (bremsstrahlung) region. Detailed calculations are performed to verify the derived identities and to discuss their possible applications for the analysis of modern photoionization and bremsstrahlung experiments. In particular, we argue that the sum rules may help to determine the entire set of (significant) polarization correlations in the case when not all Cij are available for experimental observation.

**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.

**Spin-orbit interaction in bremsstrahlung and its effect on the electron motion in a strong Coulomb field**

**92**, 062707 (2015)

**Abstract:** Linear polarization of bremsstrahlung x rays produced in collisions of longitudinally polarized 2.1-MeV electrons with gold atoms was studied using the Compton scattering technique. We observed that the angle of x-ray polarization is strongly correlated with the incoming electron polarization. This correlation reveals the dominance of the spin-orbit interaction in bremsstrahlung and indicates a striking effect of the electron spin on the electron motion in a strong Coulomb field. The results confirm the validity of the theoretical predictions in a computationally challenging energy regime.

**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.

**QED corrections to radiative recombination and radiative decay of heavy hydrogenlike ions**

**92**, 042510 (2015)

**Abstract:** One-loop quantum electrodynamic (QED) corrections are studied for two basic atomic processes, radiative recombination of an electron with a bare nucleus and radiative decay of a hydrogenlike ion. The perturbations of the bound-state wave function and the binding energy due to the electron self-energy and the vacuum polarization are computed in the Feynman and Coulomb gauges. QED corrections induced by these perturbations are calculated for the differential cross section and the polarization of the emitted radiation in the radiative recombination of an electron and a bare uranium nuclei, as well as the corresponding corrections to the ratio of the E1 (electric dipole) and M2 (magnetic quadrupole) transition amplitudes in the 2p3/2→1s radiative decay of hydrogenlike uranium. The results obtained indicate the expected magnitude of the QED effects in these processes on a subpercent level.

**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.

**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.

**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.

**Quantum Electrodynamical Corrections to Energy Levels of Diatomic Quasimolecules**

**114**, 243004 (2015)

**Abstract:** We elaborate an ab initio approach for the evaluation of the one-loop quantum electrodynamical corrections to energy levels of diatomic quasimolecules. The approach accounts for the interaction between an electron and two nuclei in all orders in Zα and can be applied for a wide range of internuclear distances, up to R≈1000 fm. Based on the developed theory, detailed calculations are performed for the self-energy and vacuum-polarization corrections to the energy of the 1σg ground state of the U92+–U91+ dimer that can be produced in slow ion-ion collisions. The calculations predict the remarkable energy shift that arises due to the nonspherical contributions to the electron-nuclei potential taken beyond the standard monopole approximation.

**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.

**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.

**Towards a fast calculator for the radiation characteristics of radiative recombination and radiative electron capture**

**599**, 012040 (2015)

**Abstract:** The radiative capture of free electrons (radiative recombination) and bound electrons (radiative electron capture) are among the most important charge changing processes for fast, highly-charged ions. While total cross sections can be obtained by an approximate formula with reasonable accuracy, the estimation of angular distributions and polarization properties of the emitted radiation requires a fully relativistic treatment that is numerical expensive. Therefore we recently started the development of a fast calculator for these radiation characteristics. The program is based on a grid of rigorously calculated data points for free- electron capture into bare ions, between which interpolation is performed to obtain radiation characteristics for specific collision systems. Also capture into few-electron systems is taken into account in an approximate way. We present first results from this development.

**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.

**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

**Method for the production of highly charged ions with polarized nuclei and zero total electron angular momentum**

**90**, 064701 (2014)

**Abstract:** The capture of polarized electrons by H-like ions provides a method for polarizing the nuclei of He-like heavy ions with zero total electron angular momentum in storage rings for high-energy ions. A detailed analysis for Eu-151 ions with nuclear spin I=5/2 predicts a nuclear polarization degree of about 47% already after one passage through a target containing 100% polarized electrons. Almost 50% of the polarized He-like ions are predicted to be in states with zero total electron angular momentum. Such ions were recently considered as the most promising candidates in experiments at storage rings for the search for violations of the fundamental symmetries and for a nuclear and an electron electric dipole moment.

**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.

**Relativistic theory for radiative forward electron emission in heavy ion-atom encounters**

**68**, 367 (2014)

**Abstract:** The forward electron emission with simultaneous photon production during the scattering of relativistic, highly stripped projectiles from light target atoms is calculated within the Dirac theory. The method of calculation is a simplification of the impulse approximation and is based on the relation of the cross section for radiative capture to continuum of loosely bound electrons to the frame-transformed electron bremsstrahlung cross section. It is demonstrated that such an approximation is well justified in a large region of energies and photon emission angles, with the exception of the extreme forward and backward emission and the soft-photon energy limit. The cusp spectrum and the corresponding angular distribution are compared to recent experimental data for the collision system 90.38 MeV/amu U88+ + N2.

**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.

**Polarization of atomic bremsstrahlung in coincidence studies**

**90**, 032707 (2014)

**Abstract:** We present a theoretical study of bremsstrahlung produced by high-energy electrons scattered by heavy atomic targets. Considering coincident observation of the emitted photons and the scattered electrons, we pay special attention to the polarization degree and direction of the outgoing light. To investigate these properties of atomic bremsstrahlung, we apply the density matrix approach and solutions of the Dirac equation. Detailed calculations are performed for initial electron energies ranging from 100 to 500 keV and different fixed electron scattering angles. The results of these calculations are compared with predictions obtained under the assumption that the scattered electrons remain unobserved. This comparison reveals that both the degree and the direction of linear polarization of bremsstrahlung are very sensitive to the direction of the scattered electron.

**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.

**Radiative-electron-capture-to-continuum cusp in U⁸⁸⁺+N₂ collisions and the high-energy endpoint of electron-nucleus bremsstrahlung**

**90**, 022707 (2014)

**Abstract:** The radiative electron capture of a target electron into the projectile continuum has been studied for the collision system U88+ + N2 → U88+ + [N+2]∗ + e− + γ at 90 MeV/u. Using a magnetic electron spectrometer, the energy distribution of cusp electrons emitted under an angle of 0∘ with respect to the projectile beam and with a velocity close to the projectile velocity has been measured in coincidence with the emitted photons under various observation angles. The experimental results provide a stringent test for the corresponding process in inverse kinematics, namely, the theory of electron-nucleus bremsstrahlung at the high-energy endpoint. For comparison this process is calculated using fully relativistic Dirac wave functions and using semirelativistic Sommerfeld-Maue wave functions.

**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.

**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.

**Monte-Carlo simulations of the radiative recombination of ions with electrons in cold magnetized plasma**

**2014**, 014001 (2014)

**Abstract:** We report here on the results of Monte-Carlo simulations of the radiative recombination of highly charged ions with low-energy electrons in the presence of a guiding magnetic field. The simulations are based on a semi-classical geometrical model, recently proposed by our group, which has been developed in order to explain systematic discrepancies, the so-called ‘enhancement effect’, of the radiative recombination rates measured in the guiding magnetic field of electron coolers with respect to theoretical calculations. With the simulations, we demonstrate that the enhancement of radiative recombination rates in the magnetic field could be caused by ‘transverse’ collisions with the impact parameter in the μm range and the impact parameter cut-off value depending on the strength of the guiding B -field in magnetized plasma. In this paper, the methodology of the simulations, the obtained B -field dependence of the radiative recombination enhancement and the observed impact parameter cut-off will be discussed.

**Electron polarimetry with bremsstrahlung**

**488**, 012057 (2014)

**Abstract:** Due to the spin-orbit interaction, the electron scattering from the nucleus is sensitive to the spin orientation of that electron. This is used for polarimetry of electron beams in the Mott method. The spin-orbit interaction was also observed in bremsstrahlung. In this article we analyze its potential for polarimetry as an alternative to the Mott method. It can simultaneously measure all three electron polarization components. It should work in the energy range of 50 keV up to several MeV and can be applied at beam intensities higher than 100 nA. It needs a thin heavy element target, two or four x-ray detectors and one x-ray linear polarimeter.

**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.

**Double lepton pair production with electron capture in relativistic heavy-ion collisions**

**74**, 2829 (2014)

**Abstract:** We present a theoretical study of a double lepton-pair production in ultra-relativistic collision between two bare ions. Special emphasis is placed to processes in which creation of (at least one) e+e− pair is accompanied by the capture of an electron into a bound ionic state. To evaluate the probability and cross section of these processes we employ two approaches based on (i) the first-order perturbation theory and multipole expansion of Dirac wavefunctions, and (ii) the equivalent photon approximation. With the help of such approaches, detailed calculations are made for the creation of two bound–free e+e− pairs as well as of bound–free e+e− and free–free μ+μ− pairs in collisions of bare lead ions, Pb 82+ . The results of the calculations indicate that observation of the double lepton processes may become feasible at the LHC facility.

**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.

## 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.

**Differential L-shell radiative recombination rate coefficients for bare uranium ions interacting with low-energy electrons**

**222**, 2317 (2013)

**Abstract:** Results of the calculations of differential L−shell radiative recombination (RR) rate coefficients for bare uranium ions colliding with free electrons using the nonrelativistic dipole approximation and fully relativistic calculations are reported. The rate coefficients were obtained for very low, in the range of meV, relative electron-ion energies. We demonstrate that even for such low relative ion-electron energies the relativistic effects significantly modify the differential RR rate coefficients for the L−subshells and, as a result, the measurements of the relative electron energy dependence of the L-RR rates could be used for studying of the relativistic effects. These effects are strongest for the L_3-subshell, which is discussed here in more details.

**Bremsstrahlung of polarized positrons scattered off atoms**

**2013**, 014072 (2013)

**Abstract:** The leading-order positron–atom bremsstrahlung is investigated within the rigorous relativistic approach based on the partial-wave representation of the Dirac wave functions in the external atomic field. Approximating the atomic target by an effective local potential, we calculate the Stokes parameters of the emitted photon for different polarizations of the initial positron. The results for positron–atom bremsstrahlung are compared with analogous data for the electron–atom bremsstrahlung.

**Few-body quantum dynamics of high-Z ions studied at the future relativistic high-energy storage ring**

**2013**, 014086 (2013)

**Abstract:** At the FAIR facility for antiprotons and ion research, the high-energy storage ring will provide highly charged heavy ions with Z all the way to Z = 92 for beam energies ranging from 200 A MeV up to energies of approximately 5 A GeV. This opens up a wealth of opportunities for in-ring atomic physics experiments on few-body quantum dynamics ranging from, for example, the correlated dynamics of various e^(+) –e^(−) pair creation processes to quasi-photoionization of inner shells of the highest- Z ions.

**Future experiments using forward electron spectroscopy to study the quantum dynamics of high- Z ions at the ESR/CRYRING storage rings**

**2013**, 014087 (2013)

**Abstract:** At the FAIR facility for antiproton and ion research, the new ESR + CRYRING combination of storage rings CRYRING@ESR opens up a wealth of opportunities for in-ring atomic physics experiments on few-body quantum dynamics. The low-energy storage ring CRYRING will serve in its new location at FAIR/ESR for experiments with decelerated antiprotons and highly charged ions. We will discuss selected new experiments in the field of quantum dynamics of high- Z ions, for example for adiabatic superheavy quasi-molecules transiently formed with bare and H-like projectiles. Such experiments will be for the first time possible at the future CRYRING at ESR.

**K-shell differential radiative recombination rates for bare uranium ions interacting with low-energy electrons**

**2013**, 014045 (2013)

**Abstract:** We report on the calculations of the K-shell differential radiative recombination (RR) rate coefficients for very low, in the range of meV, relative electron–ion energies. The rate coefficients were derived for bare uranium ions colliding with free electrons both within the nonrelativistic dipole approximation and using fully relativistic calculations. We show that even for such low relative ion–electron energies, the differential rate coefficient reveals strong relativistic effects. We demonstrate that the measurements of the relative electron energy dependence of the RR rates represent a very sensitive tool for precise studies of the RR process and, in particular, for probing the fine details of the relativistic effects in the RR of ions with electrons. The results are discussed in the context of the first x-ray state-selective RR experiment performed for very low relative electron–ion energies.

**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+).

**Production and diagnostics of spin-polarized heavy ions in the sequential two-electron radiative recombination**

**2013**, 014046 (2013)

**Abstract:** The sequential radiative recombination of initially bare ions, which are collided with two spatially separated electron targets, is studied. It is demonstrated that the magnetic sublevel population of H-like ions, which are formed due to electron capture from the first target, depends on the first radiative recombination (RR) photon emission direction. Such a relative population, which can be parameterized in terms of the polarization parameters, affects then the angular and polarization properties of the second photon emitted in the collision with the second target. The coincidence γ – γ RR measurements may allow us to study, therefore, the process in which (i) H-like ions of some particular polarization are ‘selected out’ of the beam by detecting first recombination photons and (ii) this polarization is ‘measured’ in the second electron capture process. In order to describe the output of the (future) γ – γ correlation measurements, we derive the general expression for angular- and polarization-correlation function. Detailed calculations for the dependence of this function on the experimental setup and collision energy are performed for the RR of bare uranium ions.

**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.

**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.

**Chlorine atom densities in the (3p^5)^2P_{1/2}^{0} excited spin-orbit state measured by two-photon absorption laser-induced fluorescence in a chlorine inductively coupled plasma**

**46**, 295203 (2013)

**Abstract:** Chlorine atom densities in the (3p^{5})^{2}P_{1/2}^{0} spin–orbit excited state were measured by two-photon absorption laser-induced fluorescence (TALIF) in an inductively coupled plasma discharge in pure Cl2. The atoms were excited by two photons at 235.702 nm to the (4p)^{4}S_{3/2}^{0} state and detected by fluorescence to the (4s) ^{4}P_{5/2} state at 726 nm. The population of this state relative to that in the (3p^{5})^{2}P_{3/2}^{0} ground state, n_{P_{1/2}}/n_{P_{3/2}} was determined from the relative TALIF signal intensity from the two states, combined with new calculations of the two-photon absorption cross-sections. n_{P_{1/2}}/n_{P_{3/2}} was found to increase continuously with radio-frequency power (50–500 W), whereas with Cl2 pressure (5–90 mTorr) it passes through a maximum at 10 mTorr, reaching ~30% at 500 W. This maximum corresponds to the maximum of electron density in the discharge. Combining this density ratio measurement with previous measurements of the absolute ground state chlorine atom density [1] allows the absolute spin-orbit excited state density to be estimated. A significant fraction of the total chlorine atom density is in this excited state which should be included in plasma chemistry models.

**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.

**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.

**Bremsstrahlung polarization correlations and their application for polarimetry of electron beams**

**87**, 022707 (2013)

**Abstract:** Linear polarization of hard x rays emitted in the process of atomic-field electron bremsstrahlung has been measured with a polarized electron beam. The correlation between the initial orientation of the electron spin and the angle of photon polarization has been systematically studied by means of Compton and Rayleigh polarimetry techniques applied to a segmented germanium detector. The results are in good agreement with those of fully relativistic calculations. The observed correlations are also explained classically and in a unique way manifest that due to the spin-orbit interaction the electron scattering trajectory is not confined to a single scattering plane. The developed photon polarimetry technique with a passive scatterer is very efficient and accurate and thus allows for additional applications. Bremsstrahlung polarization correlations lead to an alternative method of polarimetry of electron beams. Such a method is sensitive to all three components of the electron spin. It can be applied in a broad range of the electron beam energies from ≈100 keV up to a few tens of MeV. The results of a measurement at 100 keV are shown. The optimum scheme for electron polarimetry is analyzed and the relevant theoretical predictions are presented.

## 2012

**Comparative study of the electron-atom and positron-atom bremsstrahlung**

**86**, 032708 (2012)

**Abstract:** Fully relativistic treatment of the electron-atom and positron-atom bremsstrahlung is reported. The calculation is based on the partial-wave expansion of the Dirac scattering states in an external atomic field. A comparison of the electron and positron bremsstrahlung is presented for the single and double differential cross sections and the Stokes parameters of the emitted photon. It is demonstrated that the electron-positron symmetry of the bremsstrahlung spectra, which is nearly exact in the nonrelativistic regime, is to a large extent removed by the relativistic effects.

**Production and diagnostics of spin-polarized heavy ions in sequential two-electron radiative recombination**

**86**, 032701 (2012)

**Abstract:** In the present work we investigate the sequential radiative recombination (RR) of initially bare ions colliding with two spatially separated electron targets. It is shown that magnetic sublevel population of the hydrogenlike ions, produced by the electron capture from the first target, depends on the emission direction of the (first) RR photon. This population, which can be expressed in terms of the polarization parameters, affects then the angular and polarization properties of the radiation emitted in the collision with the second target. The coincidence measurements of two subsequent RR photons may allow one to understand, therefore, the production and diagnostics of the ion spin polarization. In order to describe this polarization production and diagnostic scheme we derive the general expression for the γ-γ correlation function. Detailed calculations for the dependence of this function on the geometry of photon emission and collision energy are performed for the radiative recombination of bare uranium ions.

**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.

**Polarization Transfer of Bremsstrahlung Arising from Spin-Polarized Electrons**

**108**, 26480 (2012)

**Abstract:** We report on a study of the polarization transfer between transversely polarized incident electrons and the emitted x rays for electron-atom bremsstrahlung. By means of Compton polarimetry we performed for the first time an energy-differential measurement of the complete properties of bremsstrahlung emission related to linear polarization, i.e., the degree of linear polarization as well as the orientation of the polarization axis. For the high-energy end of the bremsstrahlung continuum the experimental results for both observables show a high sensitivity on the initial electron spin polarization and prove that the polarization orientation is virtually independent of the photon energy.

**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+.

**Storage ring at HIE-ISOLDE Technical design report**

**207**, 1 (2012)

**Abstract:** We propose to install a storage ring at an ISOL-type radioactive beam facility for the first time. Specifically, we intend to setup the heavy-ion, low-energy ring TSR at the HIE-ISOLDE facility in CERN, Geneva. Such a facility will provide a capability for experiments with stored secondary beams that is unique in the world. The envisaged physics programme is rich and varied, spanning from investigations of nuclear ground-state properties and reaction studies of astrophysical relevance, to investigations with highly-charged ions and pure isomeric beams. The TSR might also be employed for removal of isobaric contaminants from stored ion beams and for systematic studies within the neutrino beam programme. In addition to experiments performed using beams recirculating within the ring, cooled beams can also be extracted and exploited by external spectrometers for high-precision measurements. The existing TSR, which is presently in operation at the Max-Planck Institute for Nuclear Physics in Heidelberg, is well-suited and can be employed for this purpose. The physics cases as well as technical details of the existing ring facility and of the beam and infrastructure requirements at HIE-ISOLDE are discussed in the present technical design report.

**PEBSI – A Monte Carlo simulator for bremsstrahlung arising from electrons colliding with thin solid-state targets**

**279**, 155 (2012)

**Abstract:** We present a Monte Carlo code dedicated to the simulation of bremsstrahlung arising in collisions of polarized electrons with thin target foils. The program consists of an electron transport algorithm taking into account elastic electron-nucleus scattering and inelastic collisions with target electrons as well as a treatment of polarized-electron bremsstrahlung emission. Good agreement is found between the predictions of the electron transport code and data stemming from other simulation programs and experiments. In addition, we present first results from the bremsstrahlung simulation which indicate a significant decrease in the degree of linear polarization of bremsstrahlung even for the thinnest gold targets considered.

## 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 Of The High-Energy End Of The Electron-Nucleus Bremsstrahlung In Electron-Atom Collisions**

**1336**, 94 (2011)

**Abstract:** The linear polarization of bremsstrahlung radiation emitted in collisions of spin‐polarized and unpolarized electrons with carbon and gold targets has been measured for an incident kinetic energy of 100 keV. We present preliminary results for the degree of linear polarization for incident unpolarized electrons as a function of bremsstrahlung photon energy.

**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.

**Hyperfine transitions in He-like ions as a tool for nuclear-spin-dependent parity-nonconservation studies**

**83**, 052518 (2011)

**Abstract:** In this paper a scheme is proposed for measuring nuclear-spin-dependent parity-nonconservation effects in highly charged ions. The idea is to employ circularly polarized laser light for inducing the transition between the level (1s2s)^1S_0 and the hyperfine sublevels of (1s2s)^3S_1 in He-like ions with nonzero nuclear spin. We argue that an interference between the allowed magnetic dipole M1 and the parity-violating electric dipole E1 decay channel leads to an observable asymmetry of order 10^(-7) in the transition cross section, in the atomic range 28 ⩽ Z ⩽ 35. Experimental requirements for asymmetry measurements are discussed in the case of He-like (34)_Se^(77).

**Photon-photon polarization correlations as a tool for studying parity nonconservation in heliumlike uranium**

**83**, 052505 (2011)

**Abstract:** Due to electron-nucleus weak interaction, atomic bound states with different parities turn out to be mixed. We discuss a prospective method for measuring the mixing parameter between the nearly degenerate metastable states 1s_(1/2) 2s_(1/2):J=0 and 1s_(1/2) 2p_(1/2):J=0 in heliumlike uranium. Our analysis is based on the polarization properties of the photons emitted in the two-photon decays of such states.

**Hyperfine interaction effects on the (1s2p)P-3(1)-(1s2s)S-1(0) energy splitting in He-like ions for parity nonconservation studies**

**89**, 73 (2011)

**Abstract:** Accurate theoretical knowledge of the (1s2p)^3P_1–(1s2s)^1S_0 splitting in He-like ions is demanded for future experimental studies of the nuclear spin-dependent part of the weak interaction. In this paper we perform a calculation of the hyperfine structure of (1s2p)^3P_1–(1s2s)^1S_0 within 3 ≤ Z ≤ 35, Z being the atomic number. In this Z range parity nonconservation (PNC) effects are amplified by the close energy proximity of the opposite parity levels (1s2p)^3P_1 and (1s2s)^1S_0. We find that the hyperfine structure is relevant for Z > 12, and produces splitting among the hyperfine sublevels as large as 150 meV for medium Z He-like ions (Z ~ 35).

## 2010

**Finite basis set approach to the two-centre Dirac problem in Cassini coordinates**

**43**, 235207 (2010)

**Abstract:** We lay out a new approach to solving the two-centre Dirac eigenvalue problem. It is based on the application of B-spline basis sets constructed in Cassini coordinates. The approach provides a very promising way for the theoretical description of various atomic processes such as charge transfer, excitation, ionization and electron-positron pair production that accompany slow collisions of heavy ions. Moreover, yielding a (quasi-) complete set of eigensolutions, the finite basis set method allows a systematic analysis of the quantum electrodynamics (QED) corrections to the energy levels of heavy quasi-molecules formed in these collisions.

**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.

**Isotopic tuning of the 2 3P0−2 1S0 and 2 3P1−2 1S0 transition energies in He-like ions for future parity-nonconservation experiments**

**5**, C08006 (2010)

**Abstract:** Crossings of opposite-parity levels in He-like ions for particular values of the atomic number Z offer excellent conditions for precise experimental tests of parity-nonconservation (PNC). Such tests may be performed by inducing, through intense lasers, transitions that are only allowed in presence of PNC. Several spectroscopy experiments have been proposed in the past, but only now, with the advent of high-intensity laser facilities (e.g. PHELIX at GSI or POLARIS at Jena), their feasibility is within reach. In this paper, we use relativistic many-body perturbation theory (RMBPT) to calculate accurately the crossing conditions of the excited levels (1s2s) 1S0 and (1s2p) 3P0 and of (1s2s) 1S0 and (1s2p) 3P1 in intermediate and heavy He-like ions. Moreover, we show the dependence of the energy splittings upon the choice of the nuclear isotope.

**Isotope shift of the 1s2p P-3(0)-1s2s S-1(0) level splitting in heavy He-like ions: Implications for atomic parity-nonconservation studies**

**81**, 062503 (2010)

**Abstract:** Heavy He-like ions are considered to be promising candidates for atomic parity-nonconservation (PNC) studies, thanks to their relatively simple atomic structure and the significant mixing between the almost degenerate (for the atomic numbers Z~64 and Z~91) opposite-parity levels 1s2s 1S0 and 1s2p 3P0. A number of experiments exploiting this level mixing have been proposed, and their implementation requires a precise knowledge of the 2 3P0–2 1S0 energy splitting for different nuclear charges and isotopes. In this paper we performed a theoretical analysis of the level splitting, employing the relativistic many-body perturbation theory and including QED corrections for all isotopes in the intervals 54⩽Z⩽71 and 86⩽Z⩽93. Possible candidates for future experimental PNC studies are discussed.

## 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.