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Electron-impact ionization (EII) processes are essential for modelling high-temperature plasma in quite different research areas, from astrophysics to material science to plasma and fusion research and in several places elsewhere. In most, if not all, of these fields, partial and total EII cross sections are required, and often for a good range of electron energies, in order to determine, for instance, the level population of ions and spectral line intensities in plasma under both local and non-local thermodynamic equilibrium conditions. To obey these needs, various kinds of semi-empirical EII cross sections have been applied in practice, often simply because of the large computational demands in dealing explicitly with two free electrons within the continuum. Here, we expand Jac, the Jena Atomic Calculator, to provide such empirical EII cross sections for (most) atoms and ions across the periodic table. Five empirical models from the recent literature have been implemented to support a simple and rapid access to the partial EII cross sections for electrons from a (partly filled) shell (nℓ)q as well as the total ionization cross sections. We here restrict ourselves to the direct part of the EII cross section, whereas the impact excitation of electrons with subsequent autoionization and the resonant electron capture with double autoionization have been left aside in this first implementation. Rapid access to the (direct) EII cross sections will help already to better understand the role of electron-impact processes in the diagnostics of fusion plasma or the interpretation of astrophysical spectra.

In this study, we employ strong field approximation (SFA) to investigate the influence of the number of pulse cycles on above-threshold ionization within the framework of nondipole theory. The SFA enables the analysis of the ionization process under the dominance of the electric field, compared to other factors such as the binding potential of an atom. Nondipole effects, including higher-order multipole fields, can significantly impact ionization dynamics. However, the interaction between nondipole effects and pulse cycles remains unclear. Therefore, we investigate the pulse cycle dependence of ionization and examine peak shifts in Kr and Ar atoms. Our findings have implications for comprehensively understanding the effects of electromagnetic fields on electron behavior. The insights gained from this study provide valuable guidance for future research in strong field ionization.

The electron impact excitation and ionization processes are crucial for modeling the spectra of different astrophysical objects, from atmospheres of late-type stars to remnants of supernovae and up to the light emission from neutron star mergers, to name just a few. Despite their significance, however, little is known quantitatively about these processes for low- and medium-impact energies of, say, Ekin≲5000 eV of the free incident electron. To further explore the role of impact excitation, we here expanded Jac, the Jena Atomic Calculator, to the computation of distorted wave collision strengths for fine-structure-resolved, as well as configuration-averaged transitions. While we excluded the formation of dielectronic resonances, these tools can be readily applied for ions with a complex shell structure and by including the major relativistic contributions to these strengths. Detailed computations of the collision strengths are shown and explained for the impact excitation of lithium- and chlorine-like ions. When compared with other, well-correlated methods, good agreement was found, and hence, these tools will support studies of effective collision strengths for a wide range of electron impact energies, levels, and ionic charge states.

Radiative recombination (RR) plasma rate coefficients are often applied to estimate electron densities and temperatures under quite different plasma conditions. Despite their frequent use, however, these rate coefficients are available only for selected (few-electron) ions and isoelectronic sequences, mainly because of the computational efforts required. To overcome this limitation, we report here a (relativistic) cascade model which helps compute fine-structure and shell-resolved as well as total RR plasma rate coefficients for many, if not most, elements of the periodic table. This model is based on Jac, the Jena Atomic Calculator, and supports studies on how the electron is captured in selected levels of the recombined ion, a relativistic (Maxwellian) electron distribution, or how the multipoles beyond the electric-dipole field in the electron-photon interaction affect the RR rate coefficients and, hence, the ionization and recombination dynamics of hot plasma. As a demonstration of this model, we compute, compare, and discuss different RR plasma rate coefficients for initially helium-like ions, with an emphasis especially on Fe24+ ions.

With metallic-magnetic calorimeters (MMCs), promising detectors for high-precision X-ray spectrometry in atomic and fundamental physics experiments are available. In this work, we present a pilot experiment based on a maXs-30 type MMC-spectrometer for recording X-rays emitted in collisions of lithium-like uranium ions with a molecular nitrogen gas jet in the internal target of the ESR storage ring of the GSI. Sample spectra have been measured, and a multitude of X-ray transitions have been unambiguously identified. As a first test and for comparison with data recorded at an EBIT, the 2s Lamb shift in lithium-like uranium was estimated.

The efficient generation of high-order harmonic radiation has been a challenging task since the early days of strong-field physics. An essential requirement to achieve efficient high-order harmonic generation inside a gas medium is the phase matching of the high-order harmonic radiation and the incident laser pulse. The dominant contribution to the wave–vector mismatch Δk is associated with the ionization probability of the medium. In this work, we derive two analytical formulas to calculate the critical intensity of a general linearly polarized laser pulse that obey the phase-matching condition Δk=0. The analytic formulas are valid in the tunneling regime (ADK model) and the regime of the tunnel and multi-photon ionization (PPT model), respectively. We compare our results to numerical computations and discuss the scaling of the critical intensity depending on the pulse duration and the wavelength of a realistic incident laser pulse. The analytical approach demonstrated in this work is highly accurate and can compete with the existing numerical computational methods by an error of less than 1% and a decrease in the computation time of approximately 4 to 6 orders of magnitude. This enables complex theoretical studies of the efficiency scaling in HHG or to consider the effects of ground state depletion efficiently.

Following the work of Giulio Racah and others from the 1940s onward, the rotational symmetry of atoms and ions, e.g., the conservation of angular momentum, has been utilized in order to efficiently predict atomic behavior, from their level structure to the interaction with external fields, and up to the angular distribution and polarization of either emitted or scattered photons and electrons, while this rotational symmetry becomes apparent first of all in the block-diagonal structure of the Hamiltonian matrix, it also suggests a straight and consequent use of symmetry-adapted interaction amplitudes in expressing the observables of most atomic properties and processes. We here emphasize and discuss how atomic structure theory benefits from exploiting this symmetry, especially if open-shell atoms and ions in different charge states need to be combined with electrons in the continuum. By making use of symmetry-adapted amplitudes, a large number of excitation, ionization, recombination or even cascade processes can be formulated rather independently of the atomic shell structure and in a language close to the formal theory. The consequent use of these amplitudes in existing codes such as Grasp will therefore qualify them to deal with the recently emerging demands for developing general-purpose tools for atomic computations.

In the past, the ionization of atoms and molecules by strong, mid-infrared (IR) laser fields has attracted recurrent interest. Measurements with different IR pulses have demonstrated the crucial role of the magnetic field on the electron dynamics, classically known as the Lorentz force F_{L}=q(E+v×B), that acts upon all particles with charge q in motion. These measurements also require the advancement of theory beyond the presently applied methods. In particular, the strong-field approximation (SFA) is typically based on the dipole approximation alone and neglects both the magnetic field and the spatial dependence of the driving electric field. Here we show and discuss that several, if not most, observations from strong-field ionization experiments with mid-IR fields can be quantitatively explained within the framework of SFA, if the Lorentz force is taken into account by nondipole Volkov states in the formalism. The details of such a treatment are analyzed for the (peak) shifts of the polar-angle distribution of above-threshold ionization photoelectrons along the laser propagation, the steering of electron momenta by two not quite collinear laser beams, or the enhanced momentum transfer to photoelectrons in standing-light fields. Moreover, the same formalism promises to explain the generation of high harmonics and other strong-field rescattering phenomena when driven by mid-IR laser fields. All these results show how strong-field processes can be understood on equal footings within the SFA, if one goes beyond the commonly applied dipole approximation.

The strong-field approximation (SFA) has been widely applied in the literature to model the ionization of atoms and molecules by intense laser pulses. A recent re-formulation of the SFA in terms of partial waves and spherical tensor operators helped adopt this approach to account for realistic atomic potentials and pulses of different shape and time structure. This re-formulation also enables one to overcome certain limitations of the original SFA formulation with regard to the representation of the initial-bound and final-continuum wave functions of the emitted electrons. We here show within the framework of Jac, the Jena Atomic Calculator, how the direct SFA ionization amplitude can be readily generated and utilized in order to compute above-threshold ionization (ATI) distributions for many-electron targets and laser pulses of given frequency, intensity, polarization, pulse duration and carrier–envelope phase. Examples are shown for selected ATI energy, angular as well as momentum distributions in the strong-field ionization of atomic krypton. We also briefly discuss how this approach can be extended to incorporate rescattering and high-harmonic processes into the SFA amplitudes.

Ions with multiple inner-shell vacancies frequently arise due to their interaction with different targets, such as (intense) light pulses, atoms, clusters or bulk material. They are formed, in addition, if highly charged ions approach surfaces and capture electrons at rather large distances. To explore the interaction of such hollow ions and their subsequent relaxation, photon spectra in different frequency regions have been measured and compared to calculations. To support these and related measurements, we here show within the framework of the Jena Atomic Calculator (Jac) how (additional) electrons in outer shells modify photon emission and lead to characteristic shifts in the observed spectra. Further, for highly charged Ar ions in KLm(m=1…8) configurations, we analyze the mean relaxation time for their stabilization into the different ground configurations. These examples demonstrate how a powerful and flexible toolbox such as Jac will be useful (and necessary) in order to model the photon and electron emission of ions as they occur not only near surfaces but also in astro-, atomic and plasma physics.

Open f-shell elements still constitute a great challenge for atomic theory owing to their (very) rich fine-structure and strong correlations among the valence-shell electrons. For these medium and heavy elements, many atomic properties are sensitive to the correlated motion of electrons and, hence, require large-scale computations in order to deal consistently with all relativistic, correlation and rearrangement contributions to the electron density. Often, different concepts and notations need to be combined for just classifying the low-lying level structure of these elements. With Jac, the Jena Atomic Calculator, we here provide a toolbox that helps to explore and deal with such elements with open d- and f-shell structures. Based on Dirac’s equation, Jac is suitable for almost all atoms and ions across the periodic table. As an example, we demonstrate how reasonably accurate computations can be performed for the low-lying level structure, transition probabilities and lifetimes for Th2+ ions with a 5f6d ground configuration. Other, and more complex, shell structures are supported as well, though often for a trade-off between the size and accuracy of the computations. Owing to its simple use, however, Jac supports both quick estimates and detailed case studies on open d- or f-shell elements.

Photoionization of atoms and molecules is a complex process and requires sensitive probes to explore the ultrafast dynamics. Here the authors combine transient absorption and photo-ion spectroscopy methods to explore and control the attosecond pulse initiated excitation, ionization and Auger decay in Kr atoms.

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.

Photoelectron angular distributions of the two-photon ionization of neutral atoms are theoretically investigated. Numerical calculations of two-photon ionization cross sections and asymmetry parameters are carried out within the independent-particle approximation and relativistic second-order perturbation theory. The dependence of the asymmetry parameters on the polarization and energy of the incident light as well as on the angular momentum properties of the ionized electron are investigated. While dynamic variations of the angular distributions at photon energies near intermediate level resonances are expected, we demonstrate that equally strong variations occur near the nonlinear Cooper minimum. The described phenomena is demonstrated on the example of two-photon ionization of magnesium atom.

Scattering of light on relativistic heavy ion beams is widely used for characterizing and tuning the properties of both the light and the ion beam. Its elastic component—Rayleigh scattering—is investigated in this work for photon energies close to certain electronic transitions because of its potential usage in the Gamma Factory initiative at CERN. The angle-differential cross-section, as well as the degree of polarization of the scattered light are investigated for the cases of 1 s − 2 p 1 / 2 and 1 s − 2 p 3 / 2 resonance transitions in H-like lead ions. In order to gauge the validity and uncertainty of frequently used approximations, we compare different methods. In particular, rigorous quantum electrodynamics calculations are compared with the resonant electric-dipole approximation evaluated within the relativistic and nonrelativistic formalisms. For better understanding of the origin of the approximation, the commonly used theoretical approach is explained here in detail. We find that in most cases, the nonrelativistic resonant electric-dipole approximation fails to describe the properties of the scattered light. At the same time, its relativistic variant agrees with the rigorous treatment within a level of 10% to 20%. These findings are essential for the design of an experimental setup exploiting the scattering process, as well as for the determination of the scattered light properties.

Das Oberverwaltungsgericht (OVG) Sachsen-Anhalt hat am 24.11.2015 über die Auslegung des § 24 Absatz 4 der Tierschutz-Nutztierhaltungsverordnung geurteilt. Danach müssen Kastenstände so beschaffen sein, dass jedes Schwein ungehindert aufstehen, sich hinlegen sowie den Kopf und in Seitenlage die Gliedmaßen ausstrecken kann. Für eine Abschätzung der betriebswirtschaftlichen Kosten von Anpassungsmaßnahmen wurden vier unterschiedliche Stalltypen zur Ferkelerzeugung ausgewählt, an denen beispielhaft verschiedene Szenarien betrachtet und die Mehrkosten bzw. Mindererlöse (bei Bestands­abstockung) ermittelt werden. Je nach Wochenrhythmus und Art der Gruppenhaltung für tragende Sauen entstehen unterschiedlich hohe Mehrkosten bzw. muss der Bestand ohne Anbau unterschiedlich reduziert werden. Eine Bestandsabstockung, die sich u. a. bei dem Einbau breiterer Kastenstände zwingend ergibt, ist mit sehr hohen Kosten bzw. Mindererlösen verbunden und sollte aus betriebswirtschaftlicher Sicht vermieden werden. Ein Anbau zum Ausgleich für die reduzierten Plätze ist grundsätzlich günstiger. Betriebe, die einen 3-Wochen-Rhythmus praktizieren, müssen gegenüber Betrieben mit 1-Wochen-Rhythmus mit wesentlich höheren Kosten rechnen. Wenn sich die Verweildauer der Sauen im Kastenstand verringert, bleibt das Deckzentrums bei einem 3-Wochen-Rhythmus für einen längeren Zeitraum ungenutzt. Betriebe mit Großgruppenhaltung im Wartebereich können mit geringeren Mehrkosten kalkulieren als Betriebe mit Kleingruppenhaltung für tragende Sauen. Die günstigste Variante für den Umbau des Deckzentrums ist die Gruppenhaltung mit Fixierung im klappbaren Stand. Allerdings kann auch bei diesem Szenario die Fruchtbarkeitsleistung beeinträchtigt werden und die Anforderungen an das Management sind vergleichsweise hoch.