Approximate Atomic Green Functions

Radiative Recombination Plasma Rate Coefficients for Multiply Charged Ions

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.

Application of Symmetry-Adapted Atomic Amplitudes

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.

Level Structure and Properties of Open f-Shell Elements

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.

Symbolic Evaluation of Expressions from Racah’s Algebra

Based on the rotational symmetry of isolated quantum systems, Racah’s algebra plays a significant role in nuclear, atomic and molecular physics, and at several places elsewhere. For N-particle (quantum) systems, for example, this algebra helps carry out the integration over the angular coordinates analytically and, thus, to reduce them to systems with only N (radial) coordinates. However, the use of Racah’s algebra quickly leads to complex expressions, which are written in terms of generalized Clebsch–Gordan coefficients, Wigner n-j symbols, (tensor) spherical harmonics and/or rotation matrices. While the evaluation of these expressions is straightforward in principle, it often becomes laborious and prone to making errors in practice. We here expand Jac, the Jena Atomic Calculator, to facilitate the sum-rule evaluation of typical expressions from Racah’s algebra. A set of new and revised functions supports the simplification and subsequent use of such expressions in daily research work or as part of lengthy derivations. A few examples below show the recoupling of angular momenta and demonstrate how Jac can be readily applied to find compact expressions for further numerical studies. The present extension makes Jac a more flexible and powerful toolbox in order to deal with atomic and quantum many-particle systems.