Approximate Atomic Green Functions

Fritzsche, S.; Surzhykov, A.

doi:10.3390/molecules26092660

Cited by 7 publications

(5 citation statements)

References 56 publications

(58 reference statements)

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“…During the past years, JAC has been sizeably enlarged along different lines both to assist "additional" physics computations and to make the code more readily accessible to users. Apart from calculating the electronic structure and properties of free atoms and ions, the focus in JAC's development was placed on the treatment of open f -shell elements [46], the computations of radiative and dielectronic recombination plasma rate coefficients [47,48], the setup of approximate Green functions [49], the algebraic evaluation of expressions from Racah's algebra [50] and even estimating atomic (line) energies and decay rates under different plasma environments [51]. We here follow similar objectives, as summarized above, by adding features to JAC for providing useful empirical estimates of the partial and total EII cross sections.…”

Section: The Jac Toolboxmentioning

confidence: 99%

Rapid Access to Empirical Impact Ionization Cross Sections for Atoms and Ions across the Periodic Table

Fritzsche,

Jiao,

Visentin

2024

Plasma

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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.

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Section: The Jac Toolboxmentioning

confidence: 99%

Rapid Access to Empirical Impact Ionization Cross Sections for Atoms and Ions across the Periodic Table

Fritzsche,

Jiao,

Visentin

2024

Plasma

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“…Figure 4 displays the definition of these data types together with the CiSettings in order to control the set of active orbitals and virtual excitation. Other wave function representations, which are partly supported by the JAC toolbox, refer to a MeanFieldBasis for generating a mean-field basis and a set of orbitals, a RasExpansion for dealing with restricted active-space (RAS) wave functions or a GreenExpansion for computing an approximate (many-electron) Green function [49]. These representations are subtypes of the AbstractRepresentationType from the same module.…”

Section: Combining Syntax and Semantics: Jac's Data Structures For At...mentioning

confidence: 99%

Level Structure and Properties of Open f-Shell Elements

Fritzsche

2022

Atoms

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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.

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“…A simple access to approximate Green functions requires however a decomposition into building blocks that are suitable for atomic structure theory [50]. By making use of the rotational symmetry and parity of the ASF |α ν J ν M ν , each Green function can be split into separate channels (continua) of well-defined symmetry J ≡ J P , quite similar to the one-electron Coulomb-Green function [60].…”

Section: Towards Current Fields Of Research and Applicationsmentioning

confidence: 99%

“…A more flexible treatment of the electron continuum will enable one to model resonances embedded into the continuum, as well as the ionization, recombination and decay dynamics of free atoms and ions. It will help also to incorporate the continuum (interchannel) interactions in the construction of scattering states [49] or to construct approximate atomic Green functions [50], cf. Section 3.1.…”

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Application of Symmetry-Adapted Atomic Amplitudes

Fritzsche

2022

Atoms

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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.

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Approximate Atomic Green Functions

Cited by 7 publications

References 56 publications

Rapid Access to Empirical Impact Ionization Cross Sections for Atoms and Ions across the Periodic Table

Rapid Access to Empirical Impact Ionization Cross Sections for Atoms and Ions across the Periodic Table

Level Structure and Properties of Open f-Shell Elements

Application of Symmetry-Adapted Atomic Amplitudes

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