Special Issue "Atomic Structure Calculations of Complex Atoms"

A special issue of Atoms (ISSN 2218-2004).

Deadline for manuscript submissions: 15 July 2021.

Special Issue Editor

Dr. Igor Mykhaylovych Savukov
E-Mail
Guest Editor
Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Interests: Energy levels; g-factors; transition probabilities; hyperfine interaction; isotope shifts; actinides

Special Issue Information

Dear Colleagues,

It is known that actinide atoms and similar (lanthanides, super heavy elements) multivalence atoms and low-Z ions present a significant challenge to atomic structure theories. First of all, multiple-valence electrons lead to complex high-density spectra and strong mixing of configurations, especially in higher excited states. Second, valence electrons interact with the core electrons, and this further complicates matters since it is not sufficient to consider valence electrons in isolation. Third, there are also significant effects of relativity [1], so LS coupling, which helps in classification and calculations of transitions, is not very accurate in many cases. The classification of terms is one important task, and Cowan-code based approaches [2] have been fairly successful. Multiple adjustable parameters have been used to achieve the difference between theory and experiment on the order of tens of inverse cm. However, pure semi-empirical approaches can be deficient, and if the model is not correct, various properties of atoms can be predicted with large deviations. Introduction of core-polarization potentials somewhat helps the situation, since the important valence–core interactions are partially accounted for [3], but still, discrepancies between theory and experiments for such properties as transition amplitudes remain. Methods based on multiconfiguration Dirak–Fock (MCDF) [4], multiconfiguration Hartree–Fock MCHF, and configuration–interaction many-body perturbation theory (CI-MBPT) are quite promising, but each method has significant difficulties. For example, CI-MBPT does not have a very accurate starting potential, and large basis sets are needed to compensate for this. This is especially problematic in the case of atoms with more than three valence electrons, such as U I or Pu I, of great interest in many applications. One possible solution is to introduce adjustable parameters into essentially ab initio CI-MBPT that accounts for valence-core interaction in the 2nd order of MBPT to improve the prediction of configuration mixing and improve the accuracy of energy levels for better identification. This has really worked in case of two and three valence-electron atoms/ions, such as La II [5]. As an alternative to parametric CI-MBPT, valence–core interaction can be included ab initio using the CI-all-order approach [6,7]. However, with the increase of valence electrons, saturation of the valence basis becomes a real issue. The above methods are still promising, though. A solution to the large valence space problem has recently been proposed by introducing the method of configuration–interaction perturbation theory, CIPT, by Dzuba et al [8]. What the problems and difficulties of other methods are would be very important to understand to solve this difficult problem. This issue invites papers in various branches of atomic structure calculations for complex atoms. The applications of the theory of complex atoms are also welcome. It is also interesting to understand if molecular structure codes [9] can also lead to accurate results in atomic systems. Additionally, some unconventional approaches, such as machine-learning-based, would be of great interest [10].

References:

  1. Indelicato and E. Lindroth, “Relativistic effects, correlation, and QED corrections on Kα transitions in medium to very heavy atoms,” Phys. Rev. A 46, 2426 (1992).
  2. D. Cowan, “The theory of atomic structure and spectra,” Los Alamos Series in Basic and Applied Sciences, First edition, 1981.
  3. Kuaga-Egger and J. Migdaek ”Theoretical  radiative lifetimes of levels in singly ionized lanthanum,” J. Phys.B: At. Mol. Opt. Phys. 42, 185002 (2009).
  4. Stanek and J. Migdaek, “Relativistic MCDF oscillator strengths for 62 1S0-6s6p1P1,3P1transitions in lanthanide ions,” J. Phys. B 37, 27072712 (2004)
  5. Igor M. Savukov and Petr M. Anisimov, “Configuration-interaction many-body perturbation theory for La ii electric-dipole transition probabilities,” Phys. Rev. A 99, 032507 (2019)
  6. Savukov, U. I. Safronova, and M. S. Safronova, “Relativistic configuration interaction plus linearized-coupled-cluster calculations of U2+energies, g factors, transition rates, and lifetimes,” Phys. Rev. A 92, 052516 (2015)
  7. S. Safronova, U. I. Safronova, and Charles W. Clark, “Relativistic all-order calculations of Th, Th+, and Th 2+ atomic properties,” Phys. Rev. A 90, 032512 (2014).
  8. A. Dzuba, J. C. Berengut, C. Harabati, and V. V. Flambaum, “Combining configuration interaction with perturbation theory for atoms with a large number of valence electrons,” Phys. Rev. 95, 012503 (2017).
  9. Xiaoyan Cao and Michael Dolg, “Theoretical prediction of the second to fourth actinide ionization potentials,” Mol. Physics, 101, 961-969 (2003).
  10. Keith L.Peterson, “Classification of Cm II and Pu I energy levels using counterpropagation neural networks,” Phys. Rev. A 44, 126 (1991).

Dr. Igor Mykhaylovych Savukov
Guest Editor

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Keywords

  • atomic structure calculations
  • actinides atoms and low-Z ions
  • transition probabilities
  • isotope shift
  • hyperfine structure
  • super-heavy atoms
  • complex atoms

Published Papers (3 papers)

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Research

Open AccessArticle
Extended Atomic Structure Calculations for W11+ and W13+
Atoms 2020, 8(4), 92; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms8040092 - 07 Dec 2020
Viewed by 600
Abstract
We report an extensive and elaborate theoretical study of atomic properties for Pm-like and Eu-like Tungsten using Flexible Atomic Code (FAC). Excitation energies for 304 and 500 fine structure levels are presented respectively, for W11+ and W13+. Properties of the [...] Read more.
We report an extensive and elaborate theoretical study of atomic properties for Pm-like and Eu-like Tungsten using Flexible Atomic Code (FAC). Excitation energies for 304 and 500 fine structure levels are presented respectively, for W11+ and W13+. Properties of the 4f-core-excited states are evaluated. Different sets of configurations are used and the discrepancies in identifications of the ground level are discussed. We evaluate transition wavelength, transition probability, oscillator strength, and collisional excitation cross section for various transitions. Comparisons are made between our calculated values and previously available results, and good agreement has been achieved. We have predicted some new energy levels and transition data where no other experimental or theoretical results are available. The present set of results should be useful in line identification and interpretation of spectra as well as in modelling of fusion plasmas. Full article
(This article belongs to the Special Issue Atomic Structure Calculations of Complex Atoms)
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Open AccessArticle
CI-MBPT and Intensity-Based Lifetime Calculations for Th II
Atoms 2020, 8(4), 87; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms8040087 - 01 Dec 2020
Viewed by 510
Abstract
Lifetime calculations of Th II J = 1.5 and 2.5 odd states are performed with configuration–interaction many-body perturbation theory (CI-MBPT). For many J = 2.5 states, lifetimes are quite accurate, but two pairs of J = 2.5 odd states and many groups of [...] Read more.
Lifetime calculations of Th II J = 1.5 and 2.5 odd states are performed with configuration–interaction many-body perturbation theory (CI-MBPT). For many J = 2.5 states, lifetimes are quite accurate, but two pairs of J = 2.5 odd states and many groups of J = 1.5 states are strongly mixed, making theoretical predictions unreliable. To solve this problem, a method based on intensities is used. To relate experimental intensities to lifetimes, two parameters, one an overall coefficient of proportionality for transition rates and one temperature of the Boltzmann distribution of populations, are introduced and fitted to minimize the deviation between theoretical and intensity-derived lifetimes. For strongly mixed groups of states, the averaged lifetimes obtained from averaged transition rates were used instead of individual lifetimes in the fit. Close agreement is obtained. Then intensity branching ratios are used to extract individual lifetimes for the strongly mixed states. The resulting lifetimes are compared to available directly measured lifetimes and reasonable agreement is found, considering limited accuracy of intensity measurements. The method of intensity-based lifetime calculations with fit to theoretical lifetimes is quite general and can be applied to many complex atoms where strong mixing between multiple states exists. Full article
(This article belongs to the Special Issue Atomic Structure Calculations of Complex Atoms)
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Open AccessArticle
Numerical Procedures for Relativistic Atomic Structure Calculations
Atoms 2020, 8(4), 85; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms8040085 - 26 Nov 2020
Viewed by 721
Abstract
Variational methods are used extensively in the calculation of transition rates for numerous lines in a spectrum. In the GRASP code, solutions of the multiconfiguration Dirac–Hartree–Fock (MCDHF) equations that optimize the orbitals are represented by numerical values on a grid using finite differences [...] Read more.
Variational methods are used extensively in the calculation of transition rates for numerous lines in a spectrum. In the GRASP code, solutions of the multiconfiguration Dirac–Hartree–Fock (MCDHF) equations that optimize the orbitals are represented by numerical values on a grid using finite differences for integration and differentiation. The numerical accuracy and efficiency of existing procedures are evaluated and some modifications proposed with heavy elements in mind. Full article
(This article belongs to the Special Issue Atomic Structure Calculations of Complex Atoms)
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