Atomic Structure Calculations of Complex Atoms

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