atoms Article Relativistic Configuration-Interaction and Perturbation Theory Calculations for Heavy Atoms Igor M. Savukov * , Dmytro Filin, Pinghan Chu and Michael W. Malone   Citation: Savukov, I.M.; Filin, D.; Chu, P.; Malone, M.W. Relativistic Configuration-Interaction and Perturbation Theory Calculations for Heavy Atoms. Atoms 2021, 9, 104. https://doi.org/10.3390/atoms9040104 Academic Editor: Kanti M. Aggarwal Received: 30 September 2021 Accepted: 23 November 2021 Published: 30 November 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Los Alamos National Laboratory, Los Alamos, NM 87545, USA; dfilin@udel.edu (D.F.); pchu@lanl.gov (P.C.); mwmalone@lanl.gov (M.W.M.) * Correspondence: isavukov@lanl.gov Abstract: Heavy atoms present challenges to atomic theory calculations due to the large number of electrons and their complicated interactions. Conventional approaches such as calculations based on Cowan’s code are limited and require a large number of parameters for energy agreement. One promising approach is relativistic configuration-interaction and many-body perturbation theory (CI-MBPT) methods. We present CI-MBPT results for various atomic systems where this approach can lead to reasonable agreement: La I, La II, Th I, Th II, U I, Pu II. Among atomic properties, energies, g-factors, electric dipole moments, lifetimes, hyperfine structure constants, and isotopic shifts are discussed. While in La I and La II accuracy for transitions is better than that obtained with other methods, more work is needed for actinides. Keywords: CI-MBPT; parametric configuration-interaction many-body perturbation theory; strong state mixing; transition rates 1. Introduction Heavy atoms, such as actinides, are highly challenging for atomic calculations for at least the following reasons: (1) most actinides and lanthanides have many valence electrons, including f-electrons, and hence a large number of closely spaced fine-structure states. Together with a significant configuration mixing, this leads to difficulties in identification of states and accurate calculations of properties that depend on configurations and terms. To achieve adequate accuracy, all-order methods, such as configuration-interaction (CI) methods, are needed to account for valence-valence interactions. (2) The valence electrons strongly interact with a large number of core electrons. This interaction cannot be ignored and needs to be treated beyond the second order in many-body perturbation theory (MBPT), if the calculations are carried out in the CI-MBPT framework. Here, several options exist for improvement of accuracy: scaling second-order MBPT corrections [1–3], including higher-order effects as in CI-all-order approach [4,5], or including upper core electrons into the valence space [6]. (3) Relativistic effects are significant and lead to deviation from the LS coupling scheme. Because, for example, electric-dipole transitions conserve the total spin in non-relativistic approximation, the mixing of states of different S has a strong effect on the magnitude of the electric dipole transitions and is one reason for large uncertainty in the computed values. Codes, such as Cowan’s popular code, treat relativistic effects quite approximately, for example, by including spin-orbit terms but neglecting many other important terms. To amend this, generalization lead to relativistic analogs of Cowan’s code, such as the Los Alamos suite of relativistic atomic physics codes [7]. Even relativistic MBPT approach, which is based on the Dirac–Hartree–Fock (DHF) starting potential, does not include a number of significant relativistic effects beyond DHF. In the case of actinides, the experimental data are limited owing to difficulties of dealing with radioactive atoms. Uranium, with the relatively stable isotope U-238, is extensively studied because of its roles in global security [8–10], atomic energy [11], and more. The spectroscopy of the uranium atom can be used for detection and characterization Atoms 2021, 9, 104. https://doi.org/10.3390/atoms9040104 https://www.mdpi.com/journal/atoms