A methodology based on configuration-state-function generators (CSFGs) has recently been implemented in the General-Purpose Relativistic Atomic Structure Package (grasp) to reduce the computational load of configuration-interaction (CI) calculations Y. T. Li et al., Comput. Phys. Commun. 283, 108562 (2023)10.1016/j.cpc.2022.108562. Large CI calculations can be performed if part of the interaction is treated perturbatively. Here, we present enhancements to the perturbative estimates by implementing blockwise methods, where the blocks are given by configuration-state-functions spanned by CSFGs. We compute excitation energies for 4s24p64d, 4s24p64f, and 4s24p54d2 states in Rb-like W37+ and corresponding transition wavelengths and rates to evaluate the methods. The final relative difference between calculated and experimental wavelengths is 0.01%. Thus, the calculations provide highly accurate values for W37+ properties useful for a variety of applications, including fusion applications.

High-resolution collinear laser spectroscopy of neutron-rich actinium has been performed at TRIUMF's isotope separator and accelerator facility ISAC. By probing the 7s2S01→6d7pP11 ionic transition, the hyperfine structures and optical isotope shifts in Ac+225,226,228,229 have been measured. This allows precise determinations of the changes in mean-square charge radii, magnetic dipole moments, and electric quadrupole moments of these actinium isotopes. The improved precision of charge radii and magnetic moments clears the ambiguity in the odd-even staggering from previous studies. The electric quadrupole moments of Ac225,226,228,229 are determined for the first time.

We demonstrate behaviors of correlation effects in the calculations of atomic properties through two commonly employed many-body methods, namely the multiconfiguration Dirac-Hartree-Fock (MCDHF) and the relativistic coupled-cluster (RCC) methods. Particularly, we have benchmarked excitation energies, electric dipole (E1) matrix elements, magnetic dipole hyperfine structure constants (Ahf), and isotope shift (IS) constants in the singly ionized magnesium (Mg+) systematically at different levels of approximation of both methods. We have also estimated the E1 polarizability of the ground state and lifetimes of the excited states using the E1 matrix elements from both methods. All these results are compared with the experimental values wherever available. We find that the computed results agree well with each other with a few exceptions; in particular, the Ahf and IS constants from the RCC method are found to agree with the measurements better. This comparison analysis would be useful in evaluating the above-discussed properties in other atomic systems using the MCDHF and RCC methods more reliably.

The GRASPG program package is an extension to GRASP2018 (Froese Fischer et al. (2019) [1]) based on configuration state function generators (CSFGs). The generators keep spin-angular integrations at a minimum and reduce substantially the execution time and the memory requirement for large-scale multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (CI) atomic structure calculations. The package includes the improvements reported in Li (2023) [8] in terms of redesigned and efficient constructions of direct and exchange potentials and Lagrange multipliers. In addition, further parallelization of the diagonalization procedure has been implemented. Tools have been developed for predicting configuration state functions (CSFs) that are unimportant and can be discarded for large MCDHF or CI calculations based on results from smaller calculations, thus providing efficient methods for a priori condensation. The package provides a seamless interoperability with GRASP2018. From extensive test runs and benchmarking, we have demonstrated reductions in the execution time and disk file sizes with factors of 37 and 98, respectively, for MCDHF calculations based on large orbital sets compared to corresponding GRASP2018 calculations. For CI calculations, reductions of the execution time with factors over 200 have been attained. With a sensible use of the new possibilities for a priori condensation, CI calculations with nominally hundreds of millions of CSFs can be handled. PROGRAM SUMMARY Program Title: GRASPG CPC Library link to program files: https://doi.org/10.17632/7b5kbhy3v9.1 Licensing provisions: MIT License Programming language: Fortran 95 Nature of problem: Prediction of atomic energy levels using a multiconfiguration Dirac–Hartree–Fock approach. Solution method: The computational method is the same as in GRASP2018 [1] except that configuration state function generators (CSFGs) have been introduced, a concept that substantially reduces the execution times and memory requirements for large-scale calculations [2]. The method also relies on redesigned and more efficient constructions of direct and exchange potentials and Lagrange multipliers, along with additional parallelization of the diagonalization procedure as detailed in [3]. Additional comments including restrictions and unusual features: 1. provides a seamless interoperability with GRASP2018, 2. options to limit the Breit interaction, 3. includes tools for predicting CSFs that are unimportant and can be discarded for large MCDHF or CI calculations based on the results from smaller calculations. References [1] C. Froese Fischer, G. Gaigalas, P. Jönsson, and J. Bieroń, Comput. Phys. Commun. 237 (2019) 184-187. [2] Y. Li, K. Wang, R. Si et al. Comput. Phys. Commun. 283 (2023) 108562. [3] Y. Li, J. Li, C. Song et al. Atoms 11 (2023) 12.

Aims. The aim of this study is to provide radiative data for neutral and singly ionised silicon, in particular for the first experimental oscillator strengths for near-infrared Si I lines. In addition, we aim to perform atomic structure calculations both for neutral and singly ionised silicon while including lines from highly excited levels.

Methods. We performed large-scale atomic structure calculations with the relativistic multiconfiguration Dirac-Hartree-Fock method using the GRASP2K package to determine log(𝑔ƒ) values of Si I and Si II lines, taking into account valence-valence and core-valence electron correlation. In addition, we derived oscillator strengths of near-infrared Si I lines by combining the experimental branching fractions with radiative lifetimes from our calculations. The silicon plasma was obtained from a hollow cathode discharge lamp, and the intensity-calibrated high-resolution spectra between 1037 and 2655 nm were recorded by a Fourier transform spectrometer.

Results. We provide an extensive set of accurate experimental and theoretical log(𝑔ƒ) values. For the first time, we derived 17 log(𝑔ƒ) values of Si I lines in the infrared from experimental measurements. We report data for 1500 Si I lines and 500 Si II lines. The experimental uncertainties of our ƒ-values vary between 5% for the strong lines and 25% for the weak lines. The theoretical log(𝑔ƒ) values for Si I lines in the range 161 nm to 6340 nm agree very well with the experimental values of this study and complete the missing transitions involving levels up to 3s²3p7s (61 970 cm⁻¹). In addition, we provide accurate calculated log(𝑔ƒ) values of Si II lines from the levels up to 3s²7f (122 483 cm⁻¹) in the range 81 nm to 7324 nm.

The isotope shifts in electron affinities of Pb were measured by Walter et al. [Phys. Rev. A 106, L010801 (2022)] to be -0.002(4) meV for 207-208Pb and -0.003(4) meV for 206-208Pb by scanning the threshold of the photodetachment channel Pb-(S3/2◦4) - Pb (3P0), while Chen and Ning reported 0.015(25) and -0.050(22) meV for the isotope shifts on the binding energies measured relative to 3P2 using the SEVI method [J. Chem. Phys. 145, 084303 (2016)]. Here we revisited these isotope shifts by using our second-generation SEVI spectrometer and obtained -0.001(15) meV for 207-208Pb and -0.001(14) meV for 206-208Pb, respectively. In order to aid the experiment by theory, we performed the first ab initio theoretical calculations of isotope shifts in electron affinities and binding energies of Pb, as well as the hyperfine structure of 207Pb-, by using the MCDHF and RCI methods. The isotope shifts in electron affinities of 207-208Pb and 206-208Pb are -0.0023(8) and -0.0037(13) meV for the 3P0 channel, respectively, in good agreement with Walter et al.'s measurements. The isotope shifts in binding energies relative to 3P1,2, -0.0015(8) and -0.0026(13) meV for 207-208Pb and 206-208Pb, respectively, are compatible with the present measurements. The hyperfine constant for the ground state of 207Pb- obtained by the present calculations, A(S3/2◦4)=-1118 MHz, differs by a factor of 3 from the previous estimation by Bresteau et al. [J. Phys. B: At., Mol. Opt. Phys. 52, 065001 (2019)]. The reliability is supported by the good agreement between the theoretical and experimental hyperfine parameters of 209Bi.

Hyperfine structure constants have many applications, but are often hard to calculate accurately due to large and canceling contributions from different terms of the hyperfine interaction operator, and also from different closed and spherically symmetric core subshells that break up due to electron correlation effects. In multiconfiguration calculations, the wave functions are expanded in terms of configuration state functions (CSFs) built from sets of one-electron orbitals. The orbital sets are typically enlarged within the layer-by-layer approach. The calculations are energy-driven, and orbitals in each new layer of correlation orbitals are spatially localized in regions where the weighted total energy decreases the most, overlapping and breaking up different closed core subshells in an irregular pattern. As a result, hyperfine structure constants, computed as expectation values of the hyperfine operators, often show irregular or oscillating convergence patterns. Large orbital sets, and associated large CSF expansions, are needed to obtain converged values of the hyperfine structure constants. We analyze the situation for the states of the {2s22p3,2s22p23p,2s22p24p} odd and {2s22p23s,2s2p4,2s22p24s,2s22p23d} even configurations in N I, and show that the convergence with respect to the increasing sets of orbitals is radically improved by introducing separately optimized orbital sets targeted for describing the spin- and orbital-polarization effects of the 1s and 2s core subshells that are merged with, and orthogonalized against, the ordinary energy-optimized orbitals. In the layer-by-layer approach, the spectroscopic orbitals are kept frozen from the initial calculation and are not allowed to relax in response to the introduced layers of correlation orbitals. To compensate for this lack of variational freedom, the orbitals are transformed to natural orbitals prior to the final calculation based on single and double substitutions from an increased multireference set. The use of natural orbitals has an important impact on the states of the 2s22p23s configuration, bringing the corresponding hyperfine interaction constants in closer agreement with experiment. Relying on recent progress in methodology, the multiconfiguration calculations are based on configuration state function generators, cutting down the time for spin-angular integration by factors of up to 50, compared to ordinary calculations.

Computational atomic physics continues to play a crucial role in both increasing the understanding of fundamental physics (e.g., quantum electrodynamics and correlation) and producing atomic data for interpreting observations from large-scale research facilities ranging from fusion reactors to high-power laser systems, space-based telescopes and isotope separators. A number of different computational methods, each with their own strengths and weaknesses, is available to meet these tasks. Here, we review the relativistic multiconfiguration method as it applies to the General Relativistic Atomic Structure Package [grasp2018, C. Froese Fischer, G. Gaigalas, P. Jonsson, J. Bieron, Comput. Phys. Commun. (2018). DOI: 10.1016/j.cpc.2018.10.032]. To illustrate the capacity of the package, examples of calculations of relevance for nuclear physics and astrophysics are presented.

As the most abundant element in the universe after hydrogen and helium, oxygen plays a key role in planetary, stellar, and galactic astrophysics. Its abundance is especially influential in terms of stellar structure and evolution, and as the dominant opacity contributor at the base of the Sun's convection zone, it is central to the discussion on the solar modelling problem. However, abundance analyses require complete and reliable sets of atomic data. We present extensive atomic data for O I by using the multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction methods. We provide the lifetimes and transition probabilities for radiative electric dipole transitions and we compare them with results from previous calculations and available measurements. The accuracy of the computed transition rates is evaluated by the differences between the transition rates in Babushkin and Coulomb gauges, as well as via a cancellation factor analysis. Out of the 989 computed transitions in this work, 205 are assigned to the accuracy classes AA-B, that is, with uncertainties smaller than 10%, following the criteria defined by the Atomic Spectra Database from the National Institute of Standards and Technology. We discuss the influence of the new log(gf) values on the solar oxygen abundance, ultimately advocating for log epsilon(O) = 8.70 +/- 0.04.