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.

Accurate and extensive atomic data are essential for spectroscopic analyses of stellar atmospheres and other astronomical objects. We present energy levels, lifetimes, and transition probabilities for neutral nitrogen, the sixth most abundant element in the cosmos. The calculations employ the fully relativistic multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction methods, and span the 103 lowest states up to and including 2s(2)2p(2)5s. Our theoretical energies are in excellent agreement with the experimental data, with an average relative difference of 0.07%. In addition, our transition probabilities are in good agreement with available experimental and theoretical data. We further verify the agreement of our data with experimental results via a reanalysis of the solar nitrogen abundance, with the results from the Babushkin and Coulomb gauges consistent to 2% or 0.01 dex. We estimated the uncertainties of the computed transition data based on a statistical analysis of the differences between the transition rates in the Babushkin and Coulomb gauges. Out of the 1701 computed electric dipole transitions in this work, 83 (536) are associated with uncertainties smaller than 5% (10%).

Multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) calculations are performed for 22 states in singly ionized tin (Sn II) belonging to the 5s2ns (n=6,7), 5s2nd (n=5,6), 5s5p2 even parity configurations and the 5s2np (n=5,6,7), 5s24f odd parity configurations. Valence-valence and core-valence correlation effects are taken into account through configuration state function (CSF) expansions. Complete and consistent data sets of level energies, wavelengths, oscillator strengths, lifetimes and transition rates among all these states are given. The results are compared with existing theoretical and experimental results. There is an excellent agreement for calculated excitation energies with experimental data from the NIST database. Lifetimes and transition rates are also in agreement with the results from previous calculations and available measurements for most of the transitions.

Ab initio calculations sometimes do not reproduce the experimentally observed energy separations at a high enough accuracy. Fine-tuning of diagonal elements of the Hamiltonian matrix is a process which seeks to ensure that calculated energy separations of the states that mix are in agreement with experiment. The process gives more accurate measures of the mixing than can be obtained in ab initio calculations. Fine-tuning requires the Hamiltonian matrix to be diagonally dominant, which is generally not the case for calculations based on jj-coupled configuration state functions. We show that this problem can be circumvented by a method that transforms the Hamiltonian in jj-coupling to a Hamiltonian in LSJ-coupling for which fine-tuning applies. The fine-tuned matrix is then transformed back to a Hamiltonian in jj-coupling. The implementation of the method into the General Relativistic Atomic Structure Package is described and test runs to validate the program operations are reported. The new method is applied to the computation of the 2s(21)S(0)-2s2p(1,3)P(1) transitions in C III and to the computation of Rydberg transitions in B I, for which the 2s(2)p(22)S(1/2) perturber enters the 2s(2)ns(2)S(1/2) series. Improved convergence patterns and results are found compared with ab initio calculations.

grasp is a software package in Fortran 95, adapted to run in parallel under MPI, for research in atomic physics. The basic premise is that, given a wave function, any observed atomic property can be computed. Thus, the first step is always to determine a wave function. Different properties challenge the accuracy of the wave function in different ways. This software is distributed under the MIT Licence.