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.

In multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations, there is a strong coupling between the localization of the orbital set and the configuration state function (CSF) expansion used to determine it. Furthermore, it is well known that an orbital set resulting from calculations, including CSFs describing core-core correlation and other effects, which aims to lower the weighted energies of a number of targeted states as much as possible, may be inadequate for building CSFs that account for correlation effects that are energetically unimportant but decisive for computed properties, e.g., hyperfine structures or transition rates. This inadequacy can be traced in irregular or oscillating convergence patterns of the computed properties as functions of the increasing orbital set. In order to alleviate the above problems, we propose a procedure in which the orbital set is obtained by merging several separately optimized, and mutually non-orthogonal, orbital sets. This computational strategy preserves the advantages of capturing electron correlation on the total energy through the variational MCDHF method and allows to target efficiently the correlation effects on the considered property. The orbital sets that are merged are successively orthogonalized against each other to retain orthonormality. The merged orbital set is used to build CSFs that efficiently lower the energy and also adequately account for the correlation effects that are important for the property. We apply the procedure to compute the hyperfine structure constants for the 1s(2)2s (2)S1/2 and 1s(2)2p (2Po)(1/2, 3/2) states in Li-7 and show that it leads to considerably improved convergence patterns with respect to the increasing orbital set compared to standard calculations based on a single orbital set, energy optimized in the variational procedure. The perspectives of the new procedure are discussed in a broader context in the summary.

The latest published version of GRASP (General-purpose Relativistic Atomic Structure Package), i.e., GRASP2018, retains a few suboptimal subroutines/algorithms, which reflect the limited memory and file storage of computers available in the 1980s. Here we show how the efficiency of the relativistic self-consistent-field (SCF) procedure of the multiconfiguration-Dirac-Hartree-Fock (MCDHF) method and the relativistic configuration-interaction (RCI) calculations can be improved significantly. Compared with the original GRASP codes, the present modified version reduces the CPU times by factors of a few tens or more. The MPI performances for all the original and modified codes are carefully analyzed. Except for diagonalization, all computational processes show good MPI scaling.

In configuration interaction (CI) calculations the atomic wave functions are given as expansions over configuration state functions (CSFs) built on relativistic one-electron orbitals. The expansion coefficients of the configuration state functions are obtained by constructing and diagonalizing the Hamiltonian matrix. Here we show how a regrouping of the configuration state functions and the introduction of configuration state function generators (CSFGs) allow for a substantial reduction of the computational load in relativistic CI calculations. The computational methodology based on configuration state function generators, recently implemented in the General Relativistic Atomic Structure package (Grasp2018, Froese Fischer et al. (2019) [16]), is applied to a number of atomic systems and correlation models with increasing sets of one-electron orbitals. We demonstrate a reduction of the CPU time with factors between 10 and 14 for the largest CI calculations. The inclusion of the Breit interaction into the calculations is time consuming. By applying restrictions on the Breit integrals we show that it is possible to further reduce the CPU times with factors between 2 and 3, with negligible changes to the computed excitation energies. We also demonstrate that the introduction of configuration state function generators allows for efficient a priori condensation techniques, with reductions of the expansions sizes with factors between 1.5 and 2.5 and the CPU time with factors between 2.5 and 4.5, again with negligible changes to the excitation energies. In total we demonstrate reductions of the CPU time with factors up to 68 for CI calculations based on configuration state function generators, restrictions on the Breit integrals and with a priori condensed expansions compared to ordinary CI calculations without restrictions on the Breit integrals and with full expansions. Further perspectives of the new methodology based on configuration state function generators are given.

Atomic properties of n = 3 levels for W47+ - W55+ ions (Z = 74) are systematically calculated using two different and independent methods, namely, the second-order many-body perturbation theory and the multi-configuration Dirac-Hartree-Fock method combined with the relativistic configuration interaction approach. Wavelengths and transition rates for electric-and magnetic-dipole transitions involving the n = 3 levels of W47+ - W55+ are calculated. In addition, we discuss in detail the importance of the valence and core-valence electron correlations, the Breit interaction, the higher-order frequency-dependent retardation correction, and the leading quantum electrodynamical corrections for transition wavelengths. Spectroscopic accuracy is achieved for the present calculated wavelengths, and most of them agree with experimental values within 0.05%. Our calculated wavelengths, combined with collisional radiative model simulations, are used to identify the yet unidentified 25 observed lines in the extremely complex spectrum between 27 angstrom and 34 angstrom measured by Lennartsson et al. [Phys. Rev. A 87, 062505 (2013)]. We provide additional data for 472 strong electric-dipole transitions in the wavelength range of 17-50 angstrom, and 185 strong magnetic-dipole transitions between 36 angstrom and 4384 angstrom, with a line intensity greater than 1 photon/s. These can provide benchmark data for future experiments and theoretical calculations.

Large-scale multiconfiguration Dirac-Hartree-Fock calculations are provided for the n <= 5 states in C-like ions from O iii to Mg vii. Electron correlation effects are accounted for by using large configuration state function expansions, built from sets of orbitals with principal quantum numbers n <= 10. An accurate and complete data set of excitation energies, wavelengths, radiative transition parameters, and lifetimes is offered for the 156 (196, 215, 272, 318) lowest states of the 2s (2)2p (2), 2s2p (3), 2p (4), 2s (2)2p3s, 2s (2)2p3p, 2s (2)2p3d, 2s2p (2)3s, 2s2p (2)3p, 2s2p (2)3d, 2p (3)3s, 2p (3)3p, 2p (3)3d, 2s (2)2p4s, 2s (2)2p4p, 2s (2)2p4d, 2s (2)2p4f, 2s2p (2)4s, 2s2p (2)4p, 2s2p (2)4d, 2s2p (2)4f, 2s (2)2p5s, 2s (2)2p5p, 2s (2)2p5d, 2s (2)2p5f, and 2s (2)2p5g configurations in O iii (F iv, Ne v, Na vi, Mg vii). By comparing available experimental wavelengths with the MCDHF results, the previous line identifications for the n = 5, 4, 3 -> n = 2 transitions of Na vi in the X-ray and EUV wavelength range are revised. For several previous identifications discrepancies are found, and tentative new (or revised) identifications are proposed. A consistent atomic data set including both energy and transition data with spectroscopic accuracy is provided for the lowest hundreds of states for C-like ions from O iii to Mg vii.

We modified the Hfs92 code of the GRASP package in order to describe the magnetic octupole hyperfine interaction. To illustrate the utility of the modified code, we carried out state-of-the-art calculations of the electronic factors of the magnetic octupole hyperfine interaction constants for levels in the ground configuration of the Bi atom. The nuclear magnetic octupole moment of the Bi-209 isotope was extracted by combining old measurements of the hyperfine structures of 6p(34)S(3/2)(o) [Hull, R.; Brink, G. Phys. Rev. A 1970, 1, 685] and 2P(3/2)(o) [Landman, D.A.; Lurio, A. Phys. Rev. A 1970, 1, 1330] using the atomic-beam magnetic-resonance technique with our theoretical electronic factors. The present extracted octupole moment was consistent with all the available values but the one obtained in the single-particle nuclear shell model approximation. This observation supports the previous finding that nuclear many-body effects, such as the core polarization, significantly contribute to the nuclear magnetic octupole moment in the case of Bi-209.

A new module, RDENSITY, of the GRASP2018 package [1] is presented for evaluating the radial electron density function of an atomic state described by a multiconfiguration Dirac-Hartree-Fock or configuration interaction wave function in the fully relativistic scheme. The present module is the relativistic version of DENSITY [2] that was developed for the ATSP2K package [3]. The calculation of the spin-angular factors entering in the expression of the expectation value of the density operator is performed using the angular momentum theory in orbital, spin, and quasispin spaces, adopting a generalized graphical technique [4]. The natural orbitals (NOs) are evaluated from the diagonalization of the density matrix, taking advantage of its κ-block structure. The features of the code are discussed in detail, focusing on the advantages and properties of the NOs and on the electron radial density picture as a mean for investigating electron correlation and relativistic effects.

New 125 I atomic decay emission data of medical interest are presented. The calculations are based on two atomic structure codes that implement the multi-configuration Dirac-Hartree-Fock method. Radiative and non-radiative ransition rates are calculated in this method and then used to generate the atomic deexcitation cascade. Subshell transition rates, level widths and fluorescence yields are compared to the Evaluated Atomic Data Library. Coster-Kronig and Auger electron emission yields are also compared with results from other authors. The comparison with the experimental electron emission spectrum shows that the new calculations can reproduce very well the structure of the K-LL Auger electron peaks and improve the description of the M Auger peaks below 300 eV. The 125 I dose-point kernel is also simulated using the new data, resulting in higher values below 10 nm when compared those obtained with the Evaluated Atomic Data Library. 

Large-scale ab initio calculations of the electronic contribution to the electric quadrupole hyperfine constant B were performed for the 5s(2)5p6s( 1,3)P(1)(0)excited states of neutral tin. To probe the sensitivity of B to different electron correlation effects, three sets of variational multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction calculations employing different strategies were carried out. In addition, a fourth set of calculations was based on the configuration interaction Dirac-Fock-Sturm theory. For the 5s(2)5p6s( 1)P(1)(0) state, the final value of B/Q = 703(50) MHz/b differs by 0.4% from the one recently used by Yordanov et al. [Commun. Phys. 3, 107 (2020)] to extract the nuclear quadrupole moments Q for tin isotopes in the range Sn117-131 from collinear laser spectroscopy measurements. Efforts were made to provide a realistic theoretical uncertainty for the final B/Q value of the 5s(2)5p6s( 1)P(1)(0) state based on statistical principles and on correlation with the electronic contribution to the magnetic dipole hyperfine constant A.

Atomic properties of n=3 states of the W56+ - W61+ ions are systematically investigated through two state-of-the-art methods, namely, the second-order many-body perturbation theory, and the multi-configuration Dirac–Hartree–Fock method combined with the relativistic configuration interaction approach. The contributions of valence-valence and core-valence electron correlations, the Breit interaction, the higher-order retardation correction beyond the Breit interaction through the transverse photon interaction, and the quantum electrodynamical corrections to the excitation energies are studied in detail. The excitation energies and wavelengths obtained with the two methods agree with each other within ≈0.01%. The present results achieve spectroscopic accuracy and provide a benchmark test for various applications and other theoretical calculations of W56+ - W61+ ions. They will assist spectroscopists in their assignment and direct identification of observed lines in complex spectra.

The multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction methods are used to provide excitation energies, lifetimes, and radiative transition data for the 604 (699, 702, 704, 704, 704, and 699) lowest levels of the 3s (2)3p (2), 3s3p (3), 3s (2)3p3d, 3p (4), 3s3p (2)3d, 3s (2)3d (2), 3p (3)3d, 3s3p3d (2), 3s3d (3), 3p3d (3), 3p (2)3d (2), 3s (2)3p4s, 3s (2)3p4p, 3s (2)3p4d, 3s (2)3p4f, 3s3p (2)4s, 3s3p (2)4p, 3s3p (2)4d, 3s3p (2)4f, 3s (2)3d4s, 3s (2)3d4p, 3p (3)4s, 3p (3)4p, 3s3p3d4s, 3s (2)3p5s, and 3s (2)3p5p configurations in Cr xi, (Mn xii, Fe xiii, Co xiv, Ni xv, Cu xvi, and Zn xvii). Previous line identifications of Fe xiii and Ni xv in the EUV and X-ray wavelength ranges are reviewed by comprehensively comparing the MCDHF theoretical results with available experimental data. Many recent identifications of Fe xiii and Ni xv lines are confirmed, and several new identifications for these two ions are proposed. A consistent atomic data set with spectroscopic accuracy is provided for the lowest hundreds of levels for Si-like ions of iron-group elements of astrophysical interest, for which experimental values are scarce. The uncertainty estimation method suggested by Kramida, applied to the comparison of the length and velocity line strength values, is used for ranking the transition data. The correlation of the latter with the gauge dependency patterns of the line strengths is investigated.

The multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) methods were used to compute excitation energies and transition data for the 147 lowest states of the even 3s(3)p(4), 3s(2)3p2(3)d, 3p(4)3d, 3s(3)p(2)3d(2) configurations and for the 124 lowest states of the odd 3s23p3, 3p5, 3s3p33d, 3s(2)3p(3)d2, 3p(3)3d(2) configurations for the P-like ions: As XIX, Kr XXII, Sr XXIV, Zr XXVI, Mo XXVIII, and W LX. E1 transition rates and weighted oscillator strengths among these states are given. Valence-valence, core-valence and core-core electron correlation effects are included. Computed excitation energies and transition data are compared with the NIST recommended values and experimental or theoretical results of other authors. All calculations were performed using the general relativistic atomic structure package GRASP2018. (C) 2021 Elsevier Inc. All rights reserved.

Using the multiconfiguration Dirac-Hartree-Fock and the relativistic configuration interaction methods, a consistent set of transition energies and radiative transition data for the main states of the 2s(2)2p(4), 2s2p(5), 2p(6), 2s(2)2p(3)3s, 2s(2)2p(3)3p, 2s(2)2p(3)3d, 2s2p(4)3s, 2s2p(4)3p, and 2s2p(4)3d configurations in O-like Ions between Ar XI (Z = 18) and Cr XVII (Z = 24) is provided. Our data set is compared with the NIST compiled values and previous calculations. The data are accurate enough for identification and deblending of new emission lines from hot astrophysical and laboratory plasmas. The amount of data of high accuracy is significantly increased for the n = 3 states of several O-like ions, where experimental data are very scarce. (c) 2020 Elsevier Inc. All rights reserved.

Accurate atomic data are essential for opacity calculations and for abundance analyses of the Sun and other stars. The aim of this work is to provide accurate and extensive results of energy levels and transition data for C I-IV. The Multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction methods were used in this work. To improve the quality of the wavefunctions and reduce the relative differences between length and velocity forms for transition data involving high Rydberg states, alternative computational strategies were employed by imposing restrictions on the electron substitutions when constructing the orbital basis for each atom and ion. Transition data, for example, weighted oscillator strengths and transition probabilities, are given for radiative electric dipole (E1) transitions involving levels up to 1s(2)2s(2)2p6s for C I, up to 1s(2)2s(2)7f for C It, up to 1s(2)2s7f for C III, and up to 1s(2)8g for C IV. Using the difference between the transition rates in length and velocity gauges as an internal validation, the average uncertainties of all presented E1 transitions are estimated to be 8.05 per cent, 7.20 percent, 1.77 percent, and 0.28 percent, respectively, for C I-IV. Extensive comparisons with available experimental and theoretical results are performed and good agreement is observed for most of the transitions. In addition, the C I data were employed in a re-analysis of the solar carbon abundance. The new transition data give a line-by-line dispersion similar to the one obtained when using transition data that are typically used in stellar spectroscopic applications today.

Astronomical infrared observations are of increasing importance for stellar spectroscopy. The analysis of element abundance relies on high-quality observations, stellar models, and ultimately on accurate atomic data. With the growing number of near-IR astronomical observations and surveys, the absence of highaccuracy data is becoming apparent and a severe limiting factor.We run a program to take up the task to provide evaluated, high-accuracy atomic data for important transitions in the near-infrared spectral region, mainly 1-5 microns. A combinations of both experimental and theoretical techniques is used, to provide complete sets of data with a low uncertainty. FTS measurements of a discharge are combined with laser induced fluorescence techniques, and GRASP2k and ATSP2k atomic structure calculations for the theoretical values.

The high-resolution Sentinel-2 data potentially enable the estimation of gross primary productivity (GPP) at finer spatial resolution by better capturing the spatial variation in a heterogeneous landscapes. This study investigates the potential of 10 m resolution reflectance from the Sentinel-2 Multispectral Instrument to improve the accuracy of GPP estimation across Nordic vegetation types, compared with the 250 m and 500 m resolution reflectance from the Moderate Resolution Imaging Spectroradiometer (MODIS). We applied linear regression models with inputs of two-band enhanced vegetation index (EVI2) derived from Sentinel-2 and MODIS reflectance, respectively, together with various environmental drivers to estimate daily GPP at eight Nordic eddy covariance (EC) flux tower sites. Compared with the GPP from EC measurements, the accuracies of modelled GPP were generally high (R-2 = 0.84 for Sentinel-2; R-2 = 0.83 for MODIS), and the differences between Sentinel-2 and MODIS were minimal. This demonstrates the general consistency in GPP estimates based on the two satellite sensor systems at the Nordic regional scale. On the other hand, the model accuracy did not improve by using the higher spatial-resolution Sentinel-2 data. More analyses of different model formulations, more tests of remotely sensed indices and biophysical parameters, and analyses across a wider range of geographical locations and times will be required to achieve improved GPP estimations from Sentinel-2 satellite data.

In previous work devoted to ab initio calculations of hyperfine-structure constants in nitrogen and fluorine atoms, we observed sizable relativistic effects, a priori unexpected for such light systems, that can even largely dominate over electron correlation. We observed that the atomic wave functions calculated in the Breit-Pauli approximation describe adequately the relevant atomic levels and hyperfine structures, even in cases for which a small relativistic LS-term mixing becomes crucial. In the present work we identify levels belonging to the spectroscopic terms 2p(4)(P-3)3d(2,4)(P, D, F) of the fluorine atom, for which correlation effects on the hyperfine structures are small, but relativistic LS-term admixtures are decisive to correctly reproduce the experimental values. The Breit-Pauli analysis of the hyperfine matrix elements nails cases with large cancellation, either between LS pairs for individual hyperfine operators or between the orbital and the spin dipole contributions. Multiconfiguration Dirac-Hartree-Fock calculations are performed to support the Breit-Pauli analysis.

Atomic properties of S-like W are evaluated through a state-of-the-art method, namely, the multiconfiguration Dirac-Hartree-Fock method combined with the relativistic configuration-interaction approach. The level energies, wavelengths, and transition parameters involving the 88 lowest levels of W58+ (W LIX) are calculated. We discuss in detail the relative importance of the valence- and core-valence electron correlation effects, the Breit interaction, the higher-order retardation correction beyond the Breit interaction through the transverse photon interaction, and the quantum electrodynamical corrections. The present level energies are highly accurate, with uncertainties close to what can be achieved from spectroscopy. As such, they provide benchmark tests for other theoretical calculations of S-like W and should assist the spectroscopists in their assignment and identification of observed lines in complex spectra.

A majority of Er in the universe is synthesized by the r-process, which can occur in the mergers of neutron stars (NSs). The contribution of this element to the opacity of NS ejecta should be tested, but even the energy levels of first excited configuration have not been fully presented. The main aim of this paper is to present accurate energy levels of the ground [Xe]4f(12) and first excited [Xe]4f(11)5d configurations of Er2+. The energy level structure of the Er2+ ion was computed using the multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction (RCI) methods, as implemented in the GRASP2018 program package. The Breit interaction, self-energy, and vacuum polarization corrections were included in the RCI computations. The zero-first-order approach was used in the computations. Energy levels with the identification in LS coupling for all (399) states belonging to the [Xe]4f(12) and [Xe]4f(11)5d configurations are presented. Electric dipole (E1) transition data between the levels of these two configurations are computed. The accuracy of these data is evaluated by studying the behavior of the transition rates as functions of the gauge parameter, as well as by evaluating the cancellation factors. The core electron correlations were studied using different strategies. The rms deviations obtained in this study for states of the ground and excited configurations from the available experimental data are 649 and 754 cm(-1), respectively.

HFSZEEMAN95 is an updated and extended Fortran 95 version of the HFSZEEMAN program (Andersson and Jönsson, 2008). Given relativistic atomic state functions generated by the GRASP2018 package (Fischer et al., 2019), HFSZEEMAN95 together with the accompanying Matlab/GNU Octave program MITHIT allows for: (1) the computation and plotting of Zeeman energy splittings of magnetic fine- and hyperfine structure substates as functions of the strength of an external magnetic field, (2) the computation of transition rates between different magnetic fine- and hyperfine structure substates in the presence of an external magnetic field and rates of hyperfine-induced transitions in the field free limit, (3) the synthesization of spectral profiles for transitions obtained from (2). With the new features, HFSZEEMAN95 and the accompanying Matlab/GNU Octave program MITHIT are useful for the analysis of observational spectra and to resolve the complex features due to the splitting of the fine and hyperfine levels.

We use the multiconfiguration Dirac-Hartree-Fock (MCDHF) method combined with the relativistic configuration interaction approach (GRASP2K) to provide a consistent set of transition energies and radiative transition data for the lower n = 3 states in all Cl-like ions of astrophysical importance, from Cr VIII to Zn XIV. We also provide excitation energies calculated for Fe X using the many-body perturbation theory (MBPT, implemented within FAC). The comparison of the present MCDHF results with MBPT and with the available experimental energies indicates that the theoretical excitation energies are highly accurate, with uncertainties of only a few hundred cm(-1). Detailed comparisons for Fe X and Ni XII highlight discrepancies in the experimental energies found in the literature. Several new identifications are proposed.

Using the multiconfiguration Dirac–Hartree–Fock and the relativistic configuration interaction methods, a consistent set of transition energies and radiative transition data for the lowest 546 (623, 701, and 745) states of the  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  , and   configurations in Mn xi (Fe xii, Co xiii, and Ni xiv) is provided. The comparison between calculated excitation energies for the n = 4 states and available experimental values for Fe xii indicate that the calculations are highly accurate, with uncertainties of only a few hundred cm−1. Lines from these states are prominent in the soft X-rays. With the present calculations, several recent new identifications are confirmed. Other identifications involving   levels in Fe xii that were found to be questionable are discussed and a few new assignments are recommended. As some n = 4 states of the other ions also show large discrepancies between experimental and calculated energies, we reassess their identification. The present study provides highly accurate atomic data for the n = 4 states of P-like ions of astrophysical interest, for which experimental data are scarce.

Aims. The Lande g-factor is an important parameter in astrophysical spectropolarimetry, used to characterize the response of a line to a given value of the magnetic field. The purpose of this paper is to present accurate Lande g-factors for states in B II, C I-IV, Al I-II, Si I-IV, P II, S II, Cl III, Ar IV, Ca I, Ti II, Zr III, and Sn II.Methods. The multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2K, are employed in the present work to compute the Lande g-factors for states in B II, C I-IV, Al I-II, Si I-IV, P II, S II, Cl III, Ar IV, Ca I, Ti II, Zr III, and Sn II. The accuracy of the wave functions for the states, and thus the accuracy of the resulting Lande g-factors, is evaluated by comparing the computed excitation energies and energy separations with the National Institute of Standards and Technology (NIST) recommended data.Results. All excitation energies are in very good agreement with the NIST values except for Ti II, which has an average difference of 1.06%. The average uncertainty of the energy separations is well below 1% except for the even states of Al I; odd states of Si I, Ca I, Ti II, Zr III; and even states of Sn II for which the relative differences range between 1% and 2%. Comparisons of the computed Lande g-factors are made with available NIST data and experimental values. Analysing the LS-composition of the wave functions, we quantify the departures from LS-coupling and summarize the states for which there is a difference of more than 10% between the computed Lande g-factor and the Lande g-factor in pure LS-coupling. Finally, we compare the computed Lande g-factors with values from the Kurucz database.

We are reinvestigating the hyperfine structure of sodium using a fully relativistic multiconfiguration approach. In the fully relativistic approach, the computational strategy somewhat differs from the original nonrelativistic counterpart used by P. Jonsson et al., Phys. Rev. A 53, 4021 (1996). Numerical instabilities force us to use a layer-by-layer approach that has some broad unexpected effects. Core correlation is found to be significant and therefore should be described in an adequate orbital basis. The natural-orbital basis provides an interesting alternative to the orbital basis from the layer-by-layer approach, allowing us to overcome some deficits of the latter, giving rise to magnetic dipole hyperfine structure constant values, in excellent agreement with observations. Effort is made to assess the reliability of the natural-orbital bases and to illustrate their efficiency.

Tin is the chemical element with the largest number of stable isotopes. Its complete proton shell, comparable with the closed electron shells in the chemically inert noble gases, is not a mere precursor to extended stability; since the protons carry the nuclear charge, their spatial arrangement also drives the nuclear electromagnetism. We report high-precision measurements of the electromagnetic moments and isomeric differences in charge radii between the lowest 1/2(+), 3/2(+), and 11/2(-) states in Sn117-131, obtained by collinear laser spectroscopy. Supported by state-of-the-art atomic-structure calculations, the data accurately show a considerable attenuation of the quadrupole moments in the closed-shell tin isotopes relative to those of cadmium, with two protons less. Linear and quadratic mass-dependent trends are observed. While microscopic density functional theory explains the global behaviour of the measured quantities, interpretation of the local patterns demands higher-fidelity modelling. Measurements of the hyperfine structure of chemical elements isotopes provide unique insight into the atomic nucleus in a nuclear model-independent way. The authors present collinear laser spectroscopy data obtained at the CERN ISOLDE and measure hyperfine splitting along a long chain of odd-mass tin isotopes.

Aims. Accurate atomic data for Ti II are essential for abundance analyses in astronomical objects. The aim of this work is to provide accurate and extensive results of oscillator strengths and lifetimes for Ti II.

Methods. The multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction (RCI) methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2018, were used in the present work. In the final RCI calculations, the transverse-photon (Breit) interaction, the vacuum polarisation, and the self-energy corrections were included.

Results. Energy levels and transition data were calculated for the 99 lowest states in Ti II. Calculated excitation energies are found to be in good agreement with experimental data from the Atomic Spectra Database of the National Institute of Standards and Technology based on the study by Huldt et al. Lifetimes and transition data, for example, line strengths, weighted oscillator strengths, and transition probabilities for radiative electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2) transitions, are given and extensively compared with the results from previous calculations and measurements, when available. The present theoretical results of the oscillator strengths are, overall, in better agreement with values from the experiments than the other theoretical predictions. The computed lifetimes of the odd states are in excellent agreement with the measured lifetimes. Finally, we suggest a relabelling of the 3d2(12D)4p y2 D3/2o and z2 P3/2o levels.

Aims. We seek to present accurate and extensive transition data for the Zr III ion. These data are useful in many astrophysical applications.Methods. We used the multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction (RCI) methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2018. The transverse-photon (Breit) interaction, vacuum polarization, and self-energy corrections are included in the RCI computations.Results. Energy spectra were calculated for the 88 lowest states in the Zr III ion. The root-mean-square deviation obtained in this study for computed energy spectra from the experimental data is 450 cm(-1). Electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2) transition data, line strengths, weighted oscillator strengths, and transition rates are computed between the above states together with the corresponding lifetimes. The computed transition rates are smaller than the experimental rates and the disagreement for weaker transitions is much larger than the experimental error bars. The computed lifetimes agree with available experimental values within the experimental uncertainties.

Accurate atomic data of the iron group elements are of major importance in astrophysics. In the present work energy spectrum calculations are performed for 332 lowest states for Ni II ion. Energy levels are compared with NISI database recommended values. All computations were done using the general-purpose relativistic atomic structure package GRASP2018.

Observations of vegetation phenology at regional-to-global scales provide important information regarding seasonal variation in the fluxes of energy, carbon, and water between the biosphere and the atmosphere. Numerous algorithms have been developed to estimate phenological transition dates using time series of remotely sensed spectral vegetation indices. A key challenge, however, is that different algorithms provide inconsistent results. This study provides a comprehensive comparison of start of season (SOS) and end of season (EOS) phenological transition dates estimated from 500 m MODIS data based on two widely used sources of such data: the TIMESAT program and the MODIS Global Land Cover Dynamics (MLCD) product. Specifically, we evaluate the impact of land cover class, criteria used to identify SOS and EOS, and fitting algorithm (local versus global) on the transition dates estimated from time series of MODIS enhanced vegetation index (EVI). Satellite-derived transition dates from each source are compared against each other and against SOS and EOS dates estimated from PhenoCams distributed across the Northeastern United States and Canada. Our results show that TIMESAT and MLCD SOS transition dates are generally highly correlated (r = 0.51-0.97), except in Central Canada where correlation coefficients are as low as 0.25. Relative to SOS, EOS comparison shows lower agreement and higher magnitude of deviations. SOS and EOS dates are impacted by noise arising from snow and cloud contamination, and there is low agreement among results from TIMESAT, the MLCD product, and PhenoCams in vegetation types with low seasonal EVI amplitude or with irregular EVI time series. In deciduous forests, SOS dates from the MLCD product and TIMESAT agree closely with SOS dates from PhenoCams, with correlations as high as 0.76. Overall, our results suggest that TIMESAT is well-suited for local-to-regional scale studies because of its ability to tune algorithm parameters, which makes it more flexible than the MLCD product. At large spatial scales, where local tuning is not feasible, the MLCD product provides a readily available data set based on a globally consistent approach that provides SOS and EOS dates that are comparable to results from TIMESAT.

Astronomical spectroscopy has recently expanded into the near-infrared (nIR) wavelength region, raising the demands on atomic transition data. The interpretation of the observed spectra largely relies on theoretical results, and progress towards the production of accurate theoretical data must continuously be made. Spectrum calculations that target multiple atomic states at the same time are by no means trivial. Further, numerous atomic systems involve Rydberg series, which are associated with additional difficulties. In this work, we demonstrate how the challenges in the computations of Rydberg series can be handled in large-scale multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) calculations. By paying special attention to the construction of the radial orbital basis that builds the atomic state functions, transition data that are weakly sensitive to the choice of gauge can be obtained. Additionally, we show that the Babushkin gauge should not always be considered as the preferred gauge, and that, in the computations of transition data involving Rydberg series, the Coulomb gauge could be more appropriate for the analysis of astrophysical spectra. To illustrate the above, results from computations of transitions involving Rydberg series in the astrophysically important C IV and C III ions are presented and analyzed.

The present GRASP2018 is an updated Fortran 95 version of the recommended block versions of programs from GRASP2K Version 1_1 for large-scale calculations Jonsson et al. (2013). MPI programs are included so that all major tasks can be executed using parallel computers. Tools have been added that simplify the generation of configuration state function expansions for the multireference single- and double computational model. Names of programs have been changed to accurately reflect the task performed by the code. Modifications to the relativistic self-consistent field program have been made that, in some instances, greatly reduce the number of iterations needed for determining the requested eigenvalues and the memory required. Changes have been made to the relativistic configuration interaction program to substantially cut down on the time for constructing the Hamiltonian matrix for configuration state function expansions based on large ,orbital sets. In the case of a finite nucleus the grid points have been changed so that the first non-zero point is Z-dependent as for the point nucleus. A number of tools have been developed to generate LaTeX tables of eigenvalue composition, energies, transition data and lifetimes. Tools for plotting and analyzing computed properties along an iso-electronic sequence have also been added. A number of minor errors have been corrected. A detailed manual is included that describes different aspects of the package as well as the steps needed in order to produce reliable results. Program summary Program Title: GRAsp2018 Program Files doi: http://dx.doi.org/10.17632/x574wpp2vg.1 Licensing provisions: MIT license Programming language: Fortran 95. Nature of problem: Prediction of atomic properties - atomic energy levels, isotope shifts, oscillator strengths, radiative decay rates, hyperfine structure parameters, specific mass shift parameters, Zeeman effects - using a multiconfiguration Dirac-Hartree-Fock approach. Solution method: The computational method is the same as in the previous GRASP2K [1,2] version except that only the latest recommended versions of certain routines are included. Restrictions: All calculations are for bound state solutions. Instead of relying on packing algorithms for specifying arguments of arrays of integrals, orbitals are designated by a "short integer" requiring one byte of memory for a maximum of 127 orbitals. The tables of reduced coefficients of fractional parentage used in this version are limited to sub-shells with j <= 9/2 [3]; occupied sub-shells with j > 9/2 are, therefore, restricted to a maximum of two electrons. Some other parameters, such as the maximum number of orbitals are determined in a parameter_def _M.f 90 file that can be modified prior to compile time. Unusual features: Parallel versions are available for several applications. References [1] P. Jonsson, X. He, C. Froese Fischer, and I. P. Grant, Comput. Phys. Commun. 176, 597 (2007). [2] P. Jonsson, G. Gaigalas, J. Bieron, C. Froese Fischer, and I. P. Grant, Comput. Phys. Commun. 184, 2197 (2013). [3] G. Gaigalas, S. Fritzsche, Z. Rudzikas, Atomic Data and Nuclear Data Tables 76, 235 (2000). (C) 2018 Elsevier B.V. All rights reserved.

A new scheme to determine the neutrino mass matrix is proposed using atomic de-excitation between two states of a few eV energy spacing. The determination of the smallest neutrino mass of the order of 1 meV and neutrino mass type, Majorana or Dirac, becomes possible, if one can coherently excite more than 1 gram of atoms using two lasers.

We present extensive multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction calculations including 106 states in doubly ionized silicon (Si III) and 45 states in triply ionized silicon (Si IV), which are important for astrophysical determination of plasma properties in different objects. These calculations represents an important extension and improvement of earlier calculations especially for Si III. The calculations are in good agreement with available experiments for excitation energies, transition properties, and lifetimes. Important deviations from the NIST-database for a selection of perturbed Rydberg series are discussed in detail.

Recent climate warming has altered plant phenology at northern European latitudes, but conclusions regarding the spatial patterns of phenological change and relationships with climate are still challenging as quantitative estimates are strongly diverging. To generate consistent estimates of broad-scale spatially continuous spring plant phenology at northern European latitudes (>50 degrees N) from 2000 to 2016, we used a novel vegetation index, the plant phenology index (PPI), derived from MODerate-resolution Imaging Spectroradiometer (MODIS) data. To obtain realistic and strong estimates, the phenology trends and their relationships with temperature and precipitation over the past 17years were analyzed using a panel data method. We found that in the studied region the start of the growing season (SOS) has on average advanced by 0.30dayyear(-1). The SOS showed an overall advancement rate of 2.47day degrees C-1 to spring warming, and 0.18daycm(-1) to decreasing precipitation in spring. The previous winter and summer temperature had important effects on the SOS but were spatially heterogeneous. Overall, the onset of SOS was delayed 0.66day degrees C-1 by winter warming and 0.56day degrees C-1 by preceding summer warming. The precipitation in winter and summer influenced the SOS in a relatively weak and complex manner. The findings indicate rapid recent phenological changes driven by combined seasonal climates in northern Europe. Previously unknown spatial patterns of phenological change and relationships with climate drivers are presented that improve our capacity to understand and foresee future climate effects on vegetation.

Nuclear charge radii of Zn62-80 have been determined using collinear laser spectroscopy of bunched ion beams at CERN-ISOLDE. The subtle variations of observed charge radii, both within one isotope and along the full range of neutron numbers, are found to be well described in terms of the proton excitations across the Z = 28 shell gap, as predicted by large-scale shell model calculations. It comprehensively explains the changes in isomer-to-ground state mean square charge radii of Zn69-79, the inversion of the odd-even staggering around N = 40 and the odd-even staggering systematics of the Zn charge radii. With two protons above Z = 28, the observed charge radii of the Zn isotopic chain show a cumulative effect of different aspects of nuclear structure including single particle structure, shell closure, correlations and deformations near the proposed doubly magic nuclei, Ni-68 and Ni-78. (C) 2019 The Author(s). Published by Elsevier B.V.

Spectral lines from different isotopes display a small separation in energy, commonly referred to as the line isotope shift. The program RIS4 (Relativistic Isotope Shift) calculates normal and specific mass shift parameters as well as field shift electronic factors from relativistic multiconfiguration Dirac-Hartree-Fock wave functions. These quantities, together with available nuclear data, determine isotope-dependent energy shifts. Using a reformulation of the field shift, it is possible to study, in a model-independent way, the atomic energy shifts arising from changes in nuclear charge distributions, e.g. deformations. (C) 2018 Published by Elsevier B.V.

Aims. The main goal of this paper is to present accurate and extensive transition data for the P II ion. These data are useful in various astrophysical applications. Methods. The multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2K, were used in the present work. In the RCI calculations the transverse-photon (Breit) interaction, the vacuum polarization, and the self-energy corrections were included. Results. Energy spectra are presented for 48 even states of the 3S(2)3p(2) ,3s(2)3p{4p, 4f, 5p, 5f, 6p}, 3s3 p(2)3d configurations, and for 58 odd states of the 3s3p(3) , 3s(2)3p{3d, 4s, 4d, 5s, 5d, 6s} configurations in the P II ion. Electric dipole (E1) transition data are computed between these states along with the corresponding lifetimes. The average uncertainty of the computed transition energies is between five and ten times smaller than the uncertainties from previous calculations. The computed lifetimes for the 3s(2)3p4s(3)P degrees states are within the error bars of the most current experimental values.

Aims. The aim of this work is to present accurate and extensive results of energy spectra and transition data for the S II, Cl III, and Ar IV ions. These data are useful for understanding and probing physical processes and conditions in various types of astrophysical plasmas. Methods. The multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2K, are used in the present work. In the RCI calculations the transverse-photon (Breit) interaction, the vacuum polarization, and the self-energy corrections are included. Results. Energy spectra are presented comprising the 134, 87, and 103 lowest states in S II, Cl III, and Ar IV, respectively. Energy levels are in very good agreement with NIST database recommended values and associated with smaller uncertainties than energies from other theoretical computations. Electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2) transition data are computed between the above states together with the corresponding lifetimes. Based on internal validation, transition rates for the majority of the stronger transitions are estimated to have uncertainties of less than 3%.