Multiconfiguration Dirac Hartree Fock Research Articles

Study of Electron Impact Excitation of Na-like Kr Ion for Impurity Seeding Experiment in Large Helical Device

In this work, a krypton gas impurity seeding experiment was conducted in a Large Helical Device. Emission lines from the Na-like Kr ion in the extreme ultraviolet wavelength region, such as 22.00 nm, 17.89 nm, 16.51 nm, 15.99 nm, and 14.08 nm, respective to 2p63p(2P1/2o)−2p63s(2S1/2), 2p63p(2P3/2o)−2p63s(2S1/2), 2p63d(2D3/2)−2p63p(2P3/2o), 2p63d(2D5/2)−2p63p(2P3/2o), and 2p63d(2D3/2)−2p63p(2P1/2o) transitions, are observed. In order to generate a theoretical synthetic spectrum, an extensive calculation concerning the excitation of the Kr25+ ion through electron impact was performed for the development of a suitable plasma model. For this, the relativistic multiconfiguration Dirac–Hartree–Fock method was employed along with its extension to the relativistic configuration interaction method to compute the relativistic bound-state wave functions and excitation energies of the fine structure levels using the General Relativistic Atomic Structure Package-2018. In addition, another set of calculations was carried out utilizing the relativistic many-body perturbation theory and relativistic configuration interaction methods integrated within the Flexible Atomic Code. To investigate the reliability of our findings, the results of excitation energies, transition probabilities, and weighted oscillator strengths of different dipole-allowed transitions obtained from these different methods are presented and compared with the available data. Further, the detailed electron impact excitation cross-sections and their respective rate coefficients are obtained for various fine structure resolved transitions using the fully relativistic distorted wave method. Rate coefficients, calculated using the Flexible Atomic Code for population and de-population kinetic processes, are integrated into the collisional-radiative plasma model to generate a theoretical spectrum. Further, the emission lines observed from the Kr25+ ion in the impurity seeding experiment were compared with the present plasma model spectrum, demonstrating a noteworthy overall agreement between the measurement and the theoretical synthetic spectrum.

The magnetic dipole transition in Rb-like ion and its core-valence correlation effect

This study presents both experimental and theoretical analysis of the 4d2D5/2→2D3/2 magnetic dipole transition in Rb-like ions. Spectral lines of Xe17+, La20+ and Pr22+ ions were recorded using an electron beam ion trap. The theoretical framework employed the fully relativistic Multi-configuration Dirac–Hartree–Fock method, accounting for the Breit interaction, QED effects and comprehensive core-valence correlation. An impressive correlation is observed between the theoretical and experimental findings. Notably, this study illustrates that the contribution of the core-valence correlation, especially concerning deep core subshells, is pivotal for the fine structure splittings.

Relativistic atomic structure calculations for B-like xenon ion

Excitation energies, transition parameters and lifetimes for 255 levels with n≤ 4 configurations of B-like Xe49+ are calculated using the fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) method. Hyperfine structure constants, isotope shift and Landé gJ factors are computed for the 2s22p,2s2p2 and 2p3 levels. The contribution of the Breit interaction and QED effects, mainly self-energy and vacuum polarization corrections, on these levels is also investigated. The uncertainties in the lifetimes and line strengths are computed, and transitions are classified according to the NIST accuracy nomenclature. A comparison with the previously available results is also carried out. This study provides extensive results for B-like Xe49+, which are useful for plasma diagnosis.

Extreme field calculations for Penning ion traps and corresponding strong laser field scenarios

The extreme forces of highly charged ions and their trapping within high-precision experimental devices allow for challenging fundamental theories in yet unexplored territory. Here we focus on the theoretical side employing ab initio fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods to precisely calculate the bound-state energies of complex atoms and ions, as well as on presenting state-of-the-art high-precision g-factor calculations. In combination with similarly accurate experiments, one can competitively determine fundamental constants like the masses of the neutrino and the electron as well as setting new limits for physics beyond the standard model. Scenarios involving extreme laser pulses hold comparable potential but still require especially advances in the precision of the associated experiments.

Energy Levels and Transition Rates for Laser Cooling Os− and a General Approach to Produce Cold Atoms and Molecules

High-resolution photoelectron energy spectra of osmium anions are obtained using the slow-electron velocity-map imaging method. The energy levels of excited states 4 F 7/2, 4 F 5/2 and 4 F 3/2 of Os− are determined to be 148.730(13), 155.69(15), and 176.76(13) THz [or 4961.09(41), 5193.4(49), and 5896.1(42) cm−1], respectively. The lifetime of the opposite-parity excited state is determined to be 201(10) μs using a cold ion trap, about 15 times shorter than the previous result 3(1) ms. Our high-level multi-configuration Dirac–Hartree–Fock calculations yield a theoretical lifetime 527 μs. Our work shows that the laser cooling rate of Os− is as fast as that of Th−. The advantages of Os− are its near-IR range cooling transition and simple electronic structure, which make Os− a promising candidate for laser cooling of negative ions. We propose a general approach to produce cold atoms and molecules based on the sympathetic cooling of negative ions in combination with a threshold photodetachment.

Benchmarking calculations of excitation energies and transition properties with spectroscopic accuracy of highly charged ions used for the fusion plasma and astrophysical plasma

Atomic radiative data such as excitation energies, transition wavelengths, radiative rates, and level lifetimes with high precision are the essential parameters for the abundance analysis, simulation, and diagnostics in fusion and astrophysical plasmas. In this work, we mainly focus on reviewing our two projects performed in the past decade. One is about the ions with Z ≲ 30 that are generally of astrophysical interest, and the other one is about the highly charged krypton (Z = 36) and tungsten (Z = 74) ions that are relevant in research of magnetic confinement fusion. Two different and independent methods, namely, multiconfiguration Dirac–Hartree–Fock (MCDHF) and the relativistic many-body perturbation theory (RMBPT) are usually used in our studies. As a complement/extension to our previous works for highly charged tungsten ions with open M-shell and open N-shell, we also mainly focus on presenting and discussing our complete RMBPT and MCDHF calculations for the excitation energies, wavelengths, electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transition properties, and level lifetimes for the lowest 148 levels belonging to the 3l 3 configurations in Al-like W61+. We also summarize the uncertainties of our systematical theoretical calculations, by cross-checking/validating our datasets from our RMBPT and MCDHF calculations, and by detailed comparisons with available accurate observations and other theoretical calculations. The data are openly available in Science Data Bank at https://doi.org/10.57760/sciencedb.10569.

Energy levels and radiative transition properties of the 2s2p double K-shell vacancy state in He-like ions ([formula omitted

The energy levels of 1s2, 1s2s, and 2s2p configurations for He-like ions (4≤Z≤54) are calculated using the multi-configuration Dirac–Hartree–Fock​ methods. The transition energies, transition rates, and oscillator strengths of 2s2p→1s2 and 2s2p→1s2s are also calculated. A parallel calculation based on the Dirac–Fock–Slater method with a local central potential is performed using the Flexible Atomic Code to cross-check the accuracy of the data. The Breit interaction and quantum electrodynamics effects, including self-energy and vacuum polarization, are included as perturbations in these calculations. The average relative standard deviation of the energy levels from the available NIST data is about 0.2% for both methods. The transition energies and rates are in reasonable agreement with other available theoretical and experimental data, and the consistency between the transition energies calculated by the two methods reaches 99.9%. These results are expected to help future investigations on double K-shell vacancy decays of He-like ions.

Critically Evaluated Atomic Data for the Au iv Spectrum

A spectral investigation of triply ionized gold (Au iv) has been carried out in the wavelength region of 500–2106 Å. The gold spectra were photographed at the National Institute of Standards and Technology, USA, on a 10.7 m normal incidence vacuum spectrograph (NIVS) using a sliding spark source as well as on a 3 m NIVS at the Antigonish laboratory in Canada with a triggered spark source. Our analysis is theoretically supported by the pseudorelativistic Hartree–Fock (HFR) formalism with a superposition of configuration interactions implemented in Cowan's suite of codes. Radiative transition parameters are also calculated using the HFR+CPOL (core polarization effects) model and the multiconfiguration Dirac–Hartree–Fock approach, and their comparisons are used to evaluate the transition rate data. All the previously reported levels of the 5d 8, 5d 76s, and 5d 76p configurations are confirmed, except one, and three are newly established. The missing 1 S 0 level of 5d 8 is now established at 55,277.8 cm−1. A total of 981 observed lines (E1 type), classified to 1031 transitions, including 133 newly identified, enabled us to optimize 139 energy levels. Several astrophysically important transitions, forbidden (M1- and E2-type) lines of 5d 8 and 5d 76s, are provided with their Ritz wavelengths and radiative parameters. A critically evaluated set of energy levels, observed and Ritz wavelengths along with their uncertainties, transition rates, and uniformly scaled intensities of Au iv lines have been presented. Also, large-scale atomic data to compute the opacity of Au iv in the kilonova ejecta have been supplemented in this work.

Extended atomic data for oxygen abundance analyses

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 єO = 8.70 ± 0.04.

Theoretical investigation of Sb-like sequence: Sb I, Te II, I III, Xe IV, and Cs V

We aim to investigate atomic properties of Sb-like sequence: Sb I, Te II, I III, Xe IV, and Cs V. The multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2018, are used in the present work. The lowest energy levels of the 5s25p3, 5s5p4, 5p5, 5s5p35d, and 5s25p2{6s,7s,6p,7p,5d,6d,4f} configurations and electric dipole, magnetic dipole, and electric quadrupole transitions between states of these configurations are computed. Accuracy of energy levels are evaluated by comparing it with the National Institute of Standards and Technology Atomic Spectra Database recommended values and with other methods. Accuracy of transitions data are investigated using quantitative and qualitative evaluation method.

Energy levels, lifetimes, and transition probabilities for Sr XXXII

The fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) approach was used to calculate the excitation energies and lifetimes for the lowest 272 levels that belonging to the 2{s}^{2}2{p}^{3}, 2s2{p}^{4}, 2{p}^{5}, 2{s}^{2}2{p}^{2}3l, 2s2{p}^{3}3l, and 2{p}^{4}3l (l=s, p, d) configurations for N-like strontium, Sr XXXII, as well as the wavelengths, weighted oscillator strengths, transition probabilities, and line strengths for the electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions among these levels. The Breit-interaction (BI), and quantum electrodynamics (QED) corrections have been incorporated into the computations. In order to assess the uncertainties of the current calculations, comparisons with available data, and the results from the largest MCDHF layers have all performed.

Extended MCDHF Calculations of Energy Levels and Transition Data for N i

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 2s22p25s. 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%).

Cu Kα3,4 satellite spectrum with ab initio Auger-rate calculations

This work investigates the capability of the multiconfiguration Dirac-Hartree-Fock (MCDHF) method in predicting the Cu $K{\ensuremath{\alpha}}_{3,4}$ spectrum. Ab initio energy eigenvalues, relative intensities, and radiative widths are calculated for the Cu $2p$ and $2s$ satellite transitions. By fitting to the most accurate experimental Cu $K{\ensuremath{\alpha}}_{3,4}$ spectra available, we show that our $2p$ satellite energy eigenvalues agree with experiment to within 0.35 eV and that our $2p$ shake probability agrees with the $2p$ fitted intensity to within 0.05%. Our fits suggest a $I(2s)$:$I(2p)$ satellite intensity ratio (as a percentage of the total $K\ensuremath{\alpha}$ spectrum) of 0.03(1):0.76(1) Theoretical predictions of this ratio can be examined using shake probabilities. We calculate the probability of shake-off due to the sudden creation of a $1s$ hole in Cu, yielding an ab initio $I(2s)$:$I(2p)$ shake probability ratio of 0.194:0.742. Using MCDHF, the rates at which hole states, created through the shake processes, depopulate via Auger transitions are determined. These results explain the apparent discrepancy between experimental satellite intensities and shake probabilities, and characterize the Cu $K{\ensuremath{\alpha}}_{3,4}$ spectrum with a satellite intensity ratio of 0.04(1):0.76, consistent with the experiment.

Performance Tests and Improvements on the rmcdhf and rci Programs of GRASP

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.

Independently Optimized Orbital Sets in GRASP—The Case of Hyperfine Structure in Li I

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 1s22s2S1/2 and 1s22p2P1/2,3/2o states in 7Li 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.

Optical Lines of Ru21+ to Ru24+ Ions

In this work, we report a spectroscopy measurement of Ru21+ to Ru24+ ions in the optical region using a low energy electron beam ion trap. Twelve lines were observed. The multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods were used to calculate the atomic level energies and the transition rates. With the assistance of the theoretical results, eleven magnetic dipole lines were identified. The experimental results provide new reference data for further theoretical investigations of the complex ions.

Extended calculations of energy levels, radiative properties, and lifetimes for oxygen-like Zn XXIII

The multiconfiguration Dirac-Hartree-Fock (MCDHF) method is used to calculate excitation energies, lifetimes, and radiative transition data for the lowest 672 levels of the 2s22p3nl (n=2 - 5, l=0 - n−1), 2s2p4nl (n=2 - 4, l=0 - n−1), and 2p5nl (n=2 - 3, l=0 - n−1) configurations in Zn XXIII. The comparison of the present excitation energies with available experimental and theoretical results suggests that our MCDHF/RCI calculations are highly accurate with an average uncertainty of a few hundred cm−1. The uncertainty estimation method suggested by Kramida [1, 2], applied to the comparison of the length and velocity line strength values, is used for ranking the transition data. A consistent atomic data set including both energy and transition data with spectroscopic accuracy is provided for the lowest hundreds of states in Zn XXIII.

Extended Calculations of Atomic Structure Parameters for Na-like Ar, Kr and Xe Ions Using Relativistic MCDHF and MBPT Methods

In this study, comprehensive calculations of energies, hyperfine structure constants, Landé gJ factors and isotope shifts have been performed for the lowest 71 states of Na-like Ar7+, Kr25+ and Xe43+ ions. Radiative parameters viz., wavelengths, transition rates, oscillator strengths and lifetimes are estimated for the electric dipole E1 transitions among these levels. The states under consideration include 1s22s22p6nl for n = 3–9, l = 0–6, and the fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) method integrated in the latest version of the general-purpose relativistic atomic structure package (GRASP2018) is used for the calculations. The additional corrections, such as the Breit interaction and quantum electrodynamics effects are included in the relativistic configuration interaction calculations, and their effects on energies and other parameters are analysed. We examined the impact of including the core–core and core–valence correlations on level energies. Furthermore, to inspect the reliability of our MCDHF results, we performed another set of calculations using the many-body perturbation theory built into the Flexible Atomic Code (FAC). Moreover, we estimated the uncertainties in the computed lifetimes and transition parameters and assigned their accuracy class. A thorough comparison between the two obtained calculations and with the previous theoretical and experimental results, wherever available, is carried out and a good agreement is observed.

Opacity calculations in four to nine times ionized Pr, Nd, and Pm atoms for the spectral analysis of kilonovae

ABSTRACT New atomic data for radiative transitions in Pr V–X, Nd V–X, and Pm V–X were determined by means of large-scale calculations involving three independent theoretical methods, i.e. the pseudo-relativistic Hartree–Fock method including core-polarization corrections (HFR+CPOL), the multiconfiguration Dirac–Hartree–Fock (MCDHF) method, and the configuration interaction many-body perturbation theory (CI + MBPT) implemented in the ambit program. This multiplatform approach allowed us to estimate the reliability of the results obtained and to extract a large amount of energy levels, wavelengths, transition probabilities, and oscillator strengths for the determination of opacities required for the analysis of the spectra emitted in the early phases of kilonovae following neutron star mergers, i.e. for typical conditions corresponding to temperatures T > 20 000 K, a density ρ = 10−10 g cm−3, and a time after the merger t = 0.1 d. Our radiative parameters were compared in detail with the few experimental data published so far and their impact on the calculated opacities, in terms of atomic computation strategy, was also examined.

Pseudo-Relativistic Hartree–Fock and Fully Relativistic Dirac–Hartree–Fock Calculations of Radiative Parameters in the Fifth Spectrum of Lutetium (Lu V)

Using two independent theoretical methods based on the pseudo-relativistic Hartree–Fock (HFR) and the fully relativistic Multiconfigurational Dirac–Hartree–Fock (MCDHF) approaches, we computed the radiative parameters (transition probabilities and oscillator strengths) corresponding to the spectrum of quadruply ionized lutetium (Lu V). The agreement observed between both sets of results allowed us to deduce the radiative rates for a large amount of transitions in order to calculate the contribution of this ion to the opacity of kilonovae in their early phases, i.e., for T = 25,000 K. The results obtained were compared to previous data computed for other quadruply ionized lanthanide atoms, namely La V, Ce V, Pr V, Nd V and Pm V, in order to highlight the main contributors to the opacity among these ions under kilonovae conditions where the Vth spectra are predominant.