General-purpose Relativistic Atomic Structure Package Research Articles

Electron-impact excitation data for W2+ in support of tungsten spectroscopy and re-deposition measurements for magnetically-confined plasmas

Abstract To better understand plasma wall interactions involving tungsten, accurate atomic structure and electron-impact driven collisional processes for near-neutral ion stages of tungsten are required. Complementing existing work on neutral and singly ionised tungsten, atomic structure and collisional calculations for W2+ electron-impact excitation have been completed. These excitation calculations are an important component of S/XB coefficients for near-neutral charge states, which may be used to spectroscopically infer re-deposition of tungsten at the plasma-solid boundary of fusion relevant devices. With W2+ in particular having emission lines that can be observed at ultraviolet (UV) wavelengths, while higher charge states of tungsten are unlikely to have lines possible to observe outside of the vacuum UV range. The atomic structure was generated using the General-purpose Relativistic Atomic Structure Package (GRASP0), implementing the Multi-configuration Dirac Fock approach (MCDF). This structure was the basis for a subsequent Dirac $R$-matrix electron-impact excitation calculation (DARC) to provide Maxwellian averaged rate coefficients. A synthetic spectrum was generated from this data using a collisional-radiative model to predict the strongest W~III spectral lines and these lines were compared to emission from the Compact Toroidal Hybrid (CTH) plasma device. Several of the strongest W~III lines are observed in CTH and agree well with the modelled line wavelengths and intensities, a table of these lines is provided that could be observed in other devices.

Calculations of energy levels, radiative transition parameters, hyperfine structure constants [formula omitted] - [formula omitted], Landé [formula omitted] factors and isotope shifts for Sc XX using the MCDF-RCI method

Large scale calculations for the energy levels, transition rates, oscillator strengths, lifetimes, hyperfine interaction constants, Landé gJ factors, and isotope shift factors have been performed for 1s2 and 1snl(n=2−8andl≤n−1) levels of He-like Sc XX ion. The general-purpose relativistic atomic structure package (GRASP2018) based on the fully relativistic multiconfiguration Dirac–Fock (MCDF) method is used to carry out the calculations. The leading quantum electrodynamic corrections, Breit interaction and nuclear recoil effects are also included in the succeeding relativistic configuration interaction (RCI) calculations. The relativistic isotope shift (RIS4) programme is used to determine the mass and field shifts factors. Furthermore, the percentage uncertainty in the transition parameters and lifetimes is estimated. A detailed comparison of the present results with the corresponding values from the NIST database and other theoretical and experimental works, wherever available, has been done, and an excellent agreement is achieved. A large section of the results is reported for the first time in the present work.

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.

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.

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.

Energy Levels and Radiative Lifetimes for Four Times Ionized Xenon (Xe V)

By employing the general-purpose relativistic atomic structure package (GRASP) based on the fully relativistic multiconfiguration Dirac-Fock (MCDF) method, energies and radiative lifetimes of levels have been reported for four times ionized xenon (Xe V). In calculations, the Breit interactions for relativistic effects, quantum electrodynamical (QED) contributions have been included as a perturbation, as well as electron correlation effects (VV, CV, and CC). We have compared the results obtained from this work with other available experimental and theoretical values in available literature for Xe V. We have obtained good agreement with previous works.

Energy levels and transition properties for As-like ions Se II, Br III, Kr IV, Rb V, and Sr VI

In this theoretical study, we aim to investigate atomic properties of As-like ions: Se II, Br III, Kr IV, Rb V, and Sr VI. The multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2018, 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. By employing MCDHF method, we computed the lowest energy levels of the 4s4p4, 4s24p2{4d,5d,5s,6s} even and of the 4s24p3, 4s24p2{5p,6p,4f}, 4s4p34d odd configurations. Accuracy of energy levels is​ evaluated by comparing it with the National Institute of Standards and Technology Atomic Spectra Database (NIST ASD or database) recommended values and with experimental and theoretical methods. We obtain the average accuracy in the energy level compared with the NIST database: 0.6%, 1.7%, 0.4%, 0.9% and 0.7% for Se II, Br III, Kr IV, Rb V, and Sr VI, respectively. We calculated properties of electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2) type transitions and investigated its accuracy. We evaluated the accuracy of data, using combination of new methodology, presented in recent works. Majority (77%, 93%, 95%, 97%, and 97% for Se II–Sr VI) of our computed transition properties belongs to D or better accuracy class.

Extended Calculations of Energy Levels and Transition Rates for Singly Ionized Lanthanide Elements. II. Tb−Yb

Abstract In this work, we continue large-scale ab initio computations for single ionized lanthanides. Extended atomic calculations for the set of ions from Pr ii (Z = 59) to Gd ii (Z = 64) have been performed in our previous work. In this study, ions from Tb ii (Z = 65) to Yb ii (Z = 70) are analyzed. By employing the same multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods that are implemented in the general-purpose relativistic atomic structure package GRASP2018, the energy levels and transition data of electric dipole (E1) transitions are computed. These computations are based on the strategies (with small variations) of Paper I. Accuracy of data is evaluated by comparing the computed energy levels with the data provided by the National Institute of Standards and Technology (NIST) database and with data from various methods. We obtain the average accuracy in the energy level compared with the NIST database: 6%, 5%, 4%, 5%, 3%, and 3% for Tb ii, Dy ii, Ho ii, Er ii, Tm ii, and Yb ii, respectively. We also provide extensive comparison of transition probabilities and wavelengths. Our results reach the average accuracy of transition wavelengths: 9%, 9%, 9%, 3%, 4%, and 11% for Tb ii, Dy ii, Ho ii, Er ii, Tm ii, and Yb ii, respectively.

Electron-impact excitation of Ni II

Aims. Energy levels, transition probabilities, and oscillator strengths are calculated for the second most abundant iron peak element Ni II. The difficulty in obtaining an accurate target representation is related to the open d-shell nature of the target, which has a minimum requirement of single and double promotions from the ground state configuration to the n = 4 shells. Therefore, in order to achieve an accurate representation of the target ion, we have also included configurations containing the 4d, 5s, and 5p subshells. We have undertaken a study of the electron impact excitation of Ni II and present here the collision strengths for forbidden and allowed transitions among the lowest 800 fine-structure levels as well as the corresponding Maxwellian-averaged effective collision strengths for a range of astrophysically relevant electron temperatures. Methods. An accurate Ni II target structure was generated using the modified General-purpose Relativistic Atomic Structure Package (GRASP0) for the lowest lying 1220 jj fine-structure levels, comprising the 11 configurations: 3p63d9, 3p63d84s, 3p63d84p, 3p63d84d, 3p63d85s, 3p63d85p, 3p63d74s2, 3p63d75s2, 3p63d74s4p, 3p63d74s4d, and 3p43d94s4d. The relativistic parallel Dirac atomic R-matrix codes (DARC) were utilised in the scattering calculations to generate the collision strengths for incident electron energies between 0 and 2 Ryd and, by employing infinite dipole and non-dipole limit points, we also generated the effective collision strengths for temperatures in the range from 1000 to 400 000 K. Two separate calculations were performed, both comprised of truncated close-coupling expansions of 800 jj-levels with the first calculation retaining the theoretical ab initio energy levels generated in the GRASP0 evaluations, whereas in the second calculation these energies were shifted to their predicted National Institute of Standards and Technology (NIST) values where possible. This should provide a lower estimate on the uncertainty. Results. Comparisons are made between the radiative data and the collisional cross sections with past theoretical and experimental studies. The effective collision strengths when compared with the most recent published calculations, are found to agree to within 10% for the majority of the transitions considered. In addition, the data are used to model the spectrum of Ni II and good agreement is found with previous investigations and observations.

Theoretical investigation of oscillator strengths and lifetimes in Ti II

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.

Theoretical studies of energy levels and transition data for Zr III

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.

Extended Calculations of Energy Levels and Transition Rates for Singly Ionized Lanthanide Elements. I. Pr–Gd

Abstract Lanthanide elements play important roles as an opacity source in the ejected material from neutron star mergers. Accurate and complete atomic data are necessary to evaluate the opacities and to analyze the observed data. In this paper, we perform extended, ab initio atomic calculations from Pr ii (Z = 59) to Gd ii (Z = 64). By using multiconfiguration Dirac–Hartree–Fock and relativistic configuration-interaction methods, implemented in the general-purpose relativistic atomic structure package (GRASP2K), we calculate the energy levels and transition data of electric dipole transitions. These computations are based on strategies (with small variations) of Nd ii published by Gaigalas et al. Accuracy of data is evaluated by comparing computed energy levels with the National Institute of Standards and Technology (NIST) database or other works. For the energy levels, we obtain the average relative accuracy of 8%, 12%, 6%, 8%, and 7% for Pr ii, Pm ii, Sm ii, Eu ii, and Gd ii ions, respectively, as compared with the NIST data. Accuracy of energy transfer to the wavelength is 3%, 14%, and 11% for Pr ii, Eu ii, and Gd ii. Our computed E1 type transition probabilities are in good agreement with experimental values presented by other authors especially for strong transitions.

Theoretical studies of energy spectra and E1 transitions of Ni II ion

SynopsisAccurate 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 NIST database recommended values. All computations were done using the general-purpose relativistic atomic structure package GRASP2018.

Energies and electric dipole transitions for triply ionized Kr, Xe and Rn

Energies and transition parameters such as wavelengths, transition probabilities (rates) and oscillator strengths for the electric dipole (E1) transitions have been reported for triply ionized krypton (Z = 36), xenon (Z = 54) and radon (Z = 86) using the general-purpose relativistic atomic structure package based on a fully relativistic multiconfiguration Dirac–Fock method. The Breit interactions for the relativistic effects, quantum electrodynamical contributions and correlation effects have been included in calculations. Obtained results have been compared with available theoretical and experimental values in the literature. Most of results, in particular for Rn IV, have been presented firstly.

Analysis of discrepancy in previously published excitation energies of Ne-like ions from two independent codes and atomic data of Rb XXVIII and Ba XLVII

Fine structure energies and radiative data namely, transition wavelength, transitions rates, oscillator strength and line strength have been presented for lowest 75 levels of highly ionized Ne-like Rb27+ (Rb XXVIII) and Ne-like Ba46+ (Ba XLVII) by using Multi-Configuration Dirac-Fock (MCDF) method. Our presented transition X-ray wavelengths of Ne-like Rb match well with Ne-like Rb experimentally determined laser wavelengths from different laser techniques. We have analyzed inconsistencies and uncertainties in previous Ne-like ions results by the evaluation of results from two independent codes general purpose relativistic atomic structure package (GRASP) and flexible atomic code (FAC). Our excitation energies for Rb XXVIII and Ba XLVII match well with NIST and other available results. We demonstrate that inclusion of configuration interaction (CI) is crucial to attain the accuracy in atomic data calculations. The present results are complete, extensive and in good agreement with other results and believe that presented results will be effective and helpful in detection of other X-ray spectral lines of Ne-like Rb laser from different sources.

Energies, Wavelengths, and Transition Probabilities in Sc XIII

The fine-structure energy levels and lifetimes are calculated for the lowest 218 levels of the 2s22p5, 2s2p6, 2s22p43s, 2s22p43p, 2s22p43d, 2s2p53s, 2s2p53p, 2s2p53d, 2p63s, 2p63p, 2p63d, 2s22p44s, 2s22p44p, 2s22p44d, 2s2p54s, 2s2p54p, and 2s2p54d configurations in Sc XIII using the general-purpose relativistic atomic structure package (GRASP). The atomic data of the electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions from the levels of 2s22p5, 2s2p6, 2s22p43s, 2s22p43p, 2s22p43d, 2s2p53s, 2s2p53p, 2s2p53d, 2p63s, 2p63p, and 2p63d configurations to the levels of the 2s22p5 and 2s2p6 configurations are presented. The GRASP results are compared with the other calculations and measurements.

Energy Levels and Transition Rates for Ti XIV

Energy levels, wavelengths, oscillator strengths, transition probabilities, line strengths, and lifetimes are calculated for transitions in Ti XIV. The 2s22p5, 2s2p6, 2s22p43l, 2s2p53l, 2p63l, 2s22p44l, and 2s2p54l (l = s, p, d) configurations are used in the calculations and 218 fine-structure levels are obtained using the general-purpose relativistic atomic structure package (GRASP). The results for the electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole transitions from the levels of the 2s22p5, 2s2p6, 2s22p43l, 2s2p53l, and 2p63l (l = s, p, d) configurations to the levels of 2s22p5 and 2s2p6 configurations are presented. Comparisons are made with the available experimental and the other calculations.

Energy levels and radiative rates for transitions in S-like Sc VI, V VIII, Cr IX, and Mn X

Energy levels, radiative rates and lifetimes are reported for four S-like ions, namely Sc VI, V VIII, Cr IX, and Mn X. Two independent atomic structure codes, namely the general-purpose relativistic atomic structure package (grasp) and the flexible atomic code (fac), have been adopted for calculating the energy levels, with differing amounts of configuration interaction. This is mainly to make some assessment of accuracy. However, the grasp alone is used for calculating the remaining parameters. Results are reported for varying number of levels of these ions, and for calculating lifetimes contributions are included from all types of transitions, i.e. E1, E2, M1, and M2. Comparisons are made with the earlier available experimental and theoretical results and assessments of accuracy are given for each ion. Additionally, the presently reported data cover a significantly larger number of levels and transitions than already available in the literature for the four S-like ions.

Electric quadrupole (E2) and magnetic dipole (M1) transitions for doubly and triply ionized krypton, xenon, and radon

We have reported the wavelengths, transition probabilities (or rates), oscillator strengths, and line strengths for forbidden transitions (electric quadrupole, E2, and magnetic dipole, M1) in doubly and triply ionized krypton, xenon, and radon using the general-purpose relativistic atomic structure package (GRASP). The results obtained from transitions between the levels of ground state configuration are in agreement with other available results in the literature. The data on forbidden transitions between high levels for these ions have been firstly presented in this work.

Accurate study on the properties of spectral lines for Na-like Cr13+

An extended calculation of energy levels, radiative rates, and lifetimes are reported for sodium-like chromium. Extensive configuration interaction calculations have been performed using general-purpose relativistic atomic structure package (GRASP). The radiative rates, oscillator strengths, and line strengths are listed for all electric dipole (E1) transitions. However, for magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions, only radiative rates are listed. The importance of valence–valence (VV) and core–valence (CV) correlation effects in the calculation of energy levels have also been shown. To confirm the accuracy of the present results for energy levels by GRASP, independent calculations have been performed by using Flexible Atomic Code (FAC) and configuration interaction method (CIV3). The accuracy of the present levels, wavelengths, transition rates, and lifetimes are assessed by comparing them to available experimental and other theoretical results. We believe that our extensive results may be beneficial in fusion plasma research and astrophysical investigations and applications.