Relativistic Atomic Structure 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.

Electron–ion collision and polarization of X-ray fluorescence radiation under hot quantum plasma conditions

In the current article, the spectral properties and electron collision (total and magnetic) excitation cross sections of ions taking placed in quantum plasmas are investigated. These cross sections are further used to study the polarization and angular distribution characteristics of the de-excitation radiation X-ray spectra, which play an important role in basic theoretical research, the diagnosis of the plasma environment, and the design of optical devices. To do so, a distorted wave method within the relativistic Dirac–Coulomb atomic structure scheme is suggested. The effective interaction potential between electrons and particles in hot quantum plasmas in the method is determined using a quantum approach that incorporates the influence of effective plasma screening effects caused by collective plasma oscillations. This potential replaces the traditional Coulomb interaction potential and is used in solving the modified Dirac equation to obtain the bound and continuum electron wave functions. Higher-order relativistic effects, such as the Breit interaction and the dominant quantum electrodynamics corrections, are added to enhance the accuracy of the method. Detailed calculations for the relativistic atomic structure and collision excitation dynamics process are carried out, taking the highly stripped H-like O7+ ion of astrophysical importance as an illustrative example. Detailed investigations are also conducted on the variation of energies, collision cross sections, and fluorescence polarizations as functions of the plasma parameters. Our results suggest that the joint effects of shielding and plasma coupling lead the energies, cross sections and fluorescence polarizations decrease (compared with the isolated case). The angular distribution of the X-ray fluorescence emission shows large change, suggesting their sensitivity to these effects. This study not only offers a valuable approach to investigating the plasma shielding and plasmon coupling effects in quantum plasmas but also holds significant relevance for applications in controlled nuclear fusion, astrophysical plasmas and so on.

Accurate ab initio calculation and neural network prediction of the atomic properties of Os LXXIII, Ir LXXIV, Pt LXXV, and Au LXXVI

In this paper, we present an ab initio theoretical calculation of the atomic parameters, including energy levels, wavelengths, lifetimes, and transition parameters, associated with the 1s22snl and 1s22pnl (n= 2–4, l≤n−1) configurations of Be-like sequence: Os LXXIII, Ir LXXIV, Pt LXXV, and Au LXXVI. Our analysis is based on the relativistic wavefunctions derived from the multi-configuration Dirac–Fock (MCDF) method, which are implemented in the relativistic atomic structure package GRASP2018. The correlations within the (principal quantum number) n= 10 complex are accounted for. The Breit interaction and quantum electrodynamical effects are added in the relativistic configuration interaction (RCI) calculation. Our results are compared with the existing data. The uncertainties of the dipole transition line strengths are assessed. In addition, we propose a feed forward neural network to predict the energy levels of Au LXXVI. This is a powerful machine learning tool capable of learning from existing data and predicting unknown data. The network is trained using theoretical energy levels of Os LXXIII, Ir LXXIV, and Pt LXXV obtained from the MCDF method. Our neural network exhibits average relative deviations of approximately 0.01% and 0.02% for trained and predicted energy levels, respectively, when compared to the MCDF results. This level of deviation suggests that our results are reasonably accurate. The data set presented in this study is useful for modeling fusion plasmas.

Second-order Rayleigh–Schrödinger perturbation theory for the GRASP2018 package: Core–valence correlations

The General Relativistic Atomic Structure package [GRASP2018, C. Froese Fischer, G. Gaigalas, P. Jönsson, and J. Bieroń, Comput. Phys. Commun. (2019), DOI: 10.1016/j.cpc.2018.10.032] is based on multiconfiguration Dirac– Hartree–Fock and relativistic configuration interaction (RCI) methods for energy structure calculations. The atomic state function used in the program is built from the set of configuration state functions (CSFs). The valence–valence, core–valence and core–core correlations are explicitly included through expansions over CSFs in RCI. We present a combination of RCI and the stationary second-order Rayleigh–Schrödinger many-body perturbation theory in an irreducible tensorial form to account for electron core–valence correlations when an atom or ion has any number of valence electrons. This newly developed method, which offers two ways of use, allows a significant reduction of the CSF space for complex atoms and ions. We also demonstrate how the method and program works for the energy structure calculation of Cl III ion.

A Study of the Atomic Processes of Highly Charged Ions Embedded in Dense Plasma

The study of atomic spectroscopy and collision processes in a dense plasma environment has gained a considerable interest in the past few years due to its several applications in various branches of physics. The multiconfiguration Dirac-Fock (MCDF) method and relativistic configuration interaction (RCI) technique incorporating the uniform electron gas model (UEGM) and analytical plasma screening (APS) potentials have been employed for characterizing the interactions among the charged particles in plasma. The bound and continuum state wavefunctions are determined using the aforementioned potentials within a relativistic Dirac-Coulomb atomic structure framework. The present approach is applied for the calculation of electronic structures, radiative properties, electron impact excitation cross sections and photoionization cross sections of many electron systems confined in a plasma environment. The present study not only extends our knowledge of the plasma-screening effect but also opens the door for the modelling and diagnostics of astrophysical and laboratory plasmas.

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.

Editorial of the Special Issue “General Relativistic Atomic Structure Program—GRASP”

The year 2022 marked the 10th anniversary not only of the ATOMS journal but also of the international collaboration on Computational Atomic Structure [...]

Systematic study of the stopping power of the lanthanides

In the last decade, lanthanides have become the subject of multiple studies due to their importance in technological applications. This paper aims to systematically study the energy loss per unit length of protons on the 15 lanthanides, from lanthanum to lutetium. We investigate the stopping power cross sections by considering the influence of the relativistic atomic structure, namely the description of the $4f$ electrons, the number of electrons in the valence shells, and the electronic screening of the same or close subshells. The electronic stopping model considers separate contributions from bound and valence electrons. We employ a many-electron model for the former and a combination of perturbative and nonperturbative free-electron gas approaches for the latter. Our stopping results for the lanthanide series cover an extended energy range from very low to the MeV region. We compare them with measurements and other theoretical (dpass, casp) and semiempirical (srim) methods. Our results agree with most experimental data, even the recent values around the maximum for gadolinium. We implement Lindhard's scaling for the stopping number for all the data available of the 15 targets. Lindhard scaling for the stopping number includes all the data for the 15 targets. The present paper cast doubts on certain data sets, which should affect srim's description of lanthanides, such as La, Nd, Dy, and Tb. We call attention to the scarcity of measurements in the low and intermediate ranges, and we suggest experimental efforts to shed light on the stopping power of these relevant targets.

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.

Fine-Tuning of Atomic Energies in Relativistic Multiconfiguration Calculations

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 2s21S0−2s2p1,3P1 transitions in C III and to the computation of Rydberg transitions in B I, for which the 2s2p22S1/2 perturber enters the 2s2ns2S1/2 series. Improved convergence patterns and results are found compared with ab initio calculations.

Electric-quadrupole transition-rate measurement of a highly charged ion in an electron-beam ion trap using pulsed laser excitation from a metastable state

We present the lifetime measurement of the ${(4{d}_{3/2}^{\ensuremath{-}1}5s)}_{J=2}$ state in Pd-like ${\mathrm{I}}^{7+}$, which predominantly decays to the $(4{d}^{10}{)}_{J=0}$ ground state by an electric-quadrupole transition modified by strong spin-orbit mixing. We measure this microsecond-order lifetime in an electron-beam ion trap using pulsed laser excitation from a metastable state which is continuously populated by electron collisions. The measured lifetime provides a new benchmark for relativistic atomic structure calculations with $d$-state electrons.

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.

An Introduction to Relativistic Theory as Implemented in GRASP

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. Jönsson, J. Bieroń, 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.

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.

A Program Library for Computing Pure Spin–Angular Coefficients for One- and Two-Particle Operators in Relativistic Atomic Theory

A program library for computing pure spin-angular coefficients for any one- and scalar two-particle operators is presented. The method used is based on the combination of the second quantization and quasi-spin techniques with the angular momentum theory and the method of irreducible tensorial sets. A relativistic approach is assumed. This program library is integrated in the General Relativistic Atomic Structure Package but it can be implemented in other program packages, too.

Reducing the computational load – atomic multiconfiguration calculations based on configuration state function generators

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.

Relativistic Atomic Structure of Au IV and the Os Isoelectronic Sequence: Opacity Data for Kilonova Ejecta

Direct detection of gravitational waves (GWs) on 17 August 2017, propagating from a binary neutron star merger, or a “kilonova”, opened the era of multimessenger astronomy. The ejected material from neutron star mergers, or “kilonova”, is a good candidate for optical and near infrared follow-up observations after the detection of GWs. The kilonova from the ejecta of GW1780817 provided the first evidence for the astrophysical site of the synthesis of heavy nuclei through the rapid neutron capture process or r-process. Since properties of the emission are largely affected by opacities of the ejected material, enhancements in the available r-process data is important for neutron star merger modeling. However, given the complexity of the electronic structure of these heavy elements, considerable efforts are still needed to converge to a reliable set of atomic structure data. The aim of this work is to alleviate this situation for low charge state elements in the Os-like isoelectronic sequence. In this regard, the general-purpose relativistic atomic structure packages (GRASP0 and GRASP2K) were used to obtain energy levels and transition probabilities (E1 and M1). We provide line lists and expansion opacities for a range of r-process elements. We focus here on the Os isoelectronic sequence (Os I, Ir II, Pt III, Au IV, Hg V). The results are benchmarked against existing experimental data and prior calculations, and predictions of emission spectra relevant to kilonovae are provided. Fine-structure (M1) lines in the infrared potentially observable by the James Webb Space Telescope are highlighted.

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.

Calculation of atomic integrals between relativistic functions by means of algebraic methods

We propose the use of Sturmian basis set for relativistic atomic structure calculations. We describe a numerically stable algebraic calculation of one- and two-particle radial integrals. The method is illustrated on the basis set independent calculation of energies, electric dipole moments, hyperfine integrals and parity non-conserving (PNC) amplitude for Cs in Dirac-Hartree-Fock approximation with frozen core orbitals. The previously reported results for electric dipole moments and PNC amplitude are found to be strongly basis dependent. Program summaryProgram title: PASCCPC Library link to program files:https://doi.org/10.17632/xycmhhcr5h.1Licensing provisions: MITProgramming language: Fortran 2008Nature of problem: Precise atomic measurements require reliable and highly accurate atomic structure calculations. Here we deal with the problem of numerical stability of the atomic integrals and basis set independence of the calculations.Solution method: The radial parts of the electronic orbitals are expanded in a discrete Sturmian functions that are eigenfunctions of one of the generators of the so(2,1) Lie algebra. This algebraic structure is used to deduce algebraic relations between the radial parts of the atomic integrals. This leads to numerically stable calculation, which in turn allows to achieve basis set independence.Additional comments including restrictions and unusual features: The method is currently restricted to the Dirac-Hartree-Fock method. However, this limitation will be lifted in future versions, which will be extended with the coupled clusters method.