Flexible Atomic Code Research Articles

Effects of radiation damping on photorecombination ofC4+ions for theKLLresonance

A numerical method based on Zabaydullin and Dubau's work [O. Zabaydullin and J. Dubau, J. Phys. B: At. Mol. Opt. Phys. 45, 115002 (2012)] has been developed to calculate the Cauchy principal value integral in scattering matrices and obtain photorecombination (PR) cross sections of low-lying resonances according to Davies and Seaton's theory [J. Phys. B 2, 757 (1969)], in which radiation damping is included. The Dirac $R$-matrix method is employed to secure the dipole matrix. Using this method, PR cross sections of ${\mathrm{C}}^{4+}$ for the KLL resonance are acquired, and compared with available experimental measurements and other close-coupling theoretical results. It is shown that our damped cross sections reproduce the experimental data and are in agreement with other theoretical results. Meanwhile, radiation damping can reduce the PR cross section for the $1s2{p}^{2}\phantom{\rule{4pt}{0ex}}^{2}P$ resonance (corresponding to two levels ${[{(1s2{p}_{1/2})}_{1}2{p}_{3/2}]}_{1/2}$ and ${[1s{(2{p}_{3/2}^{2})}_{2}]}_{3/2}$ by three orders of magnitude. The unresolved and underestimated resonances $1s2{p}^{2}\phantom{\rule{4pt}{0ex}}^{4}P, 1s2s2p\phantom{\rule{4pt}{0ex}}^{4}P$, and $1s2{p}^{2}\phantom{\rule{4pt}{0ex}}^{2}P$ in the undamped Breit-Pauli $R$-matrix calculations [H. L. Zhang et al., J. Phys. B: At. Mol. Opt. Phys. 32, 1459 (1999)] are corrected. Besides, dielectronic recombination cross sections of ${\mathrm{C}}^{4+}$ for the KLL resonance are also presented for comparison using the relativistic configuration-interaction (RCI) method implemented in flexible atomic code (fac), which show radiation damping has pronounced influences on $1s2{p}^{2}\phantom{\rule{4pt}{0ex}}^{2}P$ due to much larger radiative rates compared with autoionization rates. Furthermore, radiative and autoionization rates for the intermediate states ${[{(1s2{p}_{1/2})}_{1}2{p}_{3/2}]}_{1/2}$ and ${[1s{(2{p}_{3/2}^{2})}_{2}]}_{3/2}$ of the He-like ions with $6\ensuremath{\le}\phantom{\rule{4pt}{0ex}}Z\ensuremath{\le}83$ are calculated using fac, scaling laws of which are checked. Autoionization rates comply with the ${Z}_{\mathrm{eff}}^{0}$ scaling law for $Z\ensuremath{\ge}32$, which is caused by relativistic effects.

Atomic structure calculations and study of EUV and SXR spectral lines in Cu-like ions

In the present work, we provide a most extensive and detailed study of highly ionized Cu-like ions and diagnose extreme ultraviolet (EUV) and soft X-ray (SXR) transitions with N-shell electron excitation to M-shell and higher shells. We have determined energy levels and lifetimes for lowest 27 fine-structure levels by adopting multiconfiguration Dirac–Fock (MCDF) with the inclusion of quantum electrodynamics (QED) as well as Breit corrections as a first-order perturbation theory. We have also reported complete radiative data for strong electric dipole transitions within lowest 27 levels. We have compared our calculated results with theoretically calculated and experimentally measured results available in the literature, to measure the credibility and genuineness of our results, and achieve good agreement. Further, because of insufficiency of adequate and complete atomic data for higher levels of highly ionized Cu-like ions in the literature, we have performed other equivalent parallel calculations by implementing fully relativistic distorted wave flexible atomic code (FAC) to ensure the accuracy of our results. Additionally, we have also presented transition wavelengths of Nα transitions of high-Z Cu-like ions by using Moseley’s law. We believe that the large amount of atomic data presented in this paper may be useful in fusion and astrophysical plasma and in several applications, especially in lithography and cell biology.

Multiconfigurational Dirac-Fock Energy Levels and Radiative Rates for Kr XX

In present calculations, energy levels and radiative properties are reported for transitions in Cl-like Kr. For these calculations, the fully relativistic multiconfigurational Dirac-Fock (MCDF) approach is employed by including 54 configurations (generating 5370 levels) and the Breit and quantum electrodynamics effects. To assess the accuracy of presented results, calculations have also been performed for energy levels using the fully relativistic flexible atomic code (FAC) and comparisons are made with the existing experimental and theoretical data. Energies are reported for the lowest 100 levels corresponding to the configurations 3s 2 3p 5 , 3s3p6, 3s 2 3p 4 3d, 3s3p 5 3d, 3s 2 3p 3 3d 2 and radiative rates are provided for E1 and M2 transitions from ground state.

Atomic structure calculations and study of line intensity ratio for Kr XXIV

In this work, we provide a detailed and elaborate theoretical study of atomic data along with plasma parameters for Kr XXIV. We have computed energy levels, lifetimes, and wave-function compositions for the lowest 148 fine-structure levels by implementing the multi-configuration Dirac–Fock method with the addition of quantum electrodynamics as well as Breit corrections. We have also given the radiative data among 148 levels for electric dipole (E1) transition, which lie in the extreme ultraviolet range. We have compared our calculated results with NIST and other theoretical results available in the literature and attain a good agreement. Because of the unavailability of sufficient and complete data for higher excited levels for Kr XXIV in the literature, a similar calculation has also been compiled using fully relativistic flexible atomic code (FAC) to access the credibility and integrity of our results. On the other hand, we have also presented the line intensity ratio and plasma parameters for optically thin plasma, which are not published anywhere in the literature, and we believe that our presented results may be advantageous in plasma modeling and astrophysical and fusion plasma research applications.

Electron Impact Excitation of F-Like W LXVI

Electron impact excitation collision strengths are calculated for all transitions among 113 levels of the 2s 2 2p 5 , 2s2p 6 , 2s 2 2p 4 3ℓ, 2s2p 5 3ℓ, and 2p 6 3ℓ configurations of F-like W LXVI. For this purpose, Dirac Atomic R-matrix Code (DARC) has been adopted and results are listed over a wide energy range of 1000 to 6000 Ryd. For comparison purposes, analogous calculations have also been performed with the Flexible Atomic Code (FAC), and the results obtained are comparable with those from DARC.

Dielectronic recombination of tungsten ions

Ab initio calculations of dielectronic recombination rate coefficients of Ne-, Pd- and Ag-like tungsten have been performed. Energy levels, radiative transition probabilities and autoionization rates were calculated using the Flexible Atomic Code. The contributions from different channels to the total rate coefficients are discussed. The present calculated rate coefficients are compared with other calculations where available. Excellent agreement has been found for Ne-like W while a large discrepancy was found for Pd-like W, which implies that more ab initio calculations and experimental measurements are badly needed. Further calculations demonstrated that the influence of configuration interaction is small while nonresonant radiative stabilizing (NRS) contribution to doubly excited non-autoionizing states are vital. The data obtained are expected to be useful for modeling plasmas for fusion applications, especially for the ITER community, which makes experimental verification even more essential.

Relative Intensities of the 3d-2p Lines Emitted by Ar13+Ions after Impact Excitation by an Electron Beam

The intensity ratio R of the dipole-allowed lines 3d D3/2,5/2 → 2p P3/2 and 3d D3/2 → 2p P1/2 emitted from highly charged boron-like Ar ion collisionally excited by a monoenergetic electron beam has been theoretically studied versus electron densities from 10 to 5× 10 cm−3. The calculations were performed at different angles θ of observation with respect to the electron beam direction and various incident-electron energies e i from 0.65 to 3 keV. By taking into account all important transitions among 290 magnetic sublevels of the 2s2p, 2s2p, 2p, 2s3l, 2s2p3l, 2p3l (l = 0−2) configurations, a collisional-radiative model has been used for determining the populations of the upper magnetic sublevels of the lines. All required atomic data were computed with the Flexible Atomic Code. We find that the effect of anisotropy in the photon emission, due to the directionality of the incident electron beam, can lead to very significant differences between R(0◦) and R(90◦). Our results also indicate that the contribution from the D3/2 → P 3/2 line which blends with the D5/2 → P 3/2 line enhances the effect of anisotropy.

Investigation of M1 transitions of the ground-state configuration of In-like tungsten

Three visible lines of M1 transitions from In-like tungsten were recorded using the Shanghai Permanent Magnet Electron Beam Ion Trap. The experimental wavelengths were measured as 493.84 ± 0.15, 226.97 ± 0.13 and 587.63 ± 0.23 nm (vacuum wavelengths). These results are in good agreement with theoretical predictions obtained using the large-scale relativistic many-body perturbation theory, in the form of the flexible atomic code.

Statistical Model of Dielectronic Recombination of Heavy Ions in Plasmas

AbstractCalculation of the total dielectronic recombination (DR) rates was done in the frame of a statistical model of atoms. The model is based on the idea of collective excitations of atomic electrons with the local plasma frequency, which depends on atomic electrons density distribution. The electron density is described in a frame of the Thomas‐Fermi model of atoms. Simple scaling laws for temperature Te and nuclear charge Z dependences follow from the statistical model of DR. Results of the statistical model were compared with other numerical data following detailed level‐by‐level computations for different multielectron ions. The specific attention is paid to Ni‐like ion sequences of different chemical elements in order to check the Z ‐dependence of DR rates. A comparison with numerical data of Flexible Atomic Code (FAC) is presented for tungsten ions. The reasonable correspondence between the statistical model and the detailed numerical data is demonstrated. The application of the statistical model provides very simple and fast calculations of the DR rates useful in modern plasma modelling. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effects of lowly ionized ions on silicon K-shell absorption spectra

Context. In both astrophysical and laboratory plasmas, K-shell absorption spectra have become powerful diagnostic tools to investigate electron density and temperature. These spectra are also widely used to verify the opacity codes in laboratory settings.Aims. We report the effects of the low ionization silicon ions, namely from Si I to Si V, which have rarely been considered in previous models, on the K-shell silicon absorption spectra.Methods. The Si K-shell atomic data were calculated with the flexible atomic code, which is a fully relativistic atomic program with configuration interaction taken into consideration. Detailed level accounting models were employed to calculate the absorption spectra.Results. We calculate the Si absorption spectra in local thermodynamic equilibrium conditions with temperature and density ranges of 20−70 eV and ~1020 cm-3 to ~1022 cm-3 , respectively, and show the contributions of the lowly ionized ions to the K-shell absorption spectra of silicon. We also investigate the effects of the different atomic data on the absorption spectra. We find good agreement between our results and these from OPLIB.Conclusions. We find that the contributions from these lowly ionized ions cannot be neglected at relative low temperatures. Accurate experimental measurements are needed to benchmark the theoretical calculations.

KLL dielectronic recombination resonant strengths of He-like up to O-like tungsten ions

Dielectronic recombination (DR) is an important process in hot plasma physics as well as in atomic structure and collision theory. This work reports the studies of the KLL DR resonance strengths of He-, Li-, Be-, B-, C-, N-, and O-like tungsten ions, through both experiment and calculation. The experimental resonance strengths were determined within uncertainty below 11% at the Shanghai electron beam ion trap by employing a fast electron beam-energy scanning technique. A fully relativistic configuration interaction method implemented in the flexible atomic code was employed to calculate DR process and also radiative recombination (RR). The consideration of the interference effect between DR and RR was revealed to be necessary to determine the resonance strength.

Radiative rates for E1, E2, M1, and M2 transitions in S-like to F-like tungsten ions (W LIX to W LXVI)

Calculations of energy levels, radiative rates and lifetimes are reported for eight ions of tungsten, i.e. S-like (W LIX) to F-like (W LXVI). A large number of levels have been considered for each ion and extensive configuration interaction has been included among a range of configurations. For the calculations, the general-purpose relativistic atomic structure package (grasp) has been adopted, and radiative rates (as well as oscillator strengths and line strengths) are listed for all E1, E2, M1, and M2 transitions of the ions. Comparisons have been made with earlier available experimental and theoretical energies, although these are limited to only a few levels for most ions. Therefore for additional accuracy assessments, particularly for energy levels, analogous calculations have been performed with the flexible atomic code (fac).

Quantum interference between resonant and nonresonant photorecombination

In this paper, we present experimental and theoretical studies on the interference between resonant and nonresonant photorecombinations for the main resonances of ground-state He-, Be-, B-, C-, N-, and O-like W ions. Experiments were done using a fast electron energy scanning technique at the upgraded Shanghai electron-beam ion trap. Asymmetric resonances were observed, and their Fano factors, which measure the interference degree, were determined. The calculations were done under the framework of Fano's theory by using the flexible atomic code, in which the relativistic configuration interaction method was employed. Among the nine resonances studied in this work, eight experimental results agree with the calculation within experimental uncertainties. But the experimental result for the resonance of Be-like W ions, through the intermediate state of ${[{(1s2{s}^{2}2{p}_{1/2})}_{1}2{p}_{3/2}]}_{5/2}$, deviates from its corresponding theoretical result by 1.3 times experimental uncertainty.

Studies of x-ray emission properties of photoionized plasmas

In this paper three aspects of photoionized plasmas are discussed in both laboratory and astrophysical contexts. First, the importance of accurate atomic/ionic data for the analysis of photoionized plasmas is shown. Second, an overview of present computer codes for the analysis of photoionized plasmas is given. We introduce our computer model, radiative-collisional code based on the flexible atomic code (RCF), for calculations of the properties of such plasmas. RCF uses database generated by the flexible atomic code. Using RCF it is shown that incorporating the satellite lines from doubly excited Li-like ions into the He triplet lines is necessary for reliable analysis of observational spectra from astrophysical objects. Finally, we introduce a proposal to generate photoionized plasmas by x-ray free electron laser, which may facilitate the simulation in lab of astrophysical plasmas in photoionization equilibrium.

Observation of extreme ultraviolet transitions in highly charged Ba16+ to Ba23+ ions with electron beam ion trap

We have investigated extreme ultraviolet emission from highly charged barium using a compact electron beam ion trap at the Tokyo EBIT laboratory. The spectra were recorded for several beam energies ranging from 440 to 740 eV, while keeping the electron beam current constant at 10 mA. Radiation from charge states Zr-like Ba16+ to As-like Ba23+ were recorded and identified by varying the electron beam energy across the ionization thresholds and comparing with calculated results. The calculations were performed with a detailed relativistic configuration interaction approach using the Flexible Atomic Code. Several new lines belonging to electric dipole transitions were observed and identified.

Energy levels, lifetimes and radiative data of Ba XXVI

We report an extensive and an elaborate theoretical study of atomic data for Ba XXVI by considering Singlet, Doublet and Triplet (SDT) electron excitations within N-shell and single excitations from N-shell to O-shell. We have calculated energy levels and lifetimes for lowest 110 fine structure levels by using Multi-configuration Dirac–Fock method (MCDF). We have also considered Quantum Electrodynamics (QED) and Breit corrections in our calculations. We have presented the radiative data for electric and magnetic dipole (E1, M1) and quadrupole (E2, M2) transitions among lowest 110 levels. We have made comparisons of our calculated excitation energies and EUV (Extreme Ultraviolet) transition wavelengths with experimentally observed energy levels and wavelengths and achieved good agreement. We have also computed energy levels by performing similar relativistic distorted wave calculations using Flexible Atomic Code (FAC). Additionally, we have provided new atomic data for Ba XXVI which are not published elsewhere in the literature. We believe that our results may be beneficial in fusion plasma research and astrophysical investigations and applications.

Extreme ultraviolet and soft x-ray spectral lines in Rb XXIX

An extensive theoretical set of atomic data for Rb XXIX in a wide range with L-shell electron excitations to the M-shell has been reported. We have computed energy levels for the lowest 113 fine structure levels of Rb XXIX. The fully relativistic multiconfigurational Dirac–Fock method (MCDF) within the framework of Dirac–Coulomb Hamiltonian taking quantum electrodynamics (QED) and Breit corrections into account has been adopted for calculations. Radiative data are reported for electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions from the ground level, although calculations have been performed for a much larger number of levels. To assess the accuracy of results, we performed analogous calculations using flexible atomic code (FAC). Comparisons are made with existing available results and a good agreement has been achieved. Most of the wavelengths calculated lie in the soft x-ray (SXR) region. Lifetimes for all 113 levels have also been provided for the first time. Additionally, we have provided the spectra for allowed transitions from n = 2 to n = 3 within the x-ray region and also compared our SXR photon wavelengths with experimentally recognized wavelengths. We hope that our results will be beneficial in fusion plasma research and astrophysical applications.

Calculations with spectroscopic accuracy for the ground configuration (3d9) forbidden transition in Co-like ions

We present systematic and large-scale calculations for the fine-structure energy splitting and transition rate between the 3d(9) D-2(3/2,5/2) levels of Co-like ions with 28 <= Z <= 100. Two different fully relativistic approaches are used, based on the multiconfiguration Dirac-Hartree-Fock (MCDHF) theory and the relativistic many-body-perturbation theory (RMBPT). Especially the former gives results of similar accuracy as experiments for a large range of ions. Our calculations are therefore accurate enough to probe Breit and quantum-electro-dynamic effects. To obtain spectroscopic accuracy, we show that it is important to include deep core-valence correlation, down to and including the n = 2 shell. We estimate that the uncertainties of our wavelengths are within the uncertainty of experiments, i.e., 0.02%. We also show that the frequently used flexible atomic code has an inaccurate treatment of the self-energy (SE) contribution and of the M1-transition properties for lower-Z ions. After correcting for the SE calculation, the resulting RMBPT transition energies are in good agreement with the MCDHF ones, especially for the high-Z end of the Co-like sequence. (Less)

Collisional-radiative model for the visible spectrum of W26+ ions

Plasma diagnostics in magnetic confinement fusion plasmas by using visible spectrum strongly depends on the knowledge of fundamental atomic properties. A detailed collisional-radiative model of W26+ ions has been constructed by considering radiative and electron excitation processes, in which the necessary atomic data had been calculated by relativistic configuration interaction method with the implementation of Flexible Atomic Code. The visible spectrum observed at an electron beam ion trap (EBIT) in Shanghai in the range of 332 nm to 392 nm was reproduced by present calculations. Some transition pairs of which the intensity ratio is sensitive to the electron density were selected as potential candidates of plasma diagnostics. Their electron density dependence is theoretically evaluated for the cases of EBIT plasmas and magnetic confinement fusion plasmas.

Excitation processes in experimental photoionized plasmas

Photoionized plasmas widely exist nearby strong radiative sources in the universe. With the development of the high energy density facilities, photoionized plasmas related to astrophysical objects are generated in laboratories accordingly. RCF (radiative collisional code based on the flexible atomic code) is a theoretical model applied to steady-state photoionized plasmas. Its rate equation includes five groups of mutually inverse atomic processes, which are spontaneous decay and photoexcitation, electron impact excitation and deexcitation, photoionization and radiative recombination, electron impact ionization and three body recombination, autoionization and dielectronic capture. All of the atomic data are calculated by FAC (the flexible atomic code), and with four input parameters, RCF can calculate the charge distribution and emission spectrum of the plasma. RCF has well simulated the charge state distribution of a photoionizing Fe experiment on Z-facility and the measured spectrum of photoionizing Si experiment on GEKKO-XII laser facility. According to the simulation results, the importance of photoexcitation and electron impact excitation processes in the two photoionization experiments is discussed. In the photoionizing Fe experiment condition, high energy photons not only ionize the ions by photoionization directly, but also excite the ions to autoionizing levels, ionizing the ions indirectly. What is more, far from ionizing the ions, electrons even suppress the ionization of the plasma by exciting the ions to levels with small ionization cross sections. In the photoionizing Si experiment condition, because of high photoexcitation rate, strong resonance line of He-like ion and some Li-like ion lines, which have similar spontaneous decay rates as the resonance line, are emitted. Although the intercombination line of He-like ion has lower spontaneous decay rate than the resonance lines, strong recombination makes them have comparable strengthes. Electron impact excitation can influence the line ratio of He-like ion lines by affecting the distribution of 1s2l (l=s,p) levels.