Atomic Structure Code Research Articles

Dielectronic and Trielectronic Recombination Rate Coefficients of Be-like Ar 14+

Electron–ion recombination of Be-like 40Ar14+ has been measured by employing the electron–ion merged-beams method at the cooler storage ring CSRm. The measured absolute recombination rate coefficients for collision energies from 0 to 60 eV are presented, covering all dielectronic recombination (DR) resonances associated with 2s 2 → 2s2p core transitions. In addition, strong trielectronic recombination (TR) resonances associated with 2s 2 → 2p 2 core transitions were observed. Both DR and TR processes lead to series of peaks in the measured recombination spectrum, which have been identified by the Rydberg formula. Theoretical calculations of recombination rate coefficients were performed using the state-of-the-art multi-configuration Breit–Pauli atomic structure code AUTOSTRUCTURE to compare with the experimental results. The plasma rate coefficients for DR+TR of Ar14+ were deduced from the measured electron–ion recombination rate coefficients in the temperature range from 103 to 107 K, and compared with calculated data from the literature. The experimentally derived plasma rate coefficients are 60% larger and 30% lower than the previously recommended atomic data for the temperature ranges of photoionized plasmas and collisionally ionized plasmas, respectively. However, good agreement was found between experimental results and the calculations by Gu and Colgan et al. The plasma rate coefficients deduced from experiment and calculated by the current AUTOSTRUCTURE code show agreement that is better than 30% from 104 to 107 K. The present results constitute a set of benchmark data for use in astrophysical modeling.

Recursive determination of phase shifts for screened Coulomb potentials

In the calculation of hot-plasma atomic structure, the continuum wavefunctions are characterized by phase shifts, which therefore determine the scattering cross-sections. In this short paper, we propose a recurrence relation for the phase shifts in the case of a particular type of parametric potentials widely used in atomic-structure codes. These potentials have to be linear combinations of static screened Coulomb potentials (Yukawa-type potentials) multiplied by polynomial functions.

Energy levels and radiative rates for transitions in Cr-like Kr XIII, Tc XX and Xe XXXI

Energy levels, radiative transition probabilities, Landé g-factors, and radiative lifetimes are reported for 144 levels of the 3p63d6 and 3p53d7 configurations of the Cr-like ions Kr XIII, Tc XX and Xe XXXI. Since to our knowledge no prior data for energy levels or A-values, experimental or theoretical, are available in the literature for these ions, calculations have been performed with three independent atomic structure codes, namely GRASP, FAC and a code implementing the QR approach, with increasing configuration interaction (CI) basis with each code. This is to establish the accuracy of the calculated results so that data can be confidently applied in the modeling of plasmas. Our recommended data are determined within the QR approach, because not only has the largest CI basis been included in this calculation, the reliability has already been established in our earlier work for other Cr-like ions, for which some experimental and theoretical data were available for comparison. Results for radiative rates (A-values) and transition wavelengths (λ) are listed for all strong E1, E2 and M1 transitions among the 144 levels of each ion.

Theoretical Confirmation of the Low Experimental 3C/3D f-Value Ratio in Fe xvii.

Radiative transition probabilities (A values) are computed for the Fe xvii L-shell lines in a Breit-Pauli configuration-interaction method with the autostructure atomic structure code. It is shown that, by carefully taking into account the fine-tuning of the relativistic coupling and 2p-orbital relaxation, the measured A values of the M1 and M2 lines and, for the first time, the low f(3C)/f(3D) oscillator-strength ratio are satisfactorily reproduced by the theory. The present ratio f(3C)/f(3D)=2.82 compares well with the measurement of 2.61±0.23 by x-ray laser spectroscopy.

Optimisation and assessment of theoretical impurity line power coefficients relevant to ITER and DEMO

Total radiated line power coefficients for ions of medium to heavy weight elements, called coefficients in the atomic data and analysis structure, have been improved by algorithmically optimising the selection of configuration sets that underpin the calculation to include the most important radiating transitions driven by both the ground and metastable configurations and to establish and limit the error of truncation. The optimised calculations typically differ from Pütterich by 20%–30% with truncation error . Further appraisal of error due to atomic level bundling, atomic structure and collision strength calculation methods has been carried out. It is shown that bundling to configurations is accurate to for all ions except those with closed-shell ground configurations which give errors up to a factor 2–3. For near neutral, closed-shell ions, plane-wave Born collision strength calculations, which omit spin-change, give substantial error in comparison with distorted-wave calculations of . For highly charged ions, spin-system breakdown reduces the error in the markedly, typically . The error introduced by the atomic structure codes used here, autostructure and the Cowan code, is probably limited to .

Analysis of soft x-ray emission spectra of laser-produced dysprosium, erbium and thulium plasmas

Soft x-ray emission spectra of dysprosium, erbium and thulium ions created in laser-produced plasmas were recorded with a flat-field grazing-incidence spectrometer in the 2.5–8 nm spectral range. The ions were produced using an Nd:YAG laser of 7 ns pulse duration and the spectra were recorded at various power densities. The experimental spectra were interpreted with the aid of the Cowan suite of atomic structure codes and the flexible atomic code. At wavelengths above 5.5 nm the spectra are dominated by overlapping n = 4 − n = 4 unresolved transition arrays from adjacent ion stages. Below 6 nm, n = 4 − n = 5 transitions also give rise to a series of interesting overlapping spectral features.

Analysis of unresolved transition arrays in XUV spectral region from highly charged lead ions produced by subnanosecond laser pulse

Soft x-ray and extreme ultraviolet (XUV) spectra from lead (Pb, Z=82) laser-produced plasmas (LPPs) were measured in the 1.0–7.0nm wavelength region employing a 150-ps, 1064-nm Nd:YAG laser with focused power densities in the range from 3.1×1013W/cm2 to 1.4×1014W/cm2. The flexible atomic code (FAC) and the Cowan's suite of atomic structure codes were applied to compute and explain the radiation properties of the lead spectra observed. The most prominent structure in the spectra is a broad double peak, which is produced by Δn=0, n=4–4 and Δn=1, n=4–5 transition arrays emitted from highly charged lead ions. The emission characteristics of Δn=1, n=4–5 transitions were investigated by the use of the unresolved transition arrays (UTAs) model. Numerous new spectral features generated by Δn=1, n=4–5 transitions in ions from Pb21+ to Pb45+ are discerned with the aid of the results from present computations as well as consideration of previous theoretical predictions and experimental data.

Laser gain calculations for soft X-ray and XUV radiation emitted from copper-like ions by electron collisional pumping

Electron impact excitation rate coefficients, level population densities, and gain coefficients for six excited ions with Z = 51, 52, 53, 54, 55, 56 in the copper isoelectronic sequence have been calculated. The electron collisional excitation rate coefficients are calculated according to the analytical formulas of Vriens and Smeets. Fine structure energy levels, transition probabilities, and oscillator strengths needed in the calculations have been calculated using Cowan atomic structure code with relativistic corrections for [Ar]3d10nl with n = 4–7 and l = 0–6. The level population densities are calculated by solving the coupled rate equations involving 30 levels. Positive gain coefficients of the possible emitted lines are obtained at three selected electron temperatures, namely 1/4, 1/2, and 3/4 of the ionization energy. The present calculated data show promising values for the production of soft X-ray and XUV laser by collisional pumping for the transitions 5p–5s and 6d–5f with wavelengths between 108 and 571 Å. The values of the maximum gain coefficient are found to increase with atomic number and their order of magnitude ranges from102to 104cm−1.

Atomic Structure Calculations for Neutral Oxygen

Energy levels and oscillator strengths for neutral oxygen have been calculated using the Cowan (CW), SUPERSTRUCTURE (SS), and AUTOSTRUCTURE (AS) atomic structure codes. The results obtained with these atomic codes have been compared with MCHF calculations and experimental values from the National Institute of Standards and Technology (NIST) database.

K-shell photoabsorption and photoionisation of trace elements

Context. With the recent launching of the Hitomi X-ray space observatory, K lines and edges of chemical elements with low cosmic abundances, namely F, Na, P, Cl, K, Sc, Ti, V, Cr, Mn, Co, Cu and Zn, can be resolved and used to determine important properties of supernova remnants, galaxy clusters and accreting black holes and neutron stars.Aims. The second stage of the present ongoing project involves the computation of the accurate photoabsorption and photoionisation cross sections required to interpret the X-ray spectra of such trace elements.Methods. Depending on target complexity and computer tractability, ground-state cross sections are computed either with the close-coupling Breit-Pauli R-matrix method or with the autostructure atomic structure code in the isolated-resonance approximation. The intermediate-coupling scheme is used whenever possible. In order to determine a realistic K-edge behaviour for each species, both radiative and Auger dampings are taken into account, the latter being included in the R-matrix formalism by means of an optical potential.Results. Photoabsorption and total and partial photoionisation cross sections are reported for isoelectronic sequences with electron numbers 3 11 as they contribute significantly to the monotonic background of the cross section between the L and K edges. Configurations with 3d orbitals are important in rendering an accurate L edge, but they can be practically neglected in the K-edge region.

Atomic Data and Laser Transitions in as - Like Gallium

Fine structure calculations of the energy levels, the wavelengths, the oscillator strengths, log gf and the transition probabilities for transitions among the terms belonging to 1s2 2s2 2p6 3s2 3p6 3d104s2ns, n=5-6, 1s2 2s2 2p6 3s2 3p6 3d104s2np, n=4-6, 1s2 2s2 2p6 3s2 3p6 3d104s2nd, n=4-6 and1s2 2s2 2p6 3s2 3p6 3d104s2nf, n=4-6 configurations of As (III) have been calculated using configurations interaction Cowan atomic structure code. Our calculated values for the above mentioned quantities have been compared with the corresponding experimental data and other theoretical calculations where a satisfactory agreement is found. We also report on some unpublished values for energy levels, oscillator strengths and transition probabilities for As like gallium. These atomic data are taken as the basis for studying laser transitions between levels of As(III). Excitation rate coefficients of As like gallium are calculated using the analytical formulas of Vriens and Smeets (1980) and with considering using the collisional radiative model code CRMO of Allam (2006). A simple modification to these formulas has been included by introducing effective quantum numbers. The energy values, the radiative data and rate coefficients are then used to calculate the population densities by solving the coupled rate equations. Among these calculations positive gain coefficients are found at three selected values of electron temperature, namely 7.087 eV, 14.147 eV and 21.261 eV which are displayed as a function of the electron impact density.

Influence of the plasma environment on atomic structure using an ion-sphere model

Plasma environment effects on atomic structure are analyzed using various atomic structure codes. To monitor the effect of high free-electron density or low temperatures, Fermi-Dirac and Maxwell-Boltzmann statistics are compared. After a discussion of the implementation of the Fermi-Dirac approach within the ion-sphere model, several applications are considered. In order to check the consistency of the modifications brought here to extant codes, calculations have been performed using the Los Alamos Cowan Atomic Structure (cats) code in its Hartree-Fock or Hartree-Fock-Slater form and the parametric potential Flexible Atomic Code (fac). The ground-state energy shifts due to the plasma effects for the six most ionized aluminum ions have been calculated using the fac and cats codes and fairly agree. For the intercombination resonance line in ${\mathrm{Fe}}^{22+}$, the plasma effect within the uniform electron gas model results in a positive shift that agrees with the multiconfiguration Dirac-Fock value of B. Saha and S. Fritzsche [J. Phys. B 40, 259 (2007)]. Last, the present model is compared to experimental data in titanium measured on the terawatt Astra facility and provides values for electron temperature and density in agreement with the maria code.

Analysis of extreme ultraviolet spectra from laser produced rhenium plasmas

Extreme ultraviolet spectra of highly-charged rhenium ions were observed in the 1–7 nm region using two Nd:YAG lasers with pulse lengths of 150 ps and 10 ns, respectively, operating at a number of laser power densities. The maximum focused peak power density was 2.6 × 1014 W cm−2 for the former and 5.5 × 1012 W cm−2 for the latter. The Cowan suite of atomic structure codes and unresolved transition array (UTA) approach were used to calculate and interpret the emission properties of the different spectra obtained. The results show that n = 4-n = 4 and n = 4-n = 5 UTAs lead to two intense quasi-continuous emission bands in the 4.3–6.3 nm and 1.5–4.3 nm spectral regions. As a result of the different ion stage distributions in the plasmas induced by ps and ns laser irradiation the 1.5–4.3 nm UTA peak moves to shorter wavelength in the ps laser produced plasma spectra. For the ns spectrum, the most populated ion stage during the lifetime of this plasma that could be identified from the n = 4-n = 5 transitions was Re23+ while for the ps plasma the presence of significantly higher stages was demonstrated. For the n = 4-n = 4 4p64dN-4p54dN+1 + 4p64dN−14f transitions, the 4d-4f transitions contribute mainly in the most intense 4.7–5.5 nm region while the 4p-4d subgroup gives rise to a weaker feature in the 4.3–4.7 nm region. A number of previously unidentified spectral features produced by n = 4-n = 5 transitions in the spectra of Re XVI to Re XXXIX are identified.

Characteristics of x-ray emission from optically thin high-Z plasmas in the soft x-ray region

The characteristics of soft x-ray emission from optically thin high-Z plasmas of gold, lead and bismuth were investigated with the large helical device. Compared to optically thicker laser-produced plasmas, significantly different spectral structures were observed due to the difference in opacities and electron temperatures. Peak structures appearing in unresolved transition arrays were identified by calculations using atomic structure codes. The main contributors of discrete line emission in each case were Pd-, Ag-, and Rh-like ion stages. The present calculations point to the overestimation of contributions for 4p–4d transitions based on intensity estimates arising purely from gA distributions that predict strong emission from 4p–4d transitions. Understanding of such spectral emission is not only important for the completion of databases of high-Z highly ion charge states but also the development of promising high brightness sources for biological imaging applications.

Ab initio MCDHF calculations of electron–nucleus interactions

We present recent advances in the development of atomic ab initio multiconfiguration Dirac–Hartree–Fock theory, implemented in the GRASP relativistic atomic structure code. For neutral atoms, the deviations of properties calculated within the Dirac–Hartree–Fock (DHF) method (based on independent particle model of an atomic cloud) are usually dominated by electron correlation effects, i.e. the non-central interactions of individual electrons. We present the recent advances in accurate calculations of electron correlation effects in small, medium, and heavy neutral atoms. We describe methods of systematic development of multiconfiguration expansions leading to systematic, controlled improvement of the accuracy of the ab initio calculations. These methods originate from the concept of the complete active space (CAS) model within the DHF theory, which, at least in principle, permits fully relativistic calculations with full account of electron correlation effects. The calculations within the CAS model on currently available computer systems are feasible only for very light systems. For heavier atoms or ions with more than a few electrons, restrictions have to be imposed on the multiconfiguration expansions. We present methods and tools, which are designed to extend the numerical calculations in a controlled manner, where multiconfiguration expansions account for all leading electron correlation effects. We show examples of applications of the GRASP code to calculations of hyperfine structure constants, but the code may be used for calculations of arbitrary bound-state atomic properties. In recent years it has been applied to calculations of atomic and ionic spectra (transition energies and rates), to determinations of nuclear electromagnetic moments, as well as to calculations related to interactions of bound electrons with nuclear electromagnetic moments leading to violations of discrete symmetries.

X-ray spectra of high temperature tungsten plasma calculated with collisional radiative model

Tungsten is regarded as an important candidate of plasma facing material in international thermonuclear experimental reactor (ITER), so the determination and modeling of spectra of tungsten plasma, especially the spectra at high temperature were intensely focused on recently. In this work, using the atomic structure code of Cowan, a collisional radiative model (CRM) based on the spin—orbit-split-arrays is developed. Based on this model, the charge state distribution of tungsten ions is determined and the soft X-ray spectra from high charged ions of tungsten at different temperatures are calculated. The results show that both the average ionization charge and line positions are well agreed with others calculations and measurements with discrepancies of less than 0.63% and 1.26%, respectively. The spectra at higher temperatures are also reported and the relationship between ion abundance and temperature is predicted in this work.

Electron impact excitation of Mg VIII

Context. Mg viii emission lines are observed in a range of astronomical objects such as the Sun, other cool stars and in the coronal line region of Seyfert galaxies. Under coronal conditions Mg viii emits strongly in the extreme ultraviolet (EUV) and soft X-ray spectral regions which makes it an ideal ion for plasma diagnostics. Aims. Two theoretical atomic models, consisting of 125 fine structure levels, are developed for the Mg viii ion. The 125 levels arise from the 2s 2 2p, 2s2p 2 , 2p 3 , 2s 2 3s, 2s 2 3p, 2s 2 3d, 2s2p3s, 2s2p3p, 2s2p3d, 2p 2 3s, 2p 2 3p and 2p 2 3d configurations. Electron impact excitation collision strengths and radiative transition probabilities are calculated for both Mg viii models, compared with existing data, and the best model selected to generate a set of theoretical emission line intensities. The EUV lines, covering 312‐790 A, are compared with existing solar spectra (SERTS‐89 and SUMER), while the soft X-ray transitions (69‐97 A) are examined for potential density diagnostic line ratios and also compared with the limited available solar and stellar observational data. Methods. The R-matrix codes Breit-Pauli RMATRXI and RMATRXII are utilised, along with the PSTGF code, to calculate the collision strengths for two Mg viii models. Collision strengths are averaged over a Maxwellian distribution to produce the corresponding e ective collision strengths for use in astrophysical applications. Transition probabilities are also calculated using the CIV3 atomic structure code. The best data are then incorporated into the modelling code CLOUDY and line intensities generated for a range of electron temperatures and densities appropriate to solar and stellar coronal plasmas. Results. The present e ective collision strengths are compared with two previous calculations. Good levels of agreement are found with the most recent, but there are large di erences with the other for forbidden transitions. The resulting line intensities compare favourably with the observed values from the SERTS-89 and SUMER spectra. Theoretical soft X-ray emission lines are presented and several density diagnostic line ratios examined, which are in reasonable agreement with the limited observational data available.

Light element opacities from ATOMIC

We present new calculations of local-thermodynamic-equilibrium (LTE) light element opacities from the Los Alamos ATOMIC code. ATOMIC is a multi-purpose code that can generate LTE or non-LTE quantities of interest at various levels of approximation. A program of work is currently underway to compute new LTE opacity data for all elements H through Zn. New opacity tables for H through Ne are complete, and a new Fe opacity table will be available soon. Our calculations, which include fine-structure detail, represent a systematic improvement over previous Los Alamos opacity calculations using the LEDCOP legacy code. Our opacity calculations incorporate atomic structure data computed from the CATS code, which is based on Cowan's atomic structure codes, and photoionization cross section data computed from the Los Alamos ionization code GIPPER. We make use of a new equation-of-state (EOS) model based on the chemical picture. ATOMIC incorporates some physics packages from LEDCOP and also includes additional physical processes, such as improved free–free cross sections and additional scattering mechanisms. In this report, we briefly discuss the physics improvements included in our new opacity calculations and present comparisons of our new opacities with other work for C, O, and Fe at selected conditions.

Self-energy screening approximations in multi-electron atoms

Atomic structure calculations have reached levels of accuracy which require evaluation of many-electron QED contributions. Since exact analytic solutions do not exist, a number of heuristics have been used to approximate the screening of additional electrons. Herein we present an implementation for the widely used GRASP atomic-structure code based on Welton's concept of the electron self-energy. We show that this implementation provides far superior agreement compared with a range of other theoretical predictions, and that the discrepancy between the present implementation and that previously used is of comparable magnitude to other sources of error in high-accuracy atomic calculations. This improvement is essential for ongoing studies of complex atomic systems.

Radial profile measurement of electron temperature in edge stochastic magnetic field layer of LHD using intensity ratio of extreme ultraviolet line emissions

Vertical profile of neon line emissions in 30-650 Å wavelength range has been observed in horizontally elongated plasma cross section of Large Helical Device (LHD). Intensity ratio between the neon line emissions is studied to measure the radial profile of electron temperature in the edge stochastic magnetic field layer of LHD. The edge temperature profile successfully obtained from the line ratio of NeVIII 2s-3p to 2p-3s transitions is compared with the simulation based on three-dimensional edge transport code. The result shows a reasonably good agreement with the edge temperature profile analyzed from atomic data and analysis structure code. The electron temperature at last closed flux surface measured from the intensity ratio is also in good agreement with that measured from Thomson scattering.