Flexible Atomic Code Research Articles

Opacities of singly and doubly ionized neodymium and uranium for kilonova emission modeling

ABSTRACT Even though the electromagnetic counterpart AT2017gfo to the binary neutron star merger GW170817 is powered by the radioactive decay of r-process nuclei, only few tentative identifications of light r-process elements have been made so far. One of the major limitations for the identification of heavy nuclei is incomplete or missing atomic data. While substantial progress has been made on lanthanide atomic data over the last few years, for actinides there has been less emphasis, with the first complete set of opacity data only recently published. We perform atomic structure calculations of neodymium (Z = 60) as well as the corresponding actinide uranium (Z = 92). Using two different codes [flexible atomic code (fac) and hartree–fock-relativistic (hfr)] for the calculation of the atomic data, we investigate the accuracy of the calculated data (energy levels and electric dipole transitions) and their effect on kilonova opacities. For the fac calculations, we optimize the local central potential and the number of included configurations and use a dedicated calibration technique to improve the agreement between theoretical and available experimental atomic energy levels (AELs). For ions with vast amounts of experimental data available, the presented opacities agree quite well with previous estimations. On the other hand, the optimization and calibration method cannot be used for ions with only few available AELs. For these cases, where no experimental nor benchmarked calculations are available, a large spread in the opacities estimated from the atomic data obtained with the various atomic structure codes is observed. We find that the opacity of uranium is almost double the neodymium opacity.

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

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

Comment on “Atomic structure and electron impact excitation of Al-like ions (Ga–Br)” by HB Wang and G Jiang in At. Data Nucl. Data Tables 148 (2022) 101532

In a recent paper, Wang and Jiang (At. Data Nucl. Data Tables 148 (2022) 101532) have reported data for energy levels, radiative rates (A-values), and effective collision strengths (Υ) for some transitions of five Al-like ions, namely Ga XIX, Ge XX, As XXI, Se XXII, and Br XXIII. On a closer examination we find that their reported data for energy levels and A-values are generally correct, but not for Υ. Their Υ values, for all transitions (allowed or forbidden) and for all ions, invariably decrease at higher temperatures. This is mainly because they have adopted a limited range of electron energies for the calculations of collision strengths. We demonstrate this with our calculations with the Flexible Atomic Code (FAC), and conclude that their Υ values are inaccurate, unreliable, and should not be adopted in any applications or modelling analysis.

Measurements of the L-shell X-ray emission of fluorine-like europium

Measurements of the L-shell X-ray emission of fluorine-like europium ions (Eu54+) were made under controlled laboratory conditions on the EBIT-I electron beam ion trap at Livermore using an X-ray calorimeter, extending such measurements to the middle of the rare earth elements. Comparing the calorimeter spectra with atomic data from the flexible atomic code, we have identified and analyzed several prominent n = 3 → n = 2 transitions, including one two-electron, one-photon core changing transition and one electric quadrupole transition. We find that the measured energies are typically up to several eV higher than predicted.

Collisional-radiative modeling of the 2p3l(l = p,d) spectra of N II and application to lightning

The excitation energies, transition rates, collisional-excitation cross sections, and collisional-excitation rate coefficients of N II ions have been calculated by the relativistic configuration-interaction method with the implementation of the flexible atomic code. The population rate coefficients were subsequently investigated and shown that the net population rate coefficients of the 2p3d configuration are greater than those of the 2p3p configuration at an identical electron temperature. A reasonable collisional-radiative model has been constructed to simulate the 2p3s–2p3p and 2p3p–2p3d spectra, which were in reasonable agreement with the lightning data presently obtained in experimental measurements. A further application was implemented in effectively determining the lightning parameters, with the aid of a certain area surrounded by the intersections of contours of multiple line-intensity ratios on the two-dimensional plane of electron temperature and electron density.

Theoretical Investigation of Electron–Ion Recombination Process of Mg-like Gold

The L-shell dielectronic and trielectronic recombinations of highly charged Mg-like gold ions (Au67+) in the ground state 2s22p63s2 1S0 have been studied systematically. The recombination cross-sections and rate coefficients are carefully calculated for ∆n = 1 (2s/2p → 3l) transitions using a flexible atomic code based on the relativistic configuration interaction method and considering the Breit and QED corrections. Detailed resonance energies and resonance strengths are presented for the stronger resonances of the LMn (n = 3–12) series. It is found that the contributions of the trielectronic recombination to the total cross-section is about 13.75%, which cannot be neglected. For convenience of application, the plasma rate coefficients are also calculated and fitted to a semiempirical formula, and in the calculations, the contributions from the higher excited resonance groups n ≥ 13 are evaluated by an extrapolation method, which is about 2.93% of the total rate coefficient.

Dielectronic recombination rate coefficients of carbon-like Kr30+

Dielectronic recombination (DR) rate coefficients for carbon-like Kr30+ have been measured over the collision energy of 0–60 eV using the heavy-ion storage ring CSRe at the Institute of Modern Physics in Lanzhou, China. The present DR spectrum covers the resonances associated with the , and core excitations. The corresponding DR resonance energies and strengths have been calculated by using the flexible atomic code (FAC) to understand the measured results. An overall agreement has been obtained between the experiment and theory, except for the data at the collision energies below 7 eV and in 35–38 eV, where the electronic correlation effect is strong. In particular, the resonances from the trielectronic recombination due to have been identified with the help of the FAC calculation. Temperature-dependent plasma recombination rate coefficients were derived from the measured DR rate coefficients for the temperature range 103–107 K and compared with our FAC calculations as well as the previous AUTOSTRUCTURE calculations by Zatsarinny et al (2004 Astron. Astrophys. 417 1173–81). The FAC and AUTOSTRUCTURE calculations are in good agreement with the presently derived plasma rate coefficients. The present work provides the benchmark data for astrophysical and laboratory plasma modeling.

Electron impact ionization cross sections of highly charged open L-shell tungsten ions

L-shell electron-impact ionization (EII) cross sections for highly charged tungsten ions were measured at incident electron energies of 29.10 and 38.92 keV using the Shanghai-EBIT. Resolved x-rays from radiative recombination (RR) processes were recorded with a high-purity Ge detector in a static electron energy scanning mode. Absolute EII cross sections were obtained by normalizing to the theoretical RR cross sections. The experimental results were compared with the calculated results using the relativistic distorted-wave method implemented in the flexible atomic code and the relativistic Lotz semi-empirical equation. The measurements showed general agreement with the calculated results by two theoretical methods for Li- to N-like W ions. The experimental uncertainties are not sufficiently small to discern the two theoretical results. Furthermore, the influence of Breit interaction on the EII cross sections of open L-shell tungsten ions was studied, and the effect is small but non-negligible. The measured EII cross sections of open L-shell tungsten ions would contribute to fusion plasma studies.

Theoretical investigation of electron-impact double ionization of B-like C+ to Ne5+ ions

Electron-impact double ionization (DI) including direct and indirect processes of B-like ${\mathrm{C}}^{+}$ to ${\mathrm{Ne}}^{5+}$ ions is investigated using a two-step approach. The direct process is treated as a primary single ionization (SI) and subsequent knockout mechanism. The indirect process is considered as a primary SI of an inner-shell $1s$ electron followed by a single autoionization. Based on the two-step approach, the DI cross sections are calculated using flexible atomic code with distorted-wave approximation. The potential of the intermediate ion is approximately equivalent to the mean potential constructed by three ions involved for calculating the cross section of the direct process, while using the potential of the ionizing ion in each step of the present two-step approach overestimates results. The present cross sections agree with available theoretical and experimental data.

Determination of Electron Beam Energy in Measuring the Electron-Impact Ionization Cross Section of He-like Fe24+

In an effort to measure electron-impact ionization (EII) cross-sections of He-like Fe24+ at the electron beam ion trap (EBIT) facility of the National Institute of Standards and Technology (NIST), we have experimentally determined the corrections to the nominal beam energy determined by the voltages applied to the EBIT. High-resolution X-ray spectra were recorded at nominal electron beam energies between 6660 eV and 6750 eV using X-ray microcalorimetry based upon an array of 192 transition-edge sensors (TES). A large-scale collisional-radiative simulation of the non-Maxwellian EBIT plasma using relevant atomic data calculated with Flexible Atomic Code allowed us to determine the space-charge correction due to the electron beam including the neutralization factor by the ion cloud of the EBIT.

Study of the 6.x nm short wavelength radiation spectra of laser-produced erbium plasmas for BEUV lithography

Beyond extreme ultraviolet (BEUV) radiation with a wavelength of 6.x nm for lithography is responsible for reducing the source wavelength to enable continued miniaturization of semiconductor devices. In this work, the Required BEUV light at 6.x nm wavelength was generated in dense and hot Nd:YAG laser-produced Er plasmas. The spectral contributions from the 4p–4d and 4d–4f transitions of singly, doubly and triply excited states of Er XXIV–Er XXXII in the BEUV band were calculated using Cowan and the Flexible Atomic Code. It was also found that the radiative transitions between multiply excited states dominate the narrow wavelength window around 6.x nm. Under the assumption of collisional radiative equilibrium of the laser-produced Er plasmas, the relative ion abundance in the experiment was inferred. Using the Boltzmann quantum state energy level distribution and Gram–Charlier fitting function of unresolved transition arrays (UTAs), the synthetic spectrum around 6.x nm was finally obtained and compared with the experimental spectrum. The spatio-temporal distributions of electron density and electron temperature were calculated based on radiation hydrodynamic simulation in order to identify the contributions of various ionic states to the UTAs arising from the Er plasmas near 6.x nm.

Analysis of line intensity ratio for optical transitions of 3d6 levels and plasma screening effect on atomic structure of Fe III ion

Iron emission lines are observed from most classes of astronomical objects through a wide spectral range from infrared to X-ray. For a useful analysis of these lines, accurate atomic data for neutral iron and its ions is required. In this work, we have done calculations of energy levels and radiative data of Fe III by using the relativistic configuration interaction method with the implementation of the flexible atomic code (FAC). We have calculated emission-line intensity ratios for optical transitions among the fine-structure levels of the 3d6 configuration at temperature 104 K and density ne=104cm−3. We have also compared our results with the observed spectra of Herbig-Haro objects HH 202 of Orion Nebula, Planetary Nebula, and NGC 2392, post-asymptotic giant branch star (PAGB) HD341617. We have also discussed various discrepancies between the observed spectra from these nebulae and our calculations. The atomic structure of plasma-embedded Fe III is also analyzed using flexible atomic code (FAC). The graphical study shows that transition wavelengths, oscillator strengths, and transition rates are very sensitive to the plasma environment in the density range 1021cm−3 to 5×1022cm−3 and spectral lines associated to Δn = 0 transitions for Fe III ion are blueshifted. We have also studied the dependence of emission line intensity ratios on plasma density and temperature. We believe that our presented results are useful in spectroscopic analysis and examination of astrophysical and laboratory plasma.

Effect of the generalized Breit interaction on the [formula omitted]-shell x-ray spectra of hot krypton plasmas

K-shell spectra are widely used for the plasma diagnostics in fusion science and astrophysics. Here, we report on a theoretical investigation of the relativistic and QED effects, i.e., the Breit interaction (BI) or the generalized Breit interaction (GBI), on the simulation of K-shell x-ray spectra of hot krypton plasmas. The simulation was conducted using a collisional-radiative model, for which the atomic parameters were generated by using the flexible atomic code. As expected, the present work shows that the BI and GBI produce similar effects for such a light element as krypton, which maximum difference of 3.7% in the emission spectra. When comparing to results calculated with just the Coulomb interaction, the GBI affects the specific line intensity by up to 15%, thus bringing about approximately 4%, 13% uncertainties for deducing the electron density and temperature of plasmas, respectively.

Generation of Highly Charged Au Ion in Laser-Produced Plasma for Water Window X-ray Radiation Sources

Highly charged ions in the plasma produced by high-power laser can radiate bright and short-pulse X-rays. Owing to the unresolved transition array (UTA) from the high-Z elements, laser produced plasma has been applied for developing X-ray sources. In particular, X-rays in the water-window (WW) region (2.3–4.4 nm) is utilized as the light source of the X-ray microscopy to observe living organisms under high contrast and resolution. In this work, WW X-rays radiated from a laser (1064 nm, 6.2 ns) produced Au-plasma has been studied. UTA spectrum in the WW range has been observed through a grazing incident spectrometer (GIS). Dependence of Au-ion charge state distribution on laser intensity has been experimentally investigated and evaluated by a transition probability data calculated by the flexible atomic code. The integrated soft X-ray emission has been observed through a pinhole camera with a 1.0-μm Ti-filter, combined with a 2-D plasma radiation scanning achieved by the GIS. An intense WW emission region 200-μm away from the target surface has been observed, which indicates a more effective area is possible to be utilized for a practical use.

The Influence of Hot Electrons on the Calculation of Ionization Rates

Electron-Impact Ionization (EII) is considered one of the most important ionization methods in dynamic systems, in which elements and ions are suddenly exposed to energetic electrons. In many plasma types, it has been observed that some electrons (hot) are governed by a non-Maxwellian energy distribution. This study illustrates the effects of a non-Maxwellian distribution on beryllium and Be+2 emission lines and their effective ionization rate coefficients. The focus on beryllium as an impacted material by electron flux aimed to evaluate the EII rates for Be and generate the corresponding datasets needed for Be+2 data analysis. An interaction cross-section was generated using the Flexible Atomic Code (FAC) and used in the estimation of the EII distribution energy functions to estimate the ionization rates for a non-Maxwellian distribution. The use of non-Maxwellian energy distributions for different fractions of hot electrons showed the sensitivity of these rates to the fraction of hot electrons and the forms of the electron energy distribution. The results were in good agreement with those found in the literature.

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.

Nuclear Excitation by Free Muon Capture

Efficient excitation of nuclei via exchange of a real or virtual photon has a fundamental importance for nuclear science and technology development. Here, we present a mechanism of nuclear excitation based on the capture of a free muon into the atomic orbits (NEμC). The cross section of such a proposed process is evaluated using the Feshbach projection operator formalism and compared to other known excitation phenomena, i.e., photoexcitation and nuclear excitation by electron capture (NEEC), showing up to 10 orders of magnitude increase in cross section. NEμC is particularly interesting for MeV excitations that become accessible thanks to the stronger binding of muons to the nucleus. The binding energies of muonic atoms have been calculated introducing a state of the art modification to the Flexible Atomic Code. An analysis of experimental scenarios in the context of modern muon production facilities shows that the effect can be detectable for selected isotopes. The total probability of NEμC is predicted to be P≈1×10^{-6} per incident muon in a beam-based scenario. Given the high transition energy provided by muons, NEμC can have important consequences for isomer feeding and particle-induced fission.

Diagnosing the electron density of channel plasma in artificially triggered lightning

Transition rates, collision excitation cross sections, and collision excitation rate coefficients of neutral N I atom and N II ions were calculated by Flexible Atomic Code that is based on the multiconfiguration Dirac-Fock method. The line intensity of some strong spectral lines were calculated. Then the dependent relationship among the ratio of line intensity I′I, the electron density ne and the electron temperature T were obtained. The calculation shows that the electron density has some dependence on the temperature and the ratio of line intensity. Furthermore, through applying the theoretical calculations to the channel plasma spectra of artificially triggered lightning, the electron densities were diagnosed at different channel locations and times. The accuracy of the electron density was estimated using the degree of accordance, which can pick out the diagnostic data that can best reflect the real state of plasma from a large number of statistical data.

Electron-Impact Ionization of the Tungsten Ions: W38+ − W45+

In this manuscript, we present our calculations of detailed electron-impact single ionization cross-sections for tungsten ions, spanning charge states W38+− W45+. The level-to-level distorted-wave method implemented in the flexible atomic code (FAC) was used for calculation. Comparison between the present level-to-level distorted wave treatment and previous configuration-averaged calculations has been performed for the W45+ ion, and we explore the possible reason for the difference observed between two calculations. We demonstrate the importance of radiative damping on the total electron-impact ionization cross-section for the W43+ ion. Present calculations provide missing cross-sections for W38+− W45+. The data obtained are expected to be useful for modeling plasmas for fusion applications, especially for the ITER community.

Relativistic atomic structure calculations of KIX with plasma parameters

Systematic calculations for energy levels, lifetimes, and radiative data for the KIX are reported, including oscillator strengths, transition wavelengths, line strengths, and radiative rates of electric dipole (E1) transition, electric quadrupole (E2) transition, magnetic dipole (M1) transition, and magnetic quadrupole (M2) transition, using GRASP. Quantum electrodynamics and Breit correction have been considered in our calculations. The importance and effect of valence valence and core valence correlations on the excitation energies have been discussed in graphical and tabular forms. Analogous calculations using flexible atomic code (FAC) and the large-scale configuration interaction technique have also been done to confirm the accuracy of energy levels. The calculated results are in close agreement with NIST compiled data and other available results. The influence of plasma temperature (2 × 106–1 × 1010 K) on the line intensity ratio with the number of electron density has been studied for the hot dense plasma (HDP) graph for KIX. Our reported results will be valuable or beneficial for the characterization of HDP, astrophysical plasmas, and plasma modeling.