Flexible Atomic Code Research Articles

Theoretical Study of Laser Emission for C-Like (Ar XIII), (Ti XVII) and (Fe XXI)

Energy levels, transition probability and oscillator strengths have been calculated for the Ar XIII, Ti XVII and Fe XXI. The configurations included in the calculations are 2s2 2p2, 2s2 2p 3l (l = s, p & d) and 4l (l = s, p, d, & f) of C-like Ar XIII, Ti XVII & Fe XXI which has 69 fine structures by using the fully relativistic flexible atomic code (FAC) program. These data are used in the determination of the reduced population and gain coefficients over a wide range of electron densities from (10+18 to 10+23) and at various plasmas temperatures. The results show that the transitions in Ar18+, Ti22+, and Fe26+ ions are the most promising laser emission lines in the XUV and soft X-ray spectral regions.

Theoretical studies of dielectronic recombination for Au34+ ions

Dielectronic recombination (DR) rate coefficients of complex structure ions are very important for spectral simulation in some application researches, such as nuclear fusion and extreme ultraviolet lithography. Theoretical calculations are made for dielectronic recombination rate coefficients of Au34+ ions by using a flexible relativistic atomic code. Influences of excitation and radiation channels, configuration interactions, and decays to autoionizing levels possibly followed by radiative cascades (DAC) on DR rate coefficient are analyzed. The contribution of DAC is evident. The total DR rate coefficient is greater than either the radiation recombination coefficient or three-body recombination coefficient for electron temperature greater than 1 eV. In order to facilitate simple applications, the total DR rate coefficients for the ground state and the first excited state are fitted to an empirical formula. These results should be useful for further analyzing the DR process of complex structures ions.

Radiative rates for E1, E2, M1, and M2 transitions in F-like ions with [formula omitted

Calculations of energy levels, radiative rates and lifetimes are reported for 17 F-like ions with 37≤Z≤53. For brevity, results are only presented among the lowest 113 levels of the 2s22p5, 2s2p6, 2s22p43ℓ, 2s2p53ℓ, and 2p63ℓ configurations, although the calculations have been performed for up to 501 levels in each ion. The general-purpose relativistic atomic structure package (grasp) has been adopted for the calculations, and radiative rates (along with oscillator strengths and line strengths) are listed for all E1, E2, M1, and M2 transitions of the ions. Comparisons are 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), for up to 72 259 levels. Limited previous results are available for radiative rates for comparison purposes, and no large discrepancy is observed for any transition and/or ion.

Dielectronic recombination of Cu-like W45+

We have investigated dielectronic recombination (DR) for Cu-like W45+ forming Zn-like W44+ by theoretical calculation using the flexible atomic code based on an independent process, isolated resonance, and distorted wave approximation. We have focused on the effect of configuration mixing involving double electron core excitation as well as single electron core excitation on the DR via 3d94l4l′4l″ and 3p53d104l4l′4l″ resonances by inner-shell core excitation Δnc=1. About 20% and over 100% changes in Maxwellian rate coefficient are shown at high energies over 200eV and at low energies near the threshold, respectively, by the configuration mixing. Non-resonant stabilizations (NRS) and decays to autoionizing levels possibly followed by cascades (DAC) to non-closed inner-shells 3d94l4l′4l″ are also considered. The NRS and DAC effect on the DR Maxwellian rate coefficient is relatively smaller than the configuration mixing effect and is less than ~20%. Particular attention has been paid to the DR via 3d104lnl′ resonances by valence-shell core excitation Δnc=0 which was not considered in the previous work (Behar et al., 1997 [4]). The 3d104lnl′ resonances very dominate the DR at low energies below ~100eV. Δnc=2 core excitations are small but not negligible (~10%) relatively at high energy range around 10keV. Our total DR rate coefficient shows the difference with the recombination coefficient on the ADAS database obtained by using a simple semiempirical formula over order of magnitude at low energies and about 30–50% at 2–7keV energy range where W45+ is abundant.

Electron Impact Excitation and Dielectronic Recombination of Highly Charged Tungsten Ions

Electron impact excitation (EIE) and dielectronic recombination (DR) of tungsten ions are basic atomic processes in nuclear fusion plasmas of the International Thermonuclear Experimental Reactor (ITER) tokamak. Detailed investigation of such processes is essential for modeling and diagnosing future fusion experiments performed on the ITER. In the present work, we studied total and partial electron-impact excitation (EIE) and DR cross-sections of highly charged tungsten ions by using the multiconfiguration Dirac–Fock method. The degrees of linear polarization of the subsequent X-ray emissions from unequally-populated magnetic sub-levels of these ions were estimated. It is found that the degrees of linear polarization of the same transition lines, but populated respectively by the EIE and DR processes, are very different, which makes diagnosis of the formation mechanism of X-ray emissions possible. In addition, with the help of the flexible atomic code on the basis of the relativistic configuration interaction method, DR rate coefficients of highly charged W37+ to W46+ ions are also studied, because of the importance in the ionization equilibrium of tungsten plasmas under running conditions of the ITER.

Radiative rates and electron-impact excitation for then≤ 6 fine-structure levels in H-like ions with 13 ≤Z≤ 42

Context. Many observed emission lines from space missions are due to highly charged H-like ions. An analysis of the lines provides information on the temperature, density, and chemical composition of plasmas. A wide range of atomic parameters, such as energy levels, radiative rates, and excitation rate coefficients are needed to achieve this goal.Aims. In this paper we report on calculations for energy levels, radiative rates, collision strengths, and effective collision strengths for transitions among the 36 lowest levels of the n ≤ 6 configurations of highly charged H-like ions with 13 ≤ Z ≤ 42.Methods. The widely used Flexible Atomic Code (FAC) is adopted for the calculation. Energy levels and radiative rates are calculated within the relativistic configuration-interaction method. Employing relativistic distorted-wave approximation, direct excitation collision strengths are calculated at eleven scattered electron energies E ′ f = 0.001, 0.002, 0.005, 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1.0, and 2.5, where E ′ f is in units of Z 2 rydbergs. Collision strengths at higher energies are estimated by interpolation/extrapolation using relativistic Bethe form. Resonance contributions through the relevant He-like doubly excited n ′l ′n ′′l ′′ configurations with n ′ ≤ 7 and n ′′ ≤ 75 are explicitly taken into account using the independent-process isolated-resonance approximation. Radiation damping effects are taken into account.Results. We present the radiative rates, oscillator strengths, and line strengths for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), magnetic quadrupole (M2), electric octupole (E3), and magnetic octupole (M3) transitions. Assuming a Maxwellian electron velocity distribution, we report effective collision strengths over a wide temperature range between 2 × 103 × Z 2 and 2 × 106 × Z 2 K. We believe that the present results are the most extensive and definitive atomic dataset to date for highly charged H-like ions.

Energy levels and radiative rates for transitions in Cr-like Co IV and Ni V

We report calculations of energy levels and radiative rates (A-values) for transitions in Cr-like Co IV and Ni V. The quasi-relativistic Hartree–Fock (QRHF) code is adopted for calculating the data although grasp (general-purpose relativistic atomic structure package) and flexible atomic code (fac) have also been employed for comparison purposes. No radiative rates are available in the literature to compare with our results, but our calculated energies are in close agreement with those compiled by NIST for a majority of the levels. However, there are discrepancies for a few levels of up to 3%. The A-values are listed for all significantly contributing E1, E2 and M1 transitions, and the corresponding lifetimes reported, although unfortunately no previous theoretical or experimental results exist to compare with our data.

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.

Extreme ultraviolet and x-ray transition wavelengths in Rb XXIV**The authors, Indu Khatri and Arun Goyal, were supported by the U. G. C., India for their Junior Research Fellowship and Man Mohan by the U.G.C. for Basic Science Research Fellowship.

Energy levels, radiative rates, oscillator strengths and line strengths are reported for transitions among the lowest 97 levels of the (1s22s22p6) 3s23p2, 3s23p3d, 3s3p3, 3p4, 3s3p23d, and 3s23d2 configurations of Rb XXIV. A multiconfiguration Dirac–Fock (MCDF) method is adopted for the calculations. Radiative rates, oscillator strengths, and line strengths are provided for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions from the ground level to all 97 levels, although calculations are performed for a much larger number of levels. To achieve the accuracy of the data, comparisons are provided with similar data obtained from the Flexible Atomic Code (FAC) and also with the available theoretical and experimental results. Our energy levels are found to be accurate to better than 1.2%. Wavelengths calculated are found to lie in EUV (extreme ultraviolet) and x-ray regions. Additionally, lifetimes for all 97 levels are obtained for the first time.

Calculation of energy levels, lifetimes and radiative data for La XXIX to Sm XXXIV

We present the most comprehensive atomic data for La XXIX to Sm XXXIV with single electron excitation from M-shell to N-shell and N-shell to higher shells. We have presented energy levels, lifetimes and radiative data using Multi-configuration Dirac–Fock (MCDF) method for the lowest 27 states belonging to the configuration 3d104l (l=0,1,2,3), 3d105l (l=0,1,2,3,4), 3d106l (l=0,1,2,3,4) and 3d94s2. We have also considered relativistic effects by incorporating quantum electrodynamics (QED) and Breit corrections. We have made comparisons of our presented results with available theoretical as well as experimental results and a good agreement is achieved. Further, we have also reported energy levels by performing distorted wave calculations with fully relativistic flexible atomic code (FAC). The calculations match well with MCDF results. Additionally, we have investigated the effect of nuclear charge on transition wavelength and radiative rates for strong Extreme Ultraviolet (EUV) transitions from n=4→4. We believe that our reported data in this work may be useful in various applications of lanthanide ions related to broad area of research such as applied physics, laser physics and astrophysics etc.

Energy levels and radiative transition rates for Ba XLVIII

Energy levels and radiative rates are reported for transitions in F-like Ba XLVIII. Configuration interaction has been included among 27 configurations (generating 431 levels) over a wide energy range up to 618 Rydbergs, and the fully relativistic multi-configurational Dirac–Fock method adopted for the calculations. To assess the accuracy, calculations have also been performed with the flexible atomic code, FAC. Radiative rates, oscillator strengths and line strengths are reported for all electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transitions from the lowest 3 levels, although calculations have been performed for a much larger number of levels. We have made comparisons of our results with existing available results and a good agreement has been achieved. Additionally, lifetimes for all 431 levels are listed.

The theoretical studies on the electron-impact single ionization of Se3+

SynopsisWe have performed fully relatively level-to-level distorted-wave (LLDW) calculations for both direct ionization (DI) and excitation autoionization (EA) of ground state Se3+ ion using the flexible atomic code (FAC). Large EA contributions come from the excitations 4p to nl and 3d to nl. Our calculated total DI+EA cross section have been compared with the recent experimental results. It suggests that the contributions of resonace-excitation double-autoionization process (REDA) to electron impact single ionization of Se3+ at the near threshold are more than 25%.

Tungsten spectroscopy in the EUV range observed at a high-temperature superconducting electron-beam ion trap

We have recorded extreme ultraviolet spectra from ${\mathrm{W}}^{11+}$ to ${\mathrm{W}}^{15+}$ ions using a flat-field spectrometer installed at the Shanghai high-temperature superconducting electron-beam ion trap. The spectra were recorded at beam energies ranging between 200 and 400 eV and showed spectral lines and transition arrays in the 170--260 \AA{} region. The charge states and spectra transitions were identified by comparison with calculations using a detailed relativistic configuration interaction method and collisional-radiative model, both incorporated in the flexible atomic code. Atomic structure calculations showed that the dominant emission arises from $5d$ $\ensuremath{\rightarrow}$ $5p$ and $5p$ $\ensuremath{\rightarrow}$ $5s$ transitions. The work also identified the ground-state configuration of ${W}^{13+}$ as $4{f}^{13}5{s}^{2}$ both theoretically and experimentally.

Dielectronic recombination rate coefficients of initially rubidium-like tungsten

Ab initio calculations of dielectronic recombination (DR) rate coefficients of initially rubidium-like W37+ ions have been performed for the electron temperatures from 1 eV to 5 × 104 eV, by using the Flexible Atomic Code based on the relativistic configuration-interaction method. Special attention has been paid to the partial contributions to total DR rate coefficients as associated with the excitation of individual subshells. A detailed comparison of the calculations shows that the excitation from 4p subshell dominates total DR rate coefficients followed by the excitations from 4s and 4d subshells, while the contribution of excitations from 3l(l = s, p, d) subshells becomes important only at high temperatures. Besides, it is found that the electron excitations associated with △n = 0,1 dominate at low-temperature plasmas, however, the excitations associated with △n ≥ 2 become non-negligible at high-temperature ones.

Collisional radiative average atom code based on a relativistic Screened Hydrogenic Model

A steady-state and time-dependent collisional-radiative ‘‘average-atom’’ (AA) model (ATMED CR) is presented for the calculation of atomic and radiative properties of plasmas for a wide range of laboratory and theoretical conditions: coronal, local thermodynamic equilibrium or nonlocal thermodynamic equilibrium, optically thin or thick plasmas and photoionized plasmas. The radiative and collisional rates are a set of analytical approximations that compare well with more sophisticated quantum treatment of atomic rates that yield fast calculations. The atomic model is based on a new Relativistic Screened Hydrogenic Model (NRSHM) with a set of universal screening constants including nlj-splitting that has been obtained by fitting to a large database of ionization potentials and excitation energies compiled from the National Institute of Standards and Technology (NIST) database and the Flexible Atomic Code (FAC). The model NRSHM has been validated by comparing the results with ionization energies, transition energies and wave functions computed using sophisticated self-consistent codes and experimental data. All the calculations presented in this work were performed using ATMED CR code.

Modeling of the K and L x-ray line structures for molybdenum ions in warm dense Z-pinch plasma

For molybdenum wire implosions on the Z-machine at Sandia National Laboratories the high-resolution measurements of x-ray spectra have been recently published. The K and L x-ray spectra modeled here within the framework of Collisional-Radiative Model using the Flexible Atomic Code package reproduce well the published data to show that such model is a reasonable one.

Modeling non-local thermodynamic equilibrium plasma using the Flexible Atomic Code data

Abstract We present a new code, RCF (“Radiative–Collisional code based on FAC”), which is used to simulate steady-state plasmas under non-local thermodynamic equilibrium condition, especially photoinization-dominated plasmas. RCF takes almost all of the radiative and collisional atomic processes into a rate equation to interpret the plasmas systematically. The Flexible Atomic Code (FAC) supplies all the atomic data needed for RCF, which insures calculating completeness and consistency of atomic data. With four input parameters relating to the radiation source and target plasma, RCF calculates the population of levels and charge states, as well as potential emission spectrum. In a preliminary application, RCF successfully reproduced the results of a photoionization experiment with reliable atomic data. The effects of the most important atomic processes on the charge state distribution are also discussed.

X-ray Measurements of Highly Charged Europium

We present spectroscopic measurements of the M-shell emission of highly charged europium performed at the Livermore SuperEBIT electron beam ion trap facility using the EBIT Calorimeter Spectrometer (ECS). There is significant blending among the emission lines from the different charge states but despite the complexity of the observed spectra we have successfully identified the ten brightest n = 4 → 3 transitions from sodium-like Eu52+ utilizing the Flexible Atomic Code (FAC). We find that the difference between the calculated and measured transition energies for these ten Eu52+ lines does not exceed 3 eV. In fact, for four of the identified lines we find agreement within the measured uncertainties. Additional comparison with semi-empirical transition-energy predictions for sodium-like ions from laser-generated plasmas is included and shows that overall the semi-empirical predicted values for the transition energies are slightly higher than the measured values, while the FAC values that didnt agree with the measured transition energies are almost 1 eV lower than the measured values.

Analysis of density effects in plasmas and their influence on electron-impact cross sections

Density effects in plasmas are analyzed using a Thomas-Fermi approach for free electrons. First, scaling properties are determined for the free-electron potential and density. For hydrogen-like ions, the first two terms of an analytical expansion of this potential as a function of the plasma coupling parameter are obtained. In such ions, from these properties and numerical calculations, a simple analytical fit is proposed for the plasma potential, which holds for any electron density, temperature, and atomic number, at least assuming that Maxwell-Boltzmann statistics is applicable. This allows one to analyze perturbatively the influence of the plasma potential on energies, wave functions, transition rates, and electron-impact collision rates for single-electron ions. Second, plasmas with an arbitrary charge state are considered, using a modified version of the Flexible Atomic Code (FAC) package with a plasma potential based on a Thomas-Fermi approach. Various methods for the collision cross-section calculations are reviewed. The influence of plasma density on these cross sections is analyzed in detail. Moreover, it is demonstrated that, in a given transition, the radiative and collisional-excitation rates are differently affected by the plasma density. Some analytical expressions are proposed for hydrogen-like ions in the limit where the Born or Lotz approximation applies and are compared to the numerical results from the FAC.

Energy levels, transition rates, oscillator strengths and lifetimes in Ne-like, Ni-like, and Cu-like uranium ions

We present the fine-structure energy levels, wavelengths, oscillator strengths, transition energies, and transition rates of optically allowed inner-shell transitions of Ne-, Ni-, and Cu-like uranium ions by using the multiconfiguration Dirac–Fock method with the fully relativistic GRASP2 code (partly improved by us). In order to compare these results, we have performed other independent calculations with a fully relativistic Flexible Atomic Code (FAC). We have determined extensive configuration interaction wavefunctions to calculate the level energies of the inner-shell excited states of these three uranium ionic states. Overall, our calculated energy levels, wavelengths, transition rates, and oscillator strengths within the levels of selected configurations show better agreement with the available experimental and other theoretical results. Furthermore, we report radiative lifetimes of all the excited states of these three uranium ions. We also present many unpublished data about energy values, wavelengths, transitions rates, and oscillator strengths for inner-shell transitions. We believe that our calculated inner shell transition energies are of interest for the analysis of uranium x-ray spectra.