Flexible Atomic Code Research Articles

Energy levels, radiative rates, and electron impact excitation rates for transitions in Li-like ions with [formula omitted

We report calculations of energy levels, radiative rates, and electron impact excitation rates for transitions in Li-like ions with 12≤Z≤20. The grasp (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative rates, while for determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code is used. Oscillator strengths, radiative rates, and line strengths are reported for all E1, E2, M1, and M2 transitions among the lowest 24 levels of the Li-like ions considered. Collision strengths have been averaged over a Maxwellian velocity distribution, and the effective collision strengths obtained are reported over a wide temperature range up to 107.4 K. Additionally, lifetimes are also listed for all calculated levels of the ions. Finally, extensive comparisons are made with results available in the literature, as well as with our parallel calculations for all parameters with the Flexible Atomic Code, in order to assess the accuracy of the reported results.

Energy levels, radiative rates and electron impact excitation rates for transitions in He-like Kr XXXV

We report calculations of energy levels, radiative rates and electron impact excitation cross sections and rates for transitions in He-like Kr XXXV. The grasp (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative rates. For determining the collision strengths and subsequently the excitation rates, the Dirac Atomic R-matrix Code (darc) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 49 levels. Additionally, theoretical lifetimes are listed for all 49 levels. Collision strengths are averaged over a Maxwellian velocity distribution and the effective collision strengths obtained listed over a wide temperature range up to 108.1 K. Comparisons are made with similar data obtained with the Flexible Atomic Code (fac) to assess the accuracy of the results and to highlight the importance of resonances, included in calculations with darc, in the determination of effective collision strengths. Differences between the collision strengths from darc and fac, particularly for forbidden transitions, are also discussed. Finally, discrepancies between the present results of effective collision strengths from the darc code and earlier semi-relativistic R-matrix data are noted over a wide range of electron temperatures for many transitions of Kr XXXV.

Theoretical electron-impact-ionization cross section for Fe11+forming Fe12+

We have calculated cross sections for electron impact ionization (EII) of P-like Fe${}^{11+}$ forming Si-like Fe${}^{12+}$. We have used the flexible atomic code (FAC) and a distorted-wave (DW) approximation. Particular attention has been paid to the ionization through the $3l\ensuremath{\rightarrow}n{l}^{\ensuremath{'}}$ and $2l\ensuremath{\rightarrow}n{l}^{\ensuremath{'}}$ excitation autoionization (EA) channels. We compare our results to previously published FAC DW results and recent experimental results. We find that the previous discrepancy between theory and experiment at the EII threshold can be accounted for by the $3l\ensuremath{\rightarrow}n{l}^{\ensuremath{'}}$ EA channels which were not included in the earlier calculations. At higher energies the discrepancy previously seen between theory and experiment for the magnitude of the $2l\ensuremath{\rightarrow}n{l}^{\ensuremath{'}}\phantom{\rule{4pt}{0ex}}(n\ensuremath{\ge}4)$ EA remains, though the difference has been reduced by our newer results. The resulting Maxwellian rate coefficient derived from our calculations lies within 11$%$ of the experimentally derived rate coefficient in the temperature range where Fe${}^{11+}$ forms in collisional ionization equilibrium.

Calculation and evaluation of energy levels and radiative rates for [formula omitted] and [formula omitted] transitions in Cu XX

Energy levels, oscillator strengths, and radiative rates have been calculated for 2s22p6–2s2p6np and 2s22p6–2s22p5nd transitions with 4≤n≤20 in Cu XX ions. In the calculations, the Flexible Atomic Code has been used, and systematic analysis and evaluation of the accuracy of the calculated results for the two types of transitions are also given with different indicators. It is shown that the results for the transitions with a 2s hole are greatly improved by using the present method comparing to those from RELAC code. Furthermore, our results show that the energy levels of the 2s2p6(n+1)l and 2s22p5(n+2)l configurations closely interact with those of the 2s2p6np series and it is essential to include the 2s22p5(n+1)l configurations in the calculations for the 2s22p5nd series.

Atomic data and spectral line intensities for Ni XV

Electron impact collision strengths, energy levels, oscillator strengths, and spontaneous radiative decay rates are calculated for Ni XV. We include in the calculations the 9 lowest configurations, corresponding to 126 fine structure levels: 3s2 3p2, 3s3p3, 3s2 3p3d, 3p4, 3s3p2 3d, and 3s2 3p4l with l=,s,p,d,f. Collision strengths are calculated at five incident energies for all transitions: 7.8, 18.5, 33.5, 53.5, and 80.2 Ry above the threshold of each transition. An additional energy, very close to the transition threshold, has been added, whose value is between 0.004 and 0.28 Ry depending on the levels involved. Calculations have been carried out using the Flexible Atomic Code and the distorted-wave approximation. Excitation rate coefficients are calculated as a function of electron temperature by assuming a Maxwellian electron velocity distribution. Using the excitation rate coefficients and the radiative transition rates calculated in the present work, statistical equilibrium equations for level populations are solved at electron densities covering the 108–1014 cm−3 range and at an electron temperature of logTe(K)=6.4, corresponding to the maximum abundance of Ni XV. Spectral line intensities are calculated, and their diagnostic relevance is discussed. This dataset will be made available in the next version of the CHIANTI database.

Energy levels, radiative rates and electron impact excitation rates for transitions in He-like Ti XXI, V XXII, Cr XXIII and Mn XXIV

We report calculations of energy levels, radiative rates and electron impact excitation cross sections and rates for transitions in He-like Ti XXI, V XXII, Cr XXIII and Mn XXIV. grasp (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative rates. For determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code (darc) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 49 levels of each ion. Additionally, theoretical lifetimes are listed for all the 49 levels of the above four ions. Collision strengths are averaged over a Maxwellian velocity distribution and the effective collision strengths obtained listed over a wide temperature range up to 107.5 K. Comparisons are made with similar data obtained using the flexible atomic code (fac) to highlight the importance of resonances, included in calculations with darc, in the determination of effective collision strengths. Discrepancies between the collision strengths from darc and fac, in particular for forbidden transitions, are also discussed. Finally, discrepancies between the present results for effective collision strengths with the darc code and earlier semi-relativistic R-matrix data are noted over a wide range of electron temperatures for many transitions in all ions.

X-ray spectra simulation of Li-like nickel L-shell Ions

The X-ray emission spectra of nickel plasma were simulated under the collisional radiative model (CRM) by using the flexible atomic code (FAC). The dynamical processes including collisional excitation (CE), radiative recombination (RR), dielectronic recombination (DR), collisional ionization (CI) and resonance excitation were considered in the model, and the rate coefficients of DR, RR as well as CI were consistent with previous results within 15%. It was found that the contributions to spectra from cascades and indirect processes could not be ignored. The intensities of spectral lines for lithium-like nickel L-shell ions are sensitive to the electron temperature. The good agreement between present spectral peaks and earlier observed results can be taken as a measure of the accuracy of the present work.

Energy shifts of Kα,β,γ X-ray satellites for atoms with 13 ⩽ Z ⩽ 90: A systematic calculation and a new analytical description

The transition energy shifts of the Kα, Kβ and Kγ X-rays resulted from addition vacancies in L-shell for atoms with 13⩽Z⩽90 have been calculated systematically, by using the Flexible Atomic Code (FAC), in which the Breit interaction, QED corrections and nuclear finite mass effects are also considered. It is shown by means of concrete figures that the overall agreement among the present results, theoretical results of other authors as well as a large body of measured ones was excellent. Contrary to other discussions, we found that the energy shifts of the Kα and Kβ satellites did not varies absolutely linearly with Z, the contributions of the Z2 term cannot be neglected, and the energy differences between neighboring L satellites were not equal. Three simple empirical formulae for estimating the energy shifts of the Kα, Kβ and Kγ X-ray satellites for any atom with any number of L-shell vacancies were put forward. They will be useful in qualitative interpretation of various K X-ray spectra and better understanding of the collision processes.

Comparative semi-empirical and ab initio atomic structure calculations in Yb-like tungsten W4 +

In this paper, we report on extensive calculations of radiative data in Yb-like tungsten ion using several independent atomic structure methods, i.e. the relativistic Hartree–Fock approach, the flexible atomic code and the multiconfiguration Dirac–Fock method. This multi-platform approach allowed us to check the consistency of our results. Advantages and shortcomings of semi-empirical and ab initio methods for atomic structure calculations in such a complex heavy ion are also discussed in detail. A new set of transition probabilities and oscillator strengths is reported for electric dipole lines together with magnetic dipole and electric quadrupole lines in this ion of interest for fusion plasma diagnostics.

Dielectronic recombination of Pd-like gadolinium

As research and development of extreme ultraviolet lithography (EUVL) sources at 6.7 nm (which will be based on emission from ionized gadolinium) has already begun, reliable atomic data are required in order to determine the optimum plasma conditions. However, the complexity of the atomic structure means that ab initio level-resolved dielectronic recombination (DR) calculations are currently unavailable for the ions of interest. Here we report the first detailed calculation of the DR rate coefficients for the ground state and first excited states of Pd-like gadolinium. Energy levels, radiative transition probabilities, and autoionization rates of Ag-like gadolinium for [Kr]4${d}^{9}$4$fnl$, [Kr]4${p}^{5}$4${d}^{10}$4$fnl$, [Kr]4${d}^{9}$5$l$\ensuremath{'}$nl$, and [Kr]4${d}^{9}$6$l$\ensuremath{'}$nl$ ($n$ \ensuremath{\leqslant} 18) complexes were calculated using the flexible atomic code (FAC). It was found that inclusion of 4${p}^{5}$4${d}^{10}$4$fnl$ configurations has significant influence on the total DR rate coefficient. The DR rate coefficients obtained here are compared with radiative recombination and three-body recombination coeffcients. The results show that the DR rate coefficient is almost an order of magnitude higher than the coefficients for the other two recombination processes combined at plasma electron temperatures around 110 eV, which suggests that the DR process should be included in theoretical modeling for Pd-like gadolinium in EUVL source plasmas.

Energy levels, radiative rates and electron impact excitation rates for transitions in He-like Mg XI, Al XII, P XIV and S XV

We report calculations of energy levels, radiative rates and electron impact excitation cross sections and rates for transitions in He-like Mg XI, Al XII, P XIV and S XV. The GRASP (general-purpose relativistic atomic structure package) code is adopted to calculate energy levels and radiative rates. To determine the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code (DARC) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 49 levels of each ion. Collision strengths are averaged over a Maxwellian velocity distribution and the effective collision strengths obtained are listed over a wide temperature range up to 107.2 K. Comparisons are made with similar data obtained from the flexible atomic code (FAC) to highlight the importance of resonances, included in calculations with DARC, in the determination of effective collision strengths. Discrepancies between the collision strengths from DARC and FAC, particularly for forbidden transitions, are also discussed. Additionally, theoretical lifetimes are listed for all the 49 levels of the above four ions.

Energy levels, radiative rates and electron impact excitation rates for transitions in He-like Cl XVI, K XVIII, Ca XIX and Sc XX

We report calculations of energy levels, radiative rates and electron impact excitation cross sections and rates for transitions in He-like Cl XVI, K XVIII, Ca XIX and Sc XX. The GRASP (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative rates. To determine the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code (DARC) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 49 levels of each ion. Collision strengths are averaged over a Maxwellian velocity distribution and the effective collision strengths obtained listed over a wide temperature range up to 107.4 K. Comparisons are made with similar data obtained from the flexible atomic code (FAC) to highlight the importance of resonances, included in calculations with DARC, in the determination of effective collision strengths. Discrepancies between the collision strengths from DARC and FAC, particularly for forbidden transitions, are also discussed. Additionally, theoretical lifetimes are listed for all the 49 levels of the above four ions.

Theoretical study on 2s2p6np Rydberg states of Cu19+ ion

We report on the calculations of transition wavelengths and weighted oscillator strengths for 2s22p6−2s2p6np (4 ≤ n ≤ 20) electric dipole (E1) transitions of Cu19+ ion. The flexible atomic code (FAC) has been adopted for the calculations. Comparisons are made with the experimental data available, showing that the present results for 4 ≤ n ≤ 6 are more accurate than the previous calculated values. Furthermore, combining the quantum defect theory (QDT) with the transition energies of 2s22p6−2s2p6np, the quantum defects for 2s2p6np Rydberg series of Cu19+ ion are determined. In addition, the energies of any highly excited states (n > 20) for this series can be reliably predicted using the QDT and the given quantum defects. The ionization energies for Cu19+ and Cu20+ ions are also calculated and they excellently accord with previous experimental and calculated values.

The nonlocal thermal equilibrium simulation of Z-pinch Al plasma radiation

In this article, the atomic structure and processes for Al are calculated in details by using the flexible atomic code. With these atomic parameters, the rate equations are established and resolved in order to obtain the level populations. The X ray radiation from Z-pinch Al plasma is then calculated. The experimental spectra are identified in details according to our theoretical results.

Collisional-Radiative Modeling of W<sup>27</sup><sup>+</sup>

A detailed collisional radiative model of W27+ ions was constructed based on the atomic data calculated by relativistic atomic properties software Flexible Atomic Code. The strong electric dipole (E1) transitions mainly comes from the 4 f → 4d transition in W27+ ions with wavelength falls into VUV region (4.6 5.1 nm), while the wavelength of magnetic dipole (M1) transition among the fine structures of the first excited states falls into the visible optical region. Synthetic spectra in both regions are given theoretically with plasma condition in EBIT for experiment reference. Finally, the dependence of the intensity ratio on the electron density is provided as a potential diagnostic tool of Maxwellian plasmas.

Fe IX CALCULATIONS FOR THE SOLAR DYNAMICS OBSERVATORY

New calculations of the energy levels, radiative transition rates and collisional excitation rates of \ion{Fe}{ix} have been carried out using the Flexible Atomic Code, paying close attention to experimentally identified levels and extending existing calculations to higher energy levels. For lower levels, R-matrix collisional excitation rates from earlier work have been used. Significant emission is predicted by these calculations in the 5f-3d transitions, which will impact analysis of SDO AIA observations using the 94\AA\ filter.

Transition wavelengths and unresolved transition array statistics of ions with Z = 72–89

Potential extreme ultraviolet and soft x-ray radiation sources have been identified, using the flexible atomic code (FAC), as emission peaks arising from the 4d–4f and 4p–4d transitions in Pd-like to Rb-like ions of hafnium through actinium. The effects of configuration interaction are investigated and for increasing nuclear charge, these strong emitters are seen to separate and move to shorter wavelengths. Each source is characterized using the unresolved transition array model. They are proposed to complement the currently used nitrogen and argon sources in the ‘water window’, and as possible successors to tin in next-generation lithography.

Theoretical investigation of dielectronic recombination of Sn12+ions

Theoretical calculations have been made for the dielectronic recombination (DR) rate coefficients of Sn${}^{12+}$ ion using a relativistic flexible atomic code with configuration interaction. Comparison of the rate coefficients for $4s$, $4p$, and $4d$ subshell excitation shows that while the $4p$ subshell excitation dominates over the whole temperature region, $4d$ subshell excitation at low temperature and $4s$ subshell excitation at high temperature cannot be neglected. In order to facilitate simple applications, the calculated DR rate coefficients are fitted to an empirical formula. The total DR rate coefficient is greater than either the radiative recombination or three-body recombination coefficients for electron temperatures greater than 1 eV. Therefore, DR can strongly influence the ionization balance of laser-produced tin plasmas.

Spectra simulation of the argon plasma

In this work, a simulation calculation scheme based on a collisional radiation model and employing detailed energy levels was developed under the framework of corona approximation for low-density plasmas. Atomic data such as energy levels, radiative transition rates, Auger rates, collision excitation and ionization cross sections needed for the simulation were calculated by using the Flexible Atomic Code. In this work, the emission spectra of the first and second excited configurations of He-like Ar ions and their dielectronic and inner shell excited satellites from Li-like argon ions were studied for a low-density plasma, taking into account the influence of all satellite electrons of principal quantum number n<10. A comparison with the result of tokamak experiments under similar plasma conditions was made. Good agreement was seen for these spectra; however, the charge state balance between the He-like and Li-like Ar ions was not well modeled. A discussion of this deviation is presented.

X-ray amplification dynamics at ∼2.8 Å in intense laser irradiated xenon clusters: multiple hole dynamics

In a series of experiments (Borisov et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 105602, and references 1 through 7 cited in this paper), the amplification of 2.71–2.88 Å x-rays was observed, gain coefficients between 27 and 104 cm−1 were measured, and a number of conjectures were made concerning the ionization stages that were involved in the x-ray amplification. It was conjectured, for example, that x-ray emissions from hole states in Cl-, K-, Ca-, and Ti-like xenon were being amplified. In this paper, our earlier xenon gain model (Petrova et al 2010 J. Phys. B: At. Mol. Opt. Phys. 43 025601) is extended to include single- and double-hole state production within the Fe-like ionization stage in addition to single-hole state production within the Co-like ionization stage in order to assess these conjectures. The gain model, based on flexible atomic code generated data (Gu 2008 Can. J. Phys. 86 675), includes Co-like and Fe-like hole-state generation in xenon through photoionization of 2s and 2p electrons. The hole-state dynamics is self-consistently coupled to an extensive collisional-radiative dynamics of the Ni-, Co-, and Fe-like ionization stages of xenon. In addition, the model includes tunnelling ionization rates that confirm the initial condition assumptions that were made in our earlier paper, and they are needed to support the interpretations of the measured broadband x-ray data. With the use of tunnelling ionization rates, we demonstrate how all of the N-shell, n = 4, electrons are striped from a xenon atom in less than a femtosecond at laser intensities larger than 1019 W cm−2. Our calculations also show that, under these initial conditions and with sufficiently high pumping rates (⩾1014 s−1), a range of gains larger than 50 cm−1 are achievable under select conditions from both Co- and Fe-like xenon single hole radiative decays, in conformity with experimental observations. However, the calculated gain coefficients are sensitive to the laser intensity, laser pulse risetime, the magnitude of the hole-state pumping rates, ion density, and electron and ion heating rates, and, in general, Co-like holes are found to have much higher gains than Fe-like hole states. These model calculations are also capable of producing gains from the double-hole states in Fe-like xenon, but they are much smaller than those generated in the Fe-like single-hole states in the cases included in this paper. Thus, our model calculations do not support the experimental data interpretation in which the measured gains were attributed to double holes in much higher ionization stages of xenon (Xe32+, Xe34+, Xe35+, and Xe37+). Our calculations suggest that these ionization stages can be reached either early in time at much higher laser intensities (in excess of 1.5 × 1020 W cm−2 for a 248 nm, ∼230 fs pulse) or later in time, and only because of tunnelling ionization. In this latter case, however, the measured gains cannot be achieved since cluster densities have fallen by several orders of magnitude from their initial values and ion population have been spread over a much wider range of states.