Energy levels and radiative rates for transitions in Ti X

We report calculations of energy levels, radiative rates, oscillator strengths and line strengths for transitions among the lowest 345 levels of Ti X. These include 146 levels of the n 3 configurations and 86 of 3s ²4ℓ, 3s²5ℓ and 3s3p4ℓ, plus some of the 3s²6ℓ, 3p²4ℓ and 3s3p5ℓ levels. The general-purpose relativistic atomic structure package and flexible atomic code are 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 among the 345 levels, although calculations have been performed for a much larger number of levels. Comparisons are made with existing results and the accuracy of the data is assessed. Additionally, lifetimes for all 345 levels are listed. Extensive comparisons of lifetimes are made for the lowest 40 levels, for which discrepancies with recent theoretical work are up to 30%. Discrepancies in lifetimes are even larger, up to a factor of four, for higher excited levels. Furthermore, the effect of large configuration interaction (CI) is found to be insignificant for both the energies and lifetimes for the lowest 40 levels of Ti X which belong to the 3s²3p, 3s3p², 3s²3d, 3p³ and 3s3p3d configurations. However, the contribution of CI is more appreciable for the energy levels and radiative rates among higher excited levels. Our listed energy levels are estimated to be accurate to better than 1% (within 0.1 Ryd), whereas results for other parameters are probably accurate to better than 20%. © 2013 The Royal Swedish Academy of Sciences.

Energy levels, radiative rates and electron impact excitation rates for transitions in He-like Fe XXV, Co XXVI, Ni XXVII, Cu XXVIII and Zn XXIX

We report calculations of energy levels, radiative rates and electron impact excitation cross sections and rates for transitions in He-like Fe XXV, Co XXVI, Ni XXVII, Cu XXVIII and Zn XXIX. 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 of each ion. Additionally, theoretical lifetimes are listed for all 49 levels of the above five ions. Collision strengths are averaged over a Maxwellian velocity distribution and the effective collision strengths obtained listed over a wide temperature range up to 10 ^7.7 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, for some transitions, are also discussed. Finally, discrepancies between the present results of 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. 

Energy levels, radiative rates and electron impact excitation rates for transitions in He-like Ga XXX, Ge XXXI, As XXXII, Se XXXIII and Br XXXIV

We report calculations of energy levels, radiative rates and electron impact excitation cross sections and rates for transitions in He-like Ga XXX, Ge XXXI, As XXXII, Se XXXIII and Br XXXIV. 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 of each ion. Additionally, theoretical lifetimes are provided for all 49 levels of the above five ions. Collision strengths are averaged over a Maxwellian velocity distribution and the effective collision strengths obtained listed over a wide temperature range up to 10⁸ 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, particularly for some 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. © 2013 The Royal Swedish Academy of Sciences.

Energy levels, radiative rates, and electron impact excitation rates for transitions in Li-like ions with 21≤Z≤28

We report calculations of energy levels, radiative rates, and electron impact excitation rates for transitions in Li-like ions with 21≤Z≤28. The 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 listed 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 given over a wide temperature range up to 10^7.8 K. Additionally, lifetimes are listed for all calculated levels of these ions. Finally, extensive comparisons are made with results available in the literature, as well as with our analogous calculations for all parameters with the Flexible Atomic Code, in order to assess the accuracy of the results.

Energy levels, radiative rates and electron impact excitation rates for transitions in Be-like Ti XIX

We report calculations of energy levels, radiative rates and electron impact excitation cross sections and rates for transitions in Be-like Ti XIX. The 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 98 levels of the n≤ 4 configurations. Additionally, theoretical lifetimes are listed for all 98 levels. Collision strengths are averaged over a Maxwellian velocity distribution and the effective collision strengths obtained listed over a wide temperature range up to 10 ^7.7K. 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. 

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 10 ^8.1K. 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 KrXXXV. 

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 10 ^7.5K. 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. 

Energy levels, radiative rates, and electron impact excitation rates for transitions in Li-like ions with 12≤Z≤20

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 10^7.4 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 C III

We report energy levels, radiative rates (A-values) and lifetimes for the astrophysically important Be-like ion C III. For the calculations, 166 levels belonging to the n ≤ 5 configurations are considered and the GRASP (General-purpose Relativistic Atomic Structure Package) is adopted. Einstein A-coefficients are provided for all E1, E2, M1 and M2 transitions, while lifetimes are compared with available measurements as well as theoretical results, and no large discrepancies noted. Our energy levels are assessed to be accurate to better than 1 per cent for a majority of levels, and A-values to better than 20 per cent for most transitions. Collision strengths are also calculated, for which the Dirac Atomic R-matrix Code (DARC) is used. A wide energy range, up to 21 Ryd, is considered and resonances resolved in a fine energy mesh in the thresholds region. The collision strengths are subsequently averaged over a Maxwellian velocity distribution to determine effective collision strengths up to a temperature of 8.0 ×10[5]K, sufficient for most astrophysical applications. Our data are compared with the recent R-matrix calculations of Fernández-Menchero et al., and significant differences (up to over an order of magnitude) are noted for several transitions over the complete temperature range of the results.

Electron-impact excitation of Fe2: a comparison of intermediate coupling frame transformation, Breit-Pauli and Dirac R-matrix calculations

Modeling the spectral emission of low-charge iron group ions enables the diagnostic determination of the local physical conditions of many cool plasma environments such as those found in H II regions, planetary nebulae, active galactic nuclei etc. Electron-impact excitation drives the population of the emitting levels and, hence, their emissivities. By carrying-out Breit-Pauli and intermediate coupling frame transformation (ICFT) R-matrix calculations for the electron-impact excitation of Fe$^{2+}$ which both use the exact same atomic structure and the same close-coupling expansion, we demonstrate the validity of the application of the powerful ICFT method to low-charge iron group ions. This is in contradiction to the finding of Bautista et al. [Ap.J.Lett, 718, L189, (2010)] who carried-out ICFT and Dirac R-matrix calculations for the same ion. We discuss possible reasons.

An R-matrix approach for plasma modelling and the interpretation of astrophysical observation

Over the last decade an Auburn-Rollins-Strathclyde consortium has developed several suites of parallel R-matrix codes [1, 2, 3] that can meet the fundamental data needs required for the interpretation of astrophysical observation and/or plasma experiments. Traditionally our collisional work on light fusion-related atoms has been focused towards spectroscopy and impurity transport for magnetically confined fusion devices. Our approach has been to provide a comprehensive data set for the excitation/ionization for every ion stage of a particular element. As we progress towards a burning fusion plasma, there is a demand for the collisional processes involving tungsten, which has required a revitalization of the relativistic R-matrix approach. The implementation of these codes on massively parallel supercomputers has facilitated the progression to models involving thousands of levels in the close-coupling expansion required by the open d and f sub-shell systems of mid Z tungsten. This work also complements the electron-impact excitation of Fe-Peak elements required by astrophysics, in particular the near neutral species, which offer similar atomic structure challenges. Although electron-impact excitation work is our primary focus in terms of fusion application, the single photon photoionisation codes are also being developed in tandem, and benefit greatly from this ongoing work.

Non-equilibrium modeling of the FE XVII 3C/3D Line Ratio in an Intense X-ray Free-electron Laser Excited Plasma

Recent measurements using an X-ray Free Electron Laser (XFEL) and an Electron Beam Ion Trap at the Linac Coherent Light Source facility highlighted large discrepancies between the observed and theoretical values for the Fe XVII 3C/3D line intensity ratio. This result raised the question of whether the theoretical oscillator strengths may be significantly in error, due to insufficiencies in the atomic structure calculations. We present time-dependent spectral modeling of this experiment and show that non-equilibrium effects can dramatically reduce the predicted 3C/3D line intensity ratio, compared with that obtained by simply taking the ratio of oscillator strengths. Once these non-equilibrium effects are accounted for, the measured line intensity ratio can be used to determine a revised value for the 3C/3D oscillator strength ratio, giving a range from 3.0 to 3.5. We also provide a framework to narrow this range further, if more precise information about the pulse parameters can be determined. We discuss the implications of the new results for the use of Fe XVII spectral features as astrophysical diagnostics and investigate the importance of time-dependent effects in interpreting XFEL-excited plasmas.

Dielectronic recombination of W 35 +

Accurate data for dielectronic recombination (DR) of the ions of tungsten are of significant interest in the modelling of tungsten impurity transport and radiative power loss in current tokamaks and in ITER. However, the complexity of the atomic structure for many of these ions makes level-resolved DR calculations untenable on currently available computers, especially for open d- and f-subshell ions. The majority of DR data presently available for ITER modelling are based on an average-atom approximation. To improve upon these baseline calculations, we investigate the use of the configuration-average distorted-wave (CADW) method to calculate DR rate coefficients for complex open d-shell systems. The aim is to produce rate coefficients that are sufficiently accurate in terms of modelling, yet greatly reduced in term of computational complexity compared to level-resolved calculations. In this paper, we consider the DR of W 35 + . Initially, we carry out several large-scale level-resolved calculations for the DR associated with the 4d → 4f and 4p → 4d excitations in this ion, using both the level-resolved distorted-wave and Dirac R -matrix methods. These calculations allow us to test the validity of the CADW approach on these same excitations by comparing cross sections and rate coefficients. These comparisons demonstrate that the CADW method is relatively accurate in relation to these level-resolved methods for the temperature range for which W 35 + should exist in a collisionally ionized plasma. We then present results for CADW rate coefficients for both Δ n = 0 and Δ n = 1 excitations for this ion. This study indicates that it is now feasible to generate a much improved comprehensive set of DR data for the entire tungsten isonuclear sequence.

Collisional-radiative calculations of He line emission in low-temperature plasmas

We present spectral modeling results for neutral helium. Our underlying atomic data contains radiative transition rates that are generated from atomic structure calculations and electron-impact excitation rates, that are determined from both the standard R-matrix method and the R-matrix with pseudostates RMPS method. In this paper, we focus on transitions of particular importance to diagnostic line ratios. For example, our calculated rate coefficient for the electron-impact transition 1s3s 1S→1s3p 1P, which has a pronounced effect on the 728.1 nm diagnostic spectral line, is found to be in good agreement with previous experimental mea- surements. We also consider transitions from the 1s2 1S ground and 1s2s 3S terms to terms of the n=4 shell. They are found to be affected significantly by coupling of the bound states to the target continuum continuum coupling, which is included in our RMPS calculation, but not in our standard R-matrix calculation. We perform collisional-radiative calculations to determine spectral line intensity ratios for three ratios of particular interest, namely the 504.8 nm/471.3 nm, 492.2 nm/471.3 nm, and 492.2 nm/504.8 nm line ratios. Comparing our results determined from the RMPS excitation rates with those from the standard R-matrix excitation rates, we find that continuum coupling affects the rate coefficients significantly, leading to different values for all three line ratios. We also compare our modeling results with spectral measurements taken recently on the Auburn Helicon plasma device, finding that the ground and metastable populations are not in equilibrium, and that the experimental measurements are more consistent with the 1s2s 3S metastable term populations being short lived in the plasma.

The effects of radiative cascades on the x-ray diagnostic lines of Fe16+

We present complete collisional-radiative modelling results for the soft x-ray emission lines of Fe16+ in the 15 Å–17 Å range. These lines have been the subject of much controversy in the astrophysical and laboratory plasma community. Radiative transition rates are generated from fully relativistic atomic structure calculations. Electron-impact excitation cross sections are determined using a fully relativistic R-matrix method employing 139 coupled atomic levels through n = 5. We find that, in all cases, using a simple ratio of the collisional rate coefficient times a radiative branching factor is not sufficient to model the widely used diagnostic line ratios. One has to include the effects of collisional-radiative cascades in a population model to achieve accurate line ratios. Our line ratio results agree well with several previous calculations and reasonably well with tokamak experimental measurements, assuming a Maxwellian electron-energy distribution. Our modelling results for four EBIT line ratios, assuming a narrow Gaussian electron-energy distribution, are in generally poor agreement with all four NIST measurements but are in better agreement with the two LLNL measurements. These results suggest the need for an investigation of the theoretical polarization calculations that are required to interpret the EBIT line ratio measurements.