Intermediate Coupling Frame Transformation R-matrix Research Articles

R-matrix electron-impact excitation data for the C-like isoelectronic sequence

SynopsisEmission and absorption features from C-like ions are served as temperature and density diagnostics of astrophysical plasmas. R-matrix electron-impact excitation data for C-like ions in literature cover merely a handful of ions. Here we present a systematic intermediate coupling frame transformation R-matrix calculations for C-like ions from N II to Kr XXXI. The effective collision strengths cover a wide range of temperature. Our results are compared with archival databases and literature results.

Electron impact excitation of N-like ions from the ICFT R-matrix calculation

We carried out intermediate coupling frame transformation (ICFT) R-matrix calculations on N-like ions (11≤Z≤20), which included a total of 272 fine structure levels in both the configuration interaction (CI) and close-coupling (CC) collision expansions. Comparisons with previous theoretical values were made in terms of energy levels, radiative transition rates, and oscillator strengths. The effective collision strengths (ϒ) were estimated in the temperature range of 104–107 K. An excellent agreement with available computations was reached for dipole-allowed transitions, while differences in ϒ were found for non-dipole allowed and forbidden transitions. This discrepancy is mainly attributed to the difference in CC expansions. Our calculations provide a good supplement to the electron impact excitation data on N-like ions.

Importance of the completeness of the configuration interaction and close coupling expansions in R-matrix calculations for highly charged ions: electron-impact excitation of Fe20+

We have carried out two intermediate coupling frame transformation (ICFT) R-matrix calculations for the electron-impact excitation of -like , both of which use the same expansions for their configuration interaction (CI) and close-coupling (CC) representations. The first expansion arises from the configurations , , with n = 3, 4, for , which give rise to 564 CI/CC levels. The second adds configurations , for , which give rise to 590 CI/CC levels in total. Comparison of oscillator strengths and effective collision strengths from these two calculations demonstrates the lack of convergence in data for n = 4 from the smaller one. Comparison of results for the 564 CI/CC level calculation with an earlier ICFT R-matrix calculation which used the exact same CI expansion but truncated the CC expansion to only 200 levels demonstrates the lack of convergence of the earlier data, particularly for n = 3 levels. Also, we find that the results of our 590 CC R-matrix calculation are significantly and systematically larger than those of an earlier comparable DW-plus-resonances calculation. Thus, it is important still to take note of the (lack of) convergence in both atomic structural and collisional data, even in such a highly charged ion as Fe20+, and to treat resonances non-perturbatively. This is of particular importance for Fe ions given their importance in the spectroscopic diagnostic modelling of astrophysical plasmas.

On the validity of the ICFT R-matrix method: Fe xiv

Recently, Aggarwal & Keenan published a Dirac R-matrix (darc) calculation for the electron-impact excitation of Fe xiv. A 136-level configuration-interaction/close-coupling (CI/CC) expansion was adopted. Comparisons with earlier calculations, obtained by Liang et al. with the intermediate coupling frame transformation (ICFT) R-matrix method, showed significant discrepancies. One of the main differences was that the Liang et al. effective collision strengths were consistently larger. Aggarwal & Keenan suggested various possible causes for the differences. We discuss them in detail here. We have carried out an ICFT R-matrix calculation with the same 136-level CI/CC expansion adopted by Aggarwal & Keenan, and compared the results with theirs and with those of Liang et al., which employed a much larger CI/CC expansion. We find that the main differences arise because of the different CC and CI expansions, and not because of the use of the ICFT method, as suggested by Aggarwal & Keenan. The significant increase in the effective collision strengths obtained by Liang et al. is mainly due to the extra resonances that are present because of the larger target expansion.

Validity of the ICFT R-matrix method: Be-like Al 9+ a case study

We have carried out 98-level configuration-interaction/close-coupling (CI/CC) intermediate coupling frame transformation (ICFT) and Breit–Pauli R-matrix calculations for the electron-impact excitation of Be-like Al 9+. The close agreement that we find between the two sets of effective collision strengths demonstrates the continued robustness of the ICFT method. On the other hand, a comparison of this data with previous 238-level CI/CC ICFT effective collision strengths shows that the results for excitation up to n = 4 levels are systematically and increasingly underestimated over a wide range of temperatures by R-matrix calculations whose CC expansion extends only to n = 4 (98-levels). Thus, we find to be false a recent conjecture that the ICFT approach may not be completely robust. The conjecture was based upon a comparison of 98-level CI/CC Dirac R-matrix effective collision strengths for Al 9+ with those from the 238-level CI/CC ICFT R-matrix calculations. The disagreement found recently is due to a lack of convergence of the CC expansion in the 98-level CI/CC Dirac work. The earlier 238-level CI/CC ICFT work has a superior target to the 98-level CI/CC Dirac one and provides more accurate atomic data. Similar considerations need to be made for other Be-like ions and for other sequences.

Resolution of the forbidden (J= 0 → 0) excitation puzzle in Mg-like ions

We have carried-out 98-level configuration-interaction / close-coupling (CI/CC) intermediate coupling frame transformation (ICFT) and Breit-Pauli R-matrix calculations for the electron-impact excitation of Be-like Al$^{9+}$. The close agreement that we find between the two sets of effective collision strengths demonstrates the continued robustness of the ICFT method. On the other hand, a comparison of this data with previous 238-level CI/CC ICFT effective collision strengths shows that the results for excitation up to n=4 levels are systematically and increasingly underestimated over a wide range of temperatures by R-matrix calculations whose close-coupling expansion extends only to n=4 (98-levels). Thus, we find to be false a recent conjecture that the ICFT approach may not be completely robust. The conjecture was based upon a comparison of 98-level CI/CC Dirac R-matrix effective collision strengths for Al$^{9+}$ with those from the 238-level CI/CC ICFT R-matrix calculations. The disagreement found recently is due to a lack of convergence of the close-coupling expansion in the 98-level CI/CC Dirac work. The earlier 238-level CI/CC ICFT work has a superior target to the 98-level CI/CC Dirac one and provides more accurate atomic data. Similar considerations need to be made for other Be-like ions and for other sequences.

R-matrix electron-impact excitation data for the Mg-like iso-electronic sequence

Aims. Emission lines from ions in the Mg-like iso-electronic sequence can be used as reliable diagnostics of temperature and density of astrophysical and fusion plasmas over a wide range of parameters. Data in the literature are quite lacking, there are no calculations for many of the ions in the sequence. Methods. We have carried-out intermediate coupling frame transformation R-matrix calculations which include a total of 283 finestructure levels in both the configuration interaction target and close-coupling collision expansions. These arise from the configurations 1s 2 2s 2 2p 6 3{s, p, d}nl with n = 4, 5, and for l = 0−4. Results. We obtain ordinary collision strengths and Maxwell-averaged effective collision strengths for the electron-impact excitation of all the ions of the Mg-like sequence, from Al + to Zn 18+ . We compare our results with those from previous R-matrix and distorted waves calculations, where available, for some benchmark ions. We find good agreement with the results of previous calculations for the transitions n = 3−3. We also find good agreement for the most intense transitions n = 3−4. These transitions are important for populating the upper levels of the main diagnostic lines.

R-matrix electron-impact excitation data for the Be-like iso-electronic sequence

Aims. Emission lines from ions in the Be-like isoelectronic sequence can be used for reliable diagnostics of temperature and density of astrophysical and fusion plasmas over a wide range of temperatures. Surprisingly, interpolated data is all that is available for a number of astrophysically important ions. Methods. We have carried out intermediate coupling frame transformation R-matrix calculations which include a total of 238 finestructure levels in both the configuration interaction target and close-coupling collision expansions. These arise from the configurations 1s 2 2{s, p}nl with n = 3−7, and l = 0− 4f orn ≤ 5a ndl = 0− 2f orn = 6, 7. Results. We obtain ordinary collision strengths and Maxwell-averaged effective collision strengths for the electron-impact excitation of all the ions of the Be-like sequence, from B + to Zn 26+ . We compare with previous R-matrix calculations and interpolated values for some benchmark ions. We find good agreement for transitions n = 2−2 with previous R-matrix calculations but some disagreements with interpolated values. We also find good agreement for the most intense transitions n = 2−3 which contribute via cascade to the (n = 2) diagnostic radiating levels.

Atomic data for astrophysics: Fe IX

We present the results of a new large-scale intermediate-coupling frame transformation R-matrix scattering calculation for electron collisional excitation of Fe ix. The target includes all the main configurations up to n = 5, to improve our earlier R-matrix and distorted-wave (DW) calculations for the n = 3,4 levels. Unlike similar calculations which we carried out for the other coronal iron ions, in this case the larger target does not significantly affect the collision strengths of the strongest transitions to the n = 3,4 levels. Some differences are however present for a few transitions, in particular for the 3d–4p line at 197.86 A. For the weaker transitions, significant enhancements due to extra resonances resulting from this much bigger target are found. Several new line identifications are suggested. We find excellent agreement between predicted and observed line intensities in the EUV (Hinode EIS) showing that Fe ix lines provide a reliable temperature diagnostic. We also show that the visible forbidden lines are a good diagnostic to measure electron densities.

R-matrix electron-impact excitation data for astrophysically abundant sulphur ions

We present results for the electron-impact excitation of highly-charged sulphur ions (S8+–S11+) obtained using the intermediate-coupling frame transformation R-matrix approach. A detailed comparison of the target structure has been made for the four ions to assess the uncertainty on collision strengths from the target structure. Effective collision strengths (Υs) are presented at temperatures ranging from 2 × 102(z + 1)2 K to 2 × 106(z + 1)2 K (where z is the residual charge of ions). Detailed comparisons for the Υs are made with the results of previous calculations for these ions, which will pose insight on the uncertainty in their usage by astrophysical and fusion modelling codes.

R-matrix electron-impact excitation data for the Li-like iso-electronic sequence including Auger and radiation damping

We present results for the electron-impact excitation of all Li-like ions from Be+ to Kr33+ which we obtained using the radiation- and Auger-damped intermediate-coupling frame transformation R-matrix approach. We have included both valence- and core-electron excitations up to the 1s(2)5l and 1s2l4l' levels, respectively. A detailed comparison of the target structure and collision data has been made for four specific ions (O5+, Ar15+, Fe23+ and Kr33+) spanning the sequence so as to assess the accuracy for the entire sequence. Effective collision strengths (gamma s) are presented at temperatures ranging from 2 x 10(2)(z + 1)(2) K to 2 x 10(6)(z + 1)(2) K (where z is the residual charge of the ions, i.e. Z - 3). Detailed comparisons for the gamma s are made with the results of previous calculations for several ions which span the sequence. The radiation and Auger damping effects were explored for core-excitations along the iso-electronic sequence. Furthermore, we examined the iso-electronic trends of effective collision strengths as a function of temperature.

R -MATRIX ELECTRON-IMPACT EXCITATION OF Fe 13+ AND ITS APPLICATION TO THE SOFT X-RAY AND EXTREME-ULTRAVIOLET SPECTROSCOPY OF CORONA-LIKE PLASMAS

Accurate excitation parameters are required to interpret the ultraviolet and X-ray spectra of Fe13+. In this work, we use the AUTOSTRUCTURE code to describe the atomic structure of Fe13+. The 197 lowest-lying fine-structure levels of the 3s(x)3p(y)3d(z) (x + y + z = 3), 3s(2)4l, and 3s3p4{s, p, and d} configurations are included along with further correlation configurations: 3s3p4f, 3p(x)3d(y)4l (x + y = 2), 3l4l'4l '', and 3l3l'5l ''. The resultant level energies, lifetimes of excited states, and oscillator strengths of transitions between these levels are assessed by comparison with available experimental data and previous calculations. Electron-impact excitation data among these lowest-lying levels are generated using the intermediate-coupling frame transformation R-matrix method. We assess the present results by comparisons with laboratory measurement for the excitation to the metastable level 3s(2)3p(2)P(3/2)(0) and with available close-coupling calculations for other excitations. Using these data and a collisional-radiative model, we have analyzed soft X-ray and extreme-ultraviolet spectra from space satellite observations of a stellar corona and of solar flares, as well as measurements from an electron beam ion trap. We assess the contribution from Fe13+ emission lines in the solar and Procyon corona observations, and find and identify new lines in the X-ray region observed in the solar and Procyon coronae. The laboratory measurements also confirm that weak lines (218.177 angstrom and 224.354 angstrom) of Fe13+ contribute to the observed intensities in solar observations. The polarization effect due to the directional monoenergetic distribution of the electron energy has been taken into account in comparison with the laboratory measurements. Electron density diagnostics for the astrophysical plasma sources have been performed using the updated data so as to investigate their sensitivity to the atomic data source.

R-matrix electron-impact excitation data for the Ne-like iso-electronic sequence

We present results for the electron-impact excitation of all Ne-like ions from Na + to Kr 26+ obtained using the intermediate-coupling frame transformation R-matrix approach. For each ion’s calculation, the close-coupling expansion is taken to be the 113 LS terms (209 levels) belonging to the configurations [1s 2 ]2s 2 2p 6 ,2 s 2 2p 5 {3, 4, 5}l ,2 s2p 6 {3, 4, 5}l (l ∈ s, p, d, f, and g), and 2s 2 2p 5 {6, 7}l � (l � ∈ s, p, and d). An additional configuration interaction effect arising from configurations of 2s 2 2p 4 3l{3, 4, 5}l �� (l �� ∈ s, p, d, f and g) was included in the target expansion. A detailed comparison of the target structure has been made for six specific ions (Si 4+ ,A r 8+ ,C a 10+ ,

Relativistic radiatively damped R-matrix calculations of the electron-impact excitation of helium-like iron and krypton

Electron-impact excitation data for He-like ions are of significant importance for diagnostic applications to both laboratory and astrophysical plasmas. Here we report on the first fully relativistic R-matrix calculations with radiation damping for the He-like ions Fe24+ and Kr34+. Effective collision strengths for these two ions have been determined with and without damping over a wide temperature range for all transitions between the 49 levels through n = 5. We find that damping has a pronounced effect on the effective collision strengths for excitation to some of the low-lying levels, but its effect on excitation to the vast majority of levels is small. At the energy of a resonance peak, we also investigate the effect of radiation damping on the angular distribution of scattered electrons. Finally, we compare our results for Fe24+ with an earlier intermediate coupling frame transformation R-matrix calculation with radiation damping by Whiteford et al (J. Phys. B: At. Mol. Opt. Phys. 34 3179) and find good agreement, especially for excitation to the lower levels.

R-matrix inner-shell electron-impact excitation of the Na-like iso-electronic sequence

We present results for the inner-shell electron-impact excitation of all Na-like ions from Mg+ to Kr25+ obtained using the intermediate-coupling frame transformation R-matrix method with both Auger and radiation damping included via the optical potential approach. For each ion, the target and close-coupling expansions are taken to be the 59 LS terms (134 levels) belonging to configurations 2s22p63l, 2s22p53s3l (l ∊ s, p, d), 2s22p53p2 and 2s22p53p3d. Radial wavefunctions were obtained using autostructure. Effective collision strengths are presented at temperatures ranging from 2 × 102(q + 1)2 K to 2 × 106(q + 1)2 K (where q is the residual charge of ions, i.e. Z − 11). Comparisons for the collision strengths and effective collision strengths are made with the results of other calculations for several ions which span the sequence. The Auger and radiation damping effects along the sequence have also been explored and their importance is highlighted. We further examine iso-electronic trends of both low- and high-temperature effective collision strengths.

R-matrix calculations for electron impact excitation

The large number of high-resolution spectra routinely recorded in the astrophysical and fusion communities leads to the need for an extensive set of accurate baseline atomic data. The advantages of the intermediate-coupling frame transformation R-matrix method make it feasible to provide excitation data along iso-electronic sequences covering a substantial range of astrophysically important ions at the high level of accuracy afforded by the R-matrix method. This is one of the key goals of the UK Atomic Processes for Astrophysical Plasmas (APAP) network.

R-matrix electron-impact excitation data for the Na-like iso-electronic sequence

We present results for the outer-shell electron-impact excitation of all Na-like ions from Mg+ to Kr25+ obtained using the intermediate-coupling frame transformation R-matrix approach. For each ion's calculation, the target and close-coupling expansions are both taken to be the 18 LS terms (32 levels) belonging to configurations [1s(2)2s(2)2p(6)]3l, 4l, 5l and 6l (l = 0-5). Effective collision strengths ((sic)s) are presented at temperatures ranging from 2 x 10(2)(q + 1)(2) K to 2 x 10(6)(q + 1)(2) K (where q is the residual charge of ions, i.e. Z - 11). Detailed comparisons for the (sic)s are made with the results of previous calculations for several ions, which span the sequence. Furthermore, we examine the iso-electronic trends of both low- and high-temperature effective collision strengths

R-matrix inner-shell electron-impact excitation of Fe15+ including Auger-plus-radiation damping

We present results for the inner-shell electron-impact excitation of Fe15+ using the intermediate-coupling frame transformation R-matrix approach in which Auger-plus-radiation damping has been included. The target and close-coupling expansions are both taken to be the 134 levels belonging to the configurations 2s22p63l, 2s22p53s3l, 2s22p53p2 and 2s22p53p3d. The comparison of Maxwell-averaged effective collision strengths with and without damping shows that the damping reduction is about 30–40% for many transitions at low temperatures, but up to 80% for a few transitions. As a consequence, the results of previous Dirac R-matrix calculations (Aggarwal and Keenan 2008 J. Phys. B: At. Mol. Opt. Phys. 41 015701) overestimate the effective collision strengths due to their omission of Auger-plus-radiation damping.

Absolute cross sections for near-threshold electron-impact excitation of the dipole-allowed transitions3s21S→3s3p1PinCl5+and3s2S→3p2PinCl6+

Experimental and theoretical cross sections for electron-impact excitation of the dipole-allowed transitions 3s{sup 2 1}S {yields} 3s3p {sup 1}P in Cl{sup 5+} and 3s {sup 2}S {yields} 3p {sup 2}P in Cl{sup 6+} near the excitation thresholds are reported. Absolute cross sections are measured using the merged electron-ion beams energy-loss technique. The intermediate-coupling frame-transformation R-matrix method is used to obtain theoretical cross sections. The total cross sections, for the transitions studied in both ions, exhibit resonance structures near threshold. There is excellent agreement between theory and experiment with respect to both the shape and the magnitude of the cross section for the 3s {sup 2}S {yields} 3p {sup 2}P transition in Cl{sup 6+}. For Cl{sup 5+}, structures and trends in both the present R-matrix calculation and the previous calculation of Baluja and Mohan [J. Phys. B 20, 831 (1987)] agree well with the experimental results. However, the magnitudes of the theoretical cross sections for Cl{sup 5+} are significantly smaller than the measured cross section, which has been corrected for metastable contamination.