1
Ⅲ. Recent results as part of APAP network For a summary of earlier work by the APAP Network , see our presentation in XXVI International conference on Photonic, Electronic and atomic collisions (ICPEAC 2009) [3] R-MATRIX CALCULATIONS FOR ELECTRON-IMPACT EXCITATION AND THEIR APPLICATION IN ASTROPHYSICAL PLASMAS GY Liang 1,2 , N R Badnell 1 , G Del Zanna 3 , H E Mason 3 , P J Storey 4 and G Zhao 2 1 Department of Physics, University of Strathclyde, Glasgow, G4 0NG, UK 2 National Astronomical Observatories, CAS, Beijing 100012, China 3 DAMTP, Centre for Mathematical Sciences, Cambridge, CB3 0WA, UK 4 Department of Physics and Astronomy, University College London, London, WC1E 6BT, UK Ⅱ. Method Radial wave-functions are generated by uisng AUTOSTRUCTURE R-matrix instead of distorted-wave (DW) method was adopted here, which efficiently takes resonances in electron-ion interaction into account Intermediate-coupling frame transformation (ICFT) [1] R-matrix instead of Breit-Pauli and fully relativistic Dirac (DARC) method Advantages: 1. Less-time demanding: consider LS-coupled Hamiltonian 2. Level energy correction with available experimental data 3. Eliminates at root the deficiency of previous LS-bashed methods (e.g. JAJOM) via use of multi-channel quantum defect theory (MQDT) 4. Has comparable accuracy with other two kinds of R-matrix methods [1] 5. Auger and radiation damping via spectator electron (n 3, 4 or 5) pathways can easily be taken into account via a optical potential [2] 6. Current ICFT code has been parallelized and has shown to be highly robust * http://www.apap-network.org The participator KLn/KMn /KNn Auger and radiation pathways (1) and (3) are automatically described in the R- matrix method. However the spectator KLL/KLM/KLN Auger and radiation pathways (2) and (4) are independent of n and only low-n resonances (n 4 here) can be included in the normal close-coupling expansion. The ICFT method easily takes account of the damping pathways (1) (4) via an optical potential. The resonance state configurations are of the form 1s[2s － 4f] 2 nl (n≥5) and they decay via the following channels: 1s[2s, 2p][2s－4f] nl 1s 2 [2s－4f] + e - (1) 1s 2 nl + e - (2) 1s2[2s, 2p][2s－4f] + h (3) 1s 2 [2s－4f] nl + h (4) A. R-matrix outer- and inner-shell electron-impact excitation for Li-like iso-electronic sequence with Auger and radiation damping [4] The target CI and CC expansions are both taken to be 195 fine-structure levels (89 LS terms) of configurations: 1s 2 {2,3,4}l and 1s2l{2,3,4}l ’ Effective collision strength () of inner-shell transition lines along the Li- like iso-electronic sequence at three temperature Collision strengths calculated with ICFT R-matrix method without damping, and with radiation damping or Auger-plus-radiation damping for one transition of Ar 15+ ※ Resultant effective collision strengths are assessed to be a significant improvement than previous calculations and reliable for ions with charge higher than 5 along the sequence ※ The enhancement of s from resonances in decreases with increasing of the nuclear charge Z because of the Auger-radiation damping effects for a given transition ※ The Auger-radiation damping is more significant and widespread for more transitions with increasing Z, although the radiation damping effect increases. This is consistent with that in L-shell e.g. Na-like sequence ※ Complicate structure only appears for lower charge ions (Z<14) along the sequence, being differ from L-shell. This is due to the high core-excitation energy. ※ An independent calculation for valence-electron excitations up to levels of n =5 complexes has been done along the sequence to generate a self-consistent dataset, which is also assessed to be reliable Ⅳ. Summary An extensive set of reliable excitation data is being generated under the APAP project This will update much of DW data (via CHIANTI [7] ) presently used by astrophysical community and its use may overcome some shortcomings in astrophysical modelling; This is also of importance to fusion modelling and diagnostics via updates of the ADAS [8] database Modelling application helps line identification from sulphur ions in stellar coronae via Procyon References [1] Griffin D C, Badnell N R and Pindzola M S 1998 J.Phys. B: At. Mol. Opt. Phys. 31 3713 [2] Robicheaux F, Gorczyca T W, Pindzola M S, Badnell N R 1995 Phys. Rev. A 52 1319 [3] Liang G Y, Badnell N R, Storey P J, Whiteford A D, Del Zanna G 2009 J.Phys.: Conference series 194 062006 [4] Liang G Y and Badnell N R 2011 Astro. & Astrophys. 528 A69 [5] Liang G Y and Badnell N R 2011 Astro. & Astrophys. (in revision) [6] Li F, Liang G Y and Zhao G 2011 (in preparation) [7] Landi E, Del Zanna G, Young P R, Dere K P, Mason H E and Landini M 2006 Astrophys. J. Supp. Ser. 162 261 [8] Summers H P 2004 The ADAS User manual version 2.6 http://www.adas.ac.uk 0.0000 0.0005 0.0010 0.0015 0.0000 0.0005 0.0010 0.0015 0.0020 230 240 250 260 270 280 0.0000 0.0005 0.0010 0.0015 Collision strength () Radiation damping Without damping Energy (Ryd) Auger- plus Radiation damping GS83 The ratio of effective collision strengths between that with radiation or Auger-plus-radiation damping and that without damping ※ Soft X-ray emission lines from highly charged sulphur ions are identified in Chandra/LETG Procyon observation ※ Modelling with updated atomic data demonstrates the significant difference for some emission lines when compared with that from Chianti v6 dataset, e.g. the lines around 51.2—51.6Å from 2s2p 3 3s 4 S 3/2 → 2s2p 4 4 P 3/2, 5/2 Ⅰ. Motivation: from astrophysical and fusion communities Line identification: A large amount of emission lines in EUV and X-ray regions were observed by spectrometers on space satellites (e.g. Hinode/EIS, Chandra, XMM-Newton) with high-resolution and high collection area, and will be clarified by IXO mission with much high resolution and photon-collecting efficiencies. Diagnostics: Many emission lines detected by spectrometers show potential diagnostics of the n e and T e of coronal-like hot plasmas. Further detailed investigation of coronal structure and heating mechanism of hot-plasmas provide the need for accurate atomic data including excitation cross-section Atomic physics: Many available excitation data are from poor approximation (e.g. distorted-wave). More accurate method (R-matrix) and parallel computation are feasible now One of goals of UK APAP Atomic Processes for Astrophysical Plasmas network*: provides excitation data for iso-electronic sequence across an extensive range of astrophysically relevant elements within R-matrix framework 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Ratio of at 10 4 (z+1) 2 A+R vs U R vs U A+R vs R Line strength (S) e) Fe 23+ 4 8 12 16 20 24 28 32 36 0.000 0.003 0.006 0.009 0.012 0.000 0.005 0.010 0.015 0.020 0.000 0.005 0.010 0.015 0.020 1s 2 2p 2 P 3/2 1s2s2p 4 P 1/2 (326) Effective collision strength Atomic number Z 5 x 10 2 (z+1) 2 10 3 (z+1) 2 10 4 (z+1) 2 1s 2 2s 2 S 1/2 1s2s2p 2 P 1/2 (r) 5 x 10 2 (z+1) 2 10 3 (z+1) 2 10 4 (z+1) 2 5 x 10 2 (z+1) 2 10 3 (z+1) 2 10 4 (z+1) 2 1s 2 2s 2 S 1/2 1s2s2p 4 P 3/2 (u) B. R-matrix electron-impact excitation data of four iso-nuclear sulphur ions S 8+ , S 9+ , S 10+ and S 11+ [5] 10 -4 10 -3 10 -2 10 -1 10 0 10 -4 10 -3 10 -2 10 -1 10 0 3-22 2 D 3/2 BL03 MCHF gf (others) gf (present) S 9+ 3-21 2 D 5/2 10 -4 10 -3 10 -2 10 -1 10 0 10 -4 10 -3 10 -2 10 -1 10 0 Chianti v6 MCHF NSD07 MVG95 gf (others) gf (present) S 11+ 5-52 4-52 3-50 4-50 3-52 5-50 0.01 0.1 1 0 5 10 15 20 25 0.01 0.1 1 LB94 Collision strength () Scattered energy (Ryd) ICFT 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 10 2 logT e (K)=5.3 logT e (K)=6.3 logT e (K)=7.3 ICFT vs DW ICFT a) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.00 0.01 0.02 0.03 Collision strength Scaled energy ICFT LB03 AS-DW (9 model) AS-DW (24 model) b) 10 -3 10 -2 10 -1 10 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 12-13 4-5 1-14 7-10 KKR02 : ICFT logT e (K)=6.04 logT e (K)=6.40 logT e (K)=6.78 9-13 ICFT 8-13 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.00 0.01 0.02 0.03 0.04 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 /ln(E j /E ij + e) 1- lnC/ln(E j /E ij + C) ICFT BL03 AS-DW Chianti (v6) logT e (K)=5.1 logT e (K)=6.1 (peak) logT e (K)=7.1 Others vs ICFT ICFT 10 3 10 4 10 5 10 6 10 -2 10 -1 10 0 Effective collision strength () Temperature (K) 1-2 2-3 1-3 2-4 1-4 3-4 1-5 4-5 0.0 0.2 0.4 0.6 0.8 1.0 10 -3 10 -2 10 -1 10 0 10 4 10 5 10 6 10 7 10 8 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Scaled Scaled energy ICFT BL03 BR00 (without pseudo-resonance) 1-12 Temperature (K) ICFT BR00 BR00 (without pseudo-resonance) S 9+ 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 logT e (K)=5.2 logT e (K)=6.2 (peak) logT e (K)=6.7 BR00 vs ICFT ICFT Comparison with results from DW (Bhatia & Landi 2003, left) and from R-matrix method (right) with JAJOM transformational approach (Butler & Zeippen 1994) for S 8+ Comparison with previous R-matrix calculation by Bell & Romsbottom (2000) for S 9+ , in which pseudo-orbitals ( and ) were included d s p 4 , 4 , 3 f 4 0.00 0.20 0.40 0.60 0.80 1.00 10 3 10 4 10 5 10 6 10 7 10 8 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Effective collision strength ICFT CKA92 LB94 2-3 1-2 4-5 Temperature (K) ICFT CKA92 LB94 1-4 1-6 Comparison with previous R-matrix calculations (Lennon & Burke 1994, Conlon et al. 1992) for excitations to lower excited (n=2, top) and with previous DW calculation (Landi & Bhatia 2003) for excitation to higher levels (n=3, below) for S 10+ Comparison with previous R-matrix calculation by Keenan et al. (2002) at three different temperatures ※ Extensive configuration interactions included confirms the convergence of resultant level energies and gf-values for given transitions ※ Assessment for resultant collision strengths by comparison with previous available R-matrix calculations confirms validity and improvement of the present ICFT results ※ CI effect explains the strange behavior when compared with DW data Ⅴ. Acknowledgement UK APAP Network is funded by UK STFC, GYL acknowledges the support from One-Hundred-Talents programme of CAS (China), GZ thanks the support from NSFC (China) under grant no. 10821061 42.5 43.0 43.5 44.0 44.5 0.000 0.005 0.010 0.015 0.020 45.2 45.4 45.6 45.8 46.0 46.2 46.4 46.6 46.8 47.0 0.000 0.005 0.010 0.015 0.020 47.0 47.5 48.0 48.5 49.0 49.5 0.000 0.005 0.010 0.015 0.020 50.0 50.2 50.4 50.6 50.8 51.0 51.2 51.4 51.6 51.8 52.0 0.000 0.005 0.010 0.015 0.020 52.8 53.2 53.6 54.0 54.4 0.000 0.005 0.010 0.015 0.020 64.0 64.2 64.4 64.6 64.8 65.0 65.2 0.000 0.005 0.010 0.015 0.020 S VIII S X/Fe XVI ? Fe XVI/Si X Fe XV Si XII Si XII Si XI S IX S X Si XII Si XI Si XI Procyon obs. ICFT chianti (v6) Si X Si XI Counts s -1 Å -1 Si X Wavelength (Å) Si X C. Soft X-ray spectroscopy of highly charged sulphur ions in stellar coronae (Procyon) [6] This picture taken from NASA SDO website Observation: Chandra LETGS for three observations (Obs_IDs of 63, 1461 and 1224) Analysis model: Collisional-radiative model with new atomic data as shown in above Chandra LETGS observation (histogram) for Procyon along with synthetical spectra with updated atomic data (red) and that from Chianti v6 dataset (blue). Only the theoretical spectra of S IX (dashed-dot line) and S X (solid) are shown here for conciseness.
