Evaluation of electron impact excitation data in RDW calculation

Transcription

1 IAEA International Code Centres Network Meeting Evaluation of electron impact excitation data in RDW calculation Chenzhong Dong (C Z Dong) Key Laboratory of Atomic and Molecular Physics & Functional Materials of Gansu, College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou, China IAEA, Vienna, May.6,

2 Contents Motivation Theoretical method Results and data assessments Summary 2

3 Motivations Electron impact excitation process is one of the most essential atomic processes. A systematical study on this process will be helpful for both the understanding of atomic/ionic excited structures and the modeling of various plasma properties. ICF plasma ITER plasma Astro plasma Different questions require different accuracy for the EIE data. 3

4 Existing some experimental measurements for EIE process EBIT MOT Storage ring MOT facility EBIT facility High resolution EELS 4

5 Existing some systematic calculations for EIE process R-matrix DW The R-matrix is the most widely used for collisional excitation modeling, handle resonances naturally, but it is also computational expensive and limited to low collision energies often; the DW method is mainly used for highly ionized heavy ions, and it is regarded as an easier and more effective method for producing a large amount data of cross sections. The data in Chianti v7 5

6 3C and 3D cross sections of FeXVII Cross section (10-20 cm 2 ) Cross section (10-19 cm 2 ) C 3D Energy (ev) Model A Model B Mohan et al.[47] Chen et al.[44] FAC (Wirh RE)[54] Experiment[54] 3C: 2p 5 3d 1 P 1 2p 6 1 S 0 3D: 2p 5 3d 3 D 1 2p 6 1 S 0 Model A: 2s 2 2p 6, 2s 2 2p 5 3l, 2s2p 6 3l (l=s,p,d) Model B: ModelA + 2s 2 2p 5 4l, 2s2p 6 4l (l=s,p,d,f) G.V. Brown, et al., Phys. Rev. Lett. 96, (2006) G. X. Chen et al., Phys. Rev. Lett. 89, (2002). M. Mohan et al., Astrophys. J. 108, 389 (1997). The discrepancy among the different calculations and experiments can be up to ~40% 6

7 3C/3D line ratio of Fe XVII J. D. Gillaspy et al. (2011) ApJ Foster et al. (2012) ApJ The discrepancy reduces to 5% --20% among latest calculations and experiments. 7

8 RDW calculation based on MCDF method 8

9 Calculation of energy and wavefunction (MCDF) In this method, atomic state wave function (ASF) is expressed by a linear combination of configuration state functions (CSF) with the same symmetry n c ( PJM ) C r ( ) r ( PJM r1 ) where n c is the number of CSF and C r () denotes the representation of the atomic state in this basis. The CSF is antisymmetrized products of a common set of orthonormal orbitals which are optimized on the basis of the Dirac -- Coulomb Hamiltonian. Further relativistic contributions to the representation C r () of the atomic states due to (transverse) Breit interactions were added by diagonalizing the Dirac--Coulomb--Breit Hamiltonian matrix. The dominant QED contributions to the transition energies can also be included in the computations. GRASP92: F. A. Parpia, C. F. Fischer and I. P. Grant, CPC 94, 249 (1996) GRASP2K: P Jonsson, X. He, C.F. Fischer and I. P. Grant CPC 177, 597 (2007) 9

10 Calculation of energy and wavefunction (MCDF) The system wave function involved in the processes of electron impact excitation is constructed as an antisymmetric wave function of the total (N+1)-electron system including the target ion plus a continuum electron, ( 1 N 1 N 1 p 1 ( 1) C( Jt jm tm; JM ) t J x t p u m x 1 / 2 ( ) ( p) N 1) p1 M, m t t J t where is the target ion wave functions, which generated by GRASP92/2K, u m is the relativistic Dirac spinor for a continuum electron with given energy, it is produced by using the relativistic program COWF. RATIP (COWF): S. Fritzsche, CPC 141, 163 (2001) 10

11 Calculation of EIE scattering amplitude The scattering amplitude of the EIE (for given J i M i m si to J f M f m sf ): Scattering matrix element: Breit operator : N 1 1 R J, ; J ( V ) J, ; J f f f f Breit i i i i qp, rqp q p H. L. Zhang, D. H. Sampson and R. E. H. Clark, Phys. Rev. A 41, 198 (1990) 11

12 Calculation of EIE collision parameters The EIE rate coefficients: C DE i f 2 ca g i 2 I 0 H kt e exp( E kt e if ) if The effective collision strengths: ( i, f )exp( if 0 f kt e f ) d( kt e ) Cross sections: d 1 1 dkˆ 2J 1 2 f i M, M m, m i f si sf D. H. Sampson, H. L. Zhang, C. J. Fontes. Phys. Rep. 477, 111 (2009) B m m si sf 2 d if ( ) d dkˆ f 12

13 Computational codes based on MCDF Grasp92/2K F. A. Parpia et al. CPC 94 (1996) 249; P Jonsson et al., CPC 177, 597 (2007) REIE06 EIE process J. Jiang et al., Chin. Phys. Lett. 24,691 (2007). REDR05 DR process D H Zhang et al., Acta Physica Sinica 55,112 (2006). RERR06 RR process X. B. Ding, Ph.D thesis, NWNU 2008 REIE06 :J. Jiang, C. Z. Dong, L. Y. Xie et al., Chin. Phys. Lett. 24,691 (2007). J. Jiang, C.Z. Dong, L.Y. Xie, J.G. Wang, J. Phys. B41, (2008). 13

14 Results and data assessments 14

15 NII ions Configuration interactions: Model A includes the 2s 2 2p 2, 2s2p 3 and 2s 2 2p3l (l = s, p, d) configurations, which generate 41 levels. Model B includes the 2s 2 2p 2, 2s2p 3, 2s 2 2p3l and 2s 2 2p4l (l = s, p, d, f) configurations, generating 79 levels. Model C includes all the states in Model B and all the states from the 2s 2 2p5l (l = s, p, d) configurations, we have 105 levels. Breit interaction and QED effects are taken into account. Yang Ning-Xuan et al Chin. Phys. B 19, (2010) 15

16 Comparison of excitation energies NII ions ~2% [1] Hudson C E and Bell K L 2005 Phys. Scr [11] Stafford R P, Bell K L, Hibbert A and Wijesundera W P 1994 Mon. Not. R. Astron. Soc [12] Frost R M, Awakowicz P, Summers H P and Badnell N R 1998 J. Appl. Phys

17 Comparison of rate coefficients NII ions here is a large discrepancy among the different models for rate coefficients Up : Model A Down : Model B : Model C : Experiments of Frost at al[12] Left : R-matrix of Frost Right : 23 state R-matrix of Hundson[1] : 13 state R-matrix of Stafford [11] [1] Hudson C E and Bell K L 2005 Phys. Scr [11] Stafford R P, Bell K L, Hibbert A and Wijesundera W P 1994 Mon. Not. R. Astron. Soc [12] Frost R M, Awakowicz P, Summers H P and Badnell N R 1998 J. Appl. Phys

18 Configuration interactions: Ni-like: 3s 2 3p 6 3d 9 nl, 3s 2 3p 6 3d 10 nl, 3s3p 6 3d 10 nl (n=4,5; l=s,p,d,f), 213 CSFs Cu-like: 3s 2 3p 6 3d 10 nl, 3s 2 3p 6 3d 9 4snl, 3s 2 3p 5 3d 10 4snl, 3s3p 6 3d 10 4snl (n=4,5; l=s,p,d,f), 405 CSFs Zn-like: 3s 2 3p 6 3d 10 4s 2, 3s 2 3p 6 3d 10 4snl, 3s 2 3p 6 3d 9 4s 2 nl, 3s 2 3p 5 3d 10 4s 2 nl, 3s3p 6 3d 10 4s 2 nl, (n=4,5; l=s,p,d,f), 229 CSFs... Au ions Breit interaction and QED effects are taken into account. Z. W. Wu, C. Z. Dong and J. Jiang Phys. Rev. A. 86, (2012) N. X. Yang, C. Z. Dong and J. Jiang Chin. Phys. Lett. 26, (2009) 18

19 Comparison of level energies Au ions An agreement of <0.05% is quoted for the differences between HULLAC and the present calculated energies, there are some lines of As-like and Se-like gold ions with differences >0.1%. [23] M. J. May, et al., Phys. Rev. E 68, (2003). 19

20 Comparison of collision strengths Au ions The present collision strengths are in good agreement with the FAC data from Zeng et al., approximately 1% larger in most cases. 20 Zeng J L Et al., 2007 ADNDT

21 Comparison of cross sections Au ions Good agreement can be found for both the level energies and collision strengths. [1] Griem H R et al 1992 Phys. Fluids B [2] Lindl J et al 1995 Phys. Plasmas [3] Kiyokawa S, Yabe T et al 1985 Phys. Rev. Lett [4] Bauche-Arnoult C, Luc-Koenig E et al 1986 Phys. Rev. A [5] Foord M E, Glenzer S H et al 2000 Phys. Rev. Lett

22 Main uncertainties in our RDW calculations 22

23 The contributions of partial waves Cross sections of xenon Exp: Phys. Rev. A 72, (2005) J. Jiang, C.Z. Dong, L.Y.Xie, X.X. Zhou, J. Phys. B At. Mol. Opt. Phys. 41, (2008) 23

24 The CI effects on the energy levels Argon The discrepancy is about 6%~ 10% between the two models. Xenon Model A: single configuration Model B: multi-configuration Exp: Phys. Rev. A 72, (2005) J. Jiang, C.Z. Dong, L.Y.Xie, X.X. Zhou, J. Phys. B At. Mol. Opt. Phys. 41, (2008) G.F. Du, J. Jiang, and C.Z. Dong Eur. Phys. J. D 63, 103 (2011) 24

25 The CI effects on the cross sections EIE cross sections of 5p 5 6s 5p 5 6p for neutral xenon Exp: C. C. Lin group,phys. Rev. A 72, (2005) R. Srivastava et al, Phys. Rev. A 74, (2006) J. Jiang, C.Z. Dong, L.Y.Xie, X.X. Zhou, J. Phys. B At. Mol. Opt. Phys. 41, (2008) Triangles : single configuration Squares : multi-configuration 25

26 The CI effects on the cross sections Core preserving Core excitations changing excitations EIE cross sections of 4p 5 4s 4p 5 5p for Argon G.F. Du, J. Jiang, C.Z. Dong Eur. Phys. J. D 63, 103 (2011) Model A: single configuration Model B: multi-configuration 26

27 The effects of Breit interactions on EIE collision strengths Ni-like ions (3d 10 1 S 0 to 3d 9 4l excited states) The differences between the collision strengths with and without the Breit interaction become more evident with increasing of the atomic number and the incident electron energies. L. Y. Xie et al, Acta Phys. Sin.57, 6249 (2008) 27

28 The contribution of Breit interaction Cross sections of He-like ions ~290% ~175% ~4% Fe 24+ U 90+ ~115% E:Excitation energy (1s2s 3 S 1 1s3s 1 S 0 ) N. Y. Yang, Jun Jiang et al, Acta. Phys. Sin. 57, 2888 (2008) 28

29 The contributions of resonance processes The electron impact excitation cross sections of magnetic quadrupole line 2p 6 1 S 0 (2p 3/2 3s 1/2 ) 2 of neonlike Ba 46+ The excitation process for the magnetic sublevels of neonlike Ba 46+ can be characterized as e l j Ba p J 46 6 ( i i i) (2 ; 0) Dir Res 46 5 Ba p s J f M f e f l f j f (2 3 ; ) ( ) 45 5 Ba p n n JkMk (2 ' '; ) dir res ( M M ) ( M M ) ( M M ) i f i f i f i i i 46 5 Ba p s J f M f e f l f j f (2 3 ; ) ( ) In the isolated resonance approximation, the electron impact excitation cross section can be written as J. Jiang, C. Z. Dong, L. Y. Xie et al, Phys. Rev. A 78, (2008) 29

30 The polarization degree of magnetic quadrupole line (2p 3/2 3s 1/2 ) 2 2p 6 1 S 0 of neonlike Ba 46+ The 4l5l' resonant series have larger contributions on the excitation cross section which causing the polarization degree change from -22% to 4%. 4l6l' and 5l5l' resonant series have small contributions to the excitation cross section, but 5l5l' are more obvious than the 4l6l',which causing more serious changes of the polarizations and also observed by experiments. Our results are found to be in excellent agreement with the experimental results Exp : E. Takacs, E.S. Meyer, J.D. Gillaspy, et al., Phys. Rev. A 54, 1342 (1996) Theor: J. Jiang, C. Z. Dong, L. Y. Xie et al, Phys. Rev. A 78, (2008) 30

31 Summary and outlook Electron impact excitation is one of the most essential atomic processes, a large number of EIE data are necessary for both the understanding of atomic excited structures and the modeling of various plasma properties. On the basis of the GRASP92/2K and RATIP packages, a new RDW program, named REIE06 has been developed by our group in Lanzhou. In this talk, some selected applications of this program are shown. A special attention has been paid on the evaluation of the RDW calculation accuracy of EIE data. By using this program, we can consider the contributions from configuration interaction effect, Breit interaction effect, high partial waves, and even the intermediate resonance states in an isolated resonance approximation systematically. Therefore, the RDW method is still a very effective 31 method for producing a large amount of EIE data.

32 Dr Xie Lu you Ma Xiao yun Chen Zhan bin Dr Jiang Jun Wu Zhong wen 32

33 Acknowledgements Co-operators B. Fricke in Kassel University, Germany S. Fritzsche, A. Surzhykov, T. Stöhlker in GSI, Germany F. Koike in Kitasato University, Japan G.O Sullivan in University College Dublin, Ireland P.Jönsson in Malmo University, Sweden G.Gaigalas in Vilnius University, Lithuania T. Kato, D. Kato in NIFS, Japan M. Godefroid, ULB, Belgium E. Träbert in Ruhr-Universität Bochum Jiaming Li in Tsinghua University, China Jianguo Wang, Jun Yan in IAPCM, China Xinwen Ma, Xiaohong Cai and Guoqin Xiao in IMPCAS, China Yizhi Qu in GSCAS, China And all my colleagues and students in NWNU, China Finance supports 33

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35 Workshop on Computational Atomic Physics The 1 st announcement Dear Colleagues, We cordially invite you to attend the Workshop on Computational Atomic Physics. This is a one-day workshop which will be held at the Northwest Normal University, Lanzhou, China. The meeting is scheduled on July 31st 2013, just following the ICPEAC ( in Lanzhou. Topics This workshop will cover the utilization and the development of GRASP and relevant codes and its applications to astrophysics, plasma and nuclear physics. Tentative Invited Speakers Jacek Bieroń (Poland) Christopher Chantler (Australia) Gediminas Gaigalas (Lithuania) Per J?nsson (Sweden) Tomas Brage (Sweden) Stephan Fritzsche (Germany) Michel Godefroid (Belgium) Fumihiro Koike (Japan) Chenzhong Dong Luyou (China) There is no registration fee for this workshop, and the Northwest Normal University will serve a lunch and a dinner to all delegates. If you have any requests or suggestions related to this workshop, please do not hesitate to contact Chenzhong Dong (dongcz@nwnu.edu.cn) College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou, China 35

36 Thank you for your attention! 36

37 Continuum wavefunction The continuum Dirac spinor is defined as u m 1 P r iq m (, ) (, m ) The continuum orbitals are solutions of the Dirac Fock equations which were generated by the component COWF of RATIP package c is the speed of light, is the kinetic energy of the electron. Y(r) and X(r) are Direct and exchange potentials, These equations are solved by the method of outward integration. S. Fritzsche, Comp. Phys. Comm. 183, 1525 (2012), 37