A Proposal For Improved Iron Project Collision Strengths Anil Pradhan Iron Project/ITAMP Workshop on High Accuracy Atomic Physics in Astronomy Aug. 7-9, 2006 Harvard-Smithsonian Center For Astrophysics

Coupled Channel R-Matrix Theory vs. Distorted Wave Coupled Channel Theory Distorted Wave Theory Includes only initial and final channels in Eq. (1); no summation Neglects channel coupling Resonance states (intermediate channels) NOT included in wavefunction expansion Limited number of resonances may be considered in the isolated resonance approximation May not be adequate for highly charged ions Ab initio treatment of important atomic processes with the same expansion: Eq.(1) Electron impact excitation, radiative transitions, and a self-consistent and unified treatment of photoionization and (e + ion) recombination, including radiative and dielectronic (RR+DR)  Review: Nahar and Pradhan (2004) Significant effects are included Infinite series of resonances are considered

Fe II Emission From Accretion Disk Near Black Hole (Zhang etal 2006) HH [OIII] Doppler Double-Peaked Wavelength Fe II Sloan Quasar SDSS J Broad Line Region AGN Models by Sigut and Pradhan (1998,2003), using IP data from the OSU group computed by H. Zhang, M. Bautista, S. Nahar etal., do NOT fit all spectra; accretion disk models favored!

Close Coupling Calculations for Fe II and Ni II The most important and complex atomic systems in astrophysics Fe II observed from nearly every class of astronomical object, from stars to black hole environments in centers of galaxies Well over 100 terms, with fine structure levels, of astrophysical interest Close coupling calculations in progress since the 70’s Open 3d-shell  require multiple-electron excitations for outer-shell correlation, up to 4d, 5d configurations from 3d AND 3p RMATRIX II enables ‘complete’ configurations

Term diagram for Fe II: Overlapping Target Configurations Strong CI precludes omission of any terms from low-lying configurations

The RMATRIX II APPROACH (P.G. Burke, V.M. Burke, C.J. Noble) Enable large CI expansions, with ‘complete’ sets of allowed configurations Efficient algorithms for algebraic manipulation of multiple-electron excitations in both - N-electron target configurations - (N+1)-electron correlation “ Parallelized codes

Sets of N-electron Target Terms, (N+1)-electron Correlation Functions ModelRA1A2A3D2D3D3*E2E3 Target 1# of configurations Total # of configurations # sextet and quartet symmetries # sextet and quartet states Total # of terms in the calculation Collisional 5 D e symmetry 6# of channels # of correlation functions G e symmetry 8# of channels # of correlation functions F e symmetry 10# of channels # of correlation functions P e symmetry 12# of channels # of correlation functions

Comparison of complete sets of the ‘4d5s’ (A3) and the ‘4d5s5d’ configurations (D3) C. Ramsbottom etal

Convergence of CI Expansions: Comparison of ‘4d5s5d’ (D3) and ‘4d5d’ (E2) configurations

Ni II Target Configurations (Oelgoetz and Pradhan, in progress) # of excitations Configurations included 1 e- from 3d3d 9, 3d 8 4s, 3d 8 4p, 3d 8 4d, 3d 8 5s, 3d 8 5p, 3d 8 5d 1e- from 3p3p 5 3d 8 4s 2, 3p 5 3d 9 4s, 3p 5 3d 9 4p, 3p 5 3d 9 4d, 3p 5 3d 9 5p 1e- from 3p, 3d 3p 5 3d 8 4s 4p, 3p 5 3d 8 4p 4d, 3p 5 3d 8 4s 5p, 3p 5 3d 8 4p 5s, 3p 5 3d 8 4p 5d, 3p 5 3d 8 4d 5p, 3p 5 3d 8 5s 5p, 3p 5 3d 8 5p 5d 2e- from 3d 3d 7 4s 2, 3d 7 4s 4p, 3d 7 4s 4d, 3d 7 4s 5s, 3d 7 4s 5p, 3d 7 4s 5d, 3d 7 4p 2, 3d 7 4p 4d, 3d 7 4p 5s, 3d 7 4p 5p, 3d 7 4p 5d, 3d 7 4d 2, 3d 7 4d 5s, 3d 7 4d 5p, 3d 7 4d 5d, 3d 7 5s 2, 3d 7 5s 5p, 3d 7 5s 5d, 3d 7 5p 2, 3d 7 5p 5d, 3d 7 5d 2 2e- from 3p 3p 4 3d 10 4s, 3p 4 3d 10 4d, 3p 4 3d 9 4s 2, 3p 4 3d 9 4p 2, 3p 4 3d 9 4d 2, 3p 4 3d 10 5s, 3p 4 3d 10 5p, 3p 4 3d 10 5d, 3p 4 3d 9 5s 2, 3p 4 3d 9 5p 2, 3p 4 3d 9 5d 2, 3p 4 3d 9 4s 4p

First Few Target Energy Terms of Ni II (Over 100 considered) statesymmetry Calculated Energy (Ryd) Exp Energy (Ryd) Difference (Calc-Expt) 1 2De2De Fe4Fe Fe2Fe Pe4Pe De2De Pe2Pe Ge2Ge Fe4Fe

Partial Ni II Collision Strengths (RM II codes not yet fully operational at OSC)

Benchmarking Laboratory and Astrophysical X-Ray Sources: Electron Impact Excitation Ne- like

Fe XVII Collision Strengths: Resonances up to n = 3 and n = 4 complexes Blue: Gaussian Average Filled Points: Distorted Wave Red: n =3 resonances

Fe XVII 3s/3d Ratio: Theory and Observations Chen and Pradhan (2004) Maxwellian average – solid line; Gaussian average – solid red line Filled Blue – LLNL EBIT; Open Blue – NIST EBIT Open red circles – Solar (T~ 4MK); Filled green – Capella (Chandra); Open green – “ (XMM) Extreme left – other measurements

Proposed (Re-) Calculations of Collision Strengths ~1000-level calculation for FeII, with (i) new BPRM codes (Eissner and Chen), (ii) parallel version (Ballance etal), (iii) RM II codes (Burke etal) Similarly for Ni II Converged collision strengths approaching ionization threshold(s) for FeXVII Other heavy elements ?