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 WaveCoupled 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 [OIII]

Doppler Double-Peaked

2500 5600Wavelength

Fe II

Sloan Quasar SDSS J2125-0813

Broad Line Region AGNModels by Sigut andPradhan (1998,2003),using IP data from the OSU group computedby H. Zhang, M. Bautista, S. Nahar etal., do NOT fit all spectra;accretion disk modelsfavored!

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

Model R A1 A2 A3 D2 D3 D3* E2 E3

Target

1 # of configurations 3 5 5 5 5 5 6 5 5

2 Total # of configurations 4 6 10 15 15 21 21 25 263 # sextet and quartet symmetries 16 21 21 21 21 21 27 21 214 # sextet and quartet states 38 113 113 113 113 113 154 113 113

5Total # of terms in the

calculation70 146 740 923 1627 1889 2236 2055 2065

Collisional5De symmetry

6 # of channels 81 247 247 247 247 247 336 247 247

7 # of correlation functions 36 59 210 309 825 1083 1083 1192 12165Ge symmetry

8 # of channels 108 335 335 3359 # of correlation functions 27 261 1002 1061

5Fe symmetry 10 # of channels 103 301 301 30111 # of correlation functions 33 319 1153 1243

5Pe symmetry 12 # of channels 57 161 16113 # of correlation functions 25 232 873

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 3d 3d9 , 3d8 4s, 3d8 4p, 3d8 4d, 3d8 5s, 3d8 5p, 3d8 5d

1e- from 3p 3p5 3d8 4s2, 3p5 3d9 4s, 3p5 3d9 4p, 3p5 3d9 4d, 3p5 3d9 5p

1e- from 3p, 3d

3p5 3d8 4s 4p, 3p5 3d8 4p 4d, 3p5 3d8 4s 5p, 3p5 3d8 4p 5s, 3p5 3d8 4p 5d, 3p5 3d8 4d 5p, 3p5 3d8 5s 5p, 3p5 3d8 5p 5d

2e- from 3d3d7 4s2 , 3d7 4s 4p, 3d7 4s 4d, 3d7 4s 5s, 3d7 4s 5p, 3d7 4s 5d, 3d7 4p2, 3d7 4p 4d, 3d7 4p 5s, 3d7 4p 5p, 3d7 4p 5d, 3d7 4d2, 3d7 4d 5s, 3d7 4d 5p, 3d7 4d 5d, 3d7 5s2, 3d7 5s 5p, 3d7 5s 5d, 3d7 5p2, 3d7 5p 5d, 3d7 5d2

2e- from 3p3p4 3d10 4s, 3p4 3d10 4d, 3p4 3d9 4s2, 3p4 3d9 4p2, 3p4 3d9 4d2, 3p4 3d10 5s, 3p4 3d10 5p, 3p4 3d10 5d, 3p4 3d9 5s2, 3p4 3d9 5p2, 3p4 3d9 5d2, 3p4 3d9 4s 4p

First Few Target Energy Terms of Ni II(Over 100 considered)

state symmetryCalculated Energy

(Ryd)Exp Energy (Ryd)

Difference(Calc-Expt)

12De 0.00 0.00 0.00

24Fe 0.0797524 0.0797594 -0.000007

32Fe 0.1236313 0.1236783 -0.000047

44Pe 0.2128118 0.2294408 0.016629

52De 0.2181346 0.2280366 0.009902

62Pe 0.2610079 0.2722299 0.011222

72Ge 0.2907616 0.3217966 0.031035

84Fe 0.4699065 0.5215355 -0.051629

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 ObservationsChen 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 ?