This document discusses the need for reliable atomic data and spectral models for lowly ionized iron-peak species like Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu. Current models are inaccurate, with predicted line intensities disagreeing with observations by factors of several. The goals of the project are to compute new atomic data, construct improved spectral and opacity models, and implement the models in photoionization codes. The document outlines challenges in modeling these ions and describes ongoing work using relativistic R-matrix methods to calculate improved collision strengths and photoionization cross sections.

1. Atomic Data and Spectral Models
for Lowly Ionized Iron-peak
Species
Manuel Bautista, Vanessa Fivet
(Western Michigan University)
Pascal Quinet
(Mons University, Belgium)
Connor Ballance
(Auburn University)

2. • Reliable modeling of neutral through
doubly ionized Sc, Ti, V, Cr, Mn, Fe, Co,
Ni, Cu is of great importance in various
areas, e.g. H II regions, SNe remnants,
AGN, supernovae light curves as
cosmological candles, atmospheres of the
Sun and late type stars, afterglows of
GRBs, etc.

3. Emission spectra of η Carinae

4. Absorption spectrum of QSO 0059-2735. The spectrum is dominated by
absorption features from the ground and excited levels of Cr II, Fe II, Fe III,
Co II, Ni II, Mn II, and possibly Ti II

5. • For most of these ions there are yet no
spectral models available because even
the fundamental atomic parameters are
unknown.
• For those ions that have been studied in
the past, such as Fe II and Fe III, there
was mounting evidence on that the models
were inaccurate.

6. • For instance, predicted line intensities for
Fe II in the Orion nebula, the simplest and
best known nebular environment to
astronomy, disagree with observations by
up to several factors.

7. Ratio of CLOUDY predicted [Fe II] line intensities to
observed values in the Orion nebula (Verner et al 2000).

8. [Fe III] and [Fe IV]
• A discrepancy of about a factor ~3 remains in
the Fe abundances derived from [Fe III] and
[Fe IV]
• Rodriguez & Rubin (2004) argue that the errors
could be either in the collision strengths or the
total Fe3++e -> Fe++ recombination
• Current collision strengths (Zhang 1996), but
McLaughlin et al. (2002) report LS collision
strengths lower by a factor of 2

9. Fe II
• Excitation mechanisms for Fe II include electron
impact, photoexcitation by continuum radiation,
and fluorescence by Lyα.
• Current models include over 800 levels
(>300.000 transitions), e.g. Bautista et al.
(2004).
• But data still incomplete and unchecked.

10. Collisional coupling of pseudo-
metastable levels

11. Bautista et al. (2004)

12. Comparison between bound-free cross sections of
Bautista (1997) and hydrogenic approximations

13. Comparison of theoretical and observed emergent fluxes of
the solar atmosphere

14. Goals of the project
• Computation of reliable and complete data sets (A-
values for allowed and forbidden transitions,
collision strengths, photoionization cross sections
and recombination rate coefficients) for neutral,
singly and doubly ionized iron-peak species
• Construction of spectral and opacity models whose
quality will be benchmarked by modeling spectra of
AGN and Eta Carinae
• Distribution of the data and models among the
scientific community
• Implementing the atomic models into the
photoionization modeling codes XSTAR (Kallman &
Bautista 2001) and CLOUDY (Ferland et al. 1998)

15. Atomic Physics
Hi  Ei i
N
pi2 N
Ze2 e2
H   
i 1 2me i 1 ri i  j r  rj
i
two  electron 1 N ( N  1)

one  electron 2 ZN
1 1
For neutral atoms 
4 2

16. Atomic Physics, cont.
• The two electron terms yield electron-
electron correlations (radial and angular)
• Current methods deal with electron
correlations by:
1) optimization of radial functions
2) configuration interaction (CI)
(CI: correlated solutions are written as
linear combinations of non-correlated
configurations)

17. Why are low Fe-peak ions
difficult?
• Very large number of metastable levels
that participate in the spectra.
• Strong radial correlations
• Strong angular correlations
• CI: always large but difficult to reach
convergence
• Relativistic effects

18. Atomic structure calculations
• We use a combination of methods and codes:
- HFR (Cowan codes)
- MCDF (GRASP/GRASP92)
- TFD central potential (SUPERSTRUCTURE)
- We derive non-spherical multipole corrections
to the TFD potential (Bautista 2008) that account
for polarization and electron-electron
correlations of filled and half-filled shells.

19. Angular electron correlation
Calculated vs. measured energies in O I (2p4)
Experiment (Ry) Theory (Ry)
3P 0 0
1D 0.144 0.160
1S 0.308 0.374

20. The O I problem
• Ground configuration 1s22s22p4
3P 0 Ry
J
1D 0.144 Ry
1S 0.307 Ry
• Two important lines are the trans-auroral
line at 2972Å (1S0-3P1) and the green line
at 5577Å (1S0-1D2)

21. • The A-values recommended by NIST are
A(2972 Å) = 7.54e-2
A(5577 Å) = 1.26
and
A(5577Å)/A(2972Å) = 16.7
From Froese Fischer (1983) and Baluja &
Zeippen (1988)
Accuracy rating: B+

22. Theoretical Determination of the
OI 557.7/297.2 nm Intensity Ratio
• Condon, 1934 11.1
• Pasternack, 1940 24.4
• Garstang, 1951 16.4
• Yamanouchie and Horie, 1952 30.4
• Garstang, 1956 17.6
• Froese Fischer and Saha, 1983 13.6
• Baluja and Zeippen, 1988 13.0
• Galavis, et al., 1997 14.2
• Froese Fischer and Tachiev, 2004 16.1
• NIST 16.7

23. Observational Determination of
the OI 557.7/297.2 nm Ratio
• Sharp and Siskind, 1989 ~9
• Slanger et al., 2006 9.8±1.0
• Gattinger et al., 2009 9.3±0.5
• Gattinger et al., 2010 9.5±0.5

24. A(1S0-1D2 ) A(1S0-3P1 ) Ratio
n=3 single prom. 1.50 0.28 5.3
n=3 double prom. 1.44 0.29 4.9
n=4 single prom. 6.36 0.38 18.8
n=4 double prom. 1.45 0.29 4.9
n=4 trip prom. 1.45 0.24 6.2
n=5 double prom. 1.50 0.069 21.8
n=5 triple prom. 2.26 0.073 30.9

25. The Fe III problem
Ratio of observed [Fe III] lines in the Orion nebula lines to
predictions by previous models.

26. Approaches for scattering
calculations
• LS R-matrix + ICFT: allows for very large
CI/CC expansions and ICFT includes
relativistic effects in the outer-box region
• Breit Pauli R-matrix: includes relativistic
effects, but limited CI=CC expansion
• DARC: fully relativistic calculation but for
small CC expansion.

28. Maxwellian-averaged Collision
Strengths at 10,000 K for Fe III
Upper lRM+ICFT DARC Zhang
5D 4.57E+0 2.54E+0 2.92E+0
3
5D 1.94E+0 1.11E+0 1.24E+0
2
5D 8.79E-0 5.33E-1 5.95E-1
1
5D 2.51E-1 1.60E-1 1.80E-1
0
3P2 7.14E-1 7.14E-1 5.80E-1
2
3P2 1.84E-1 1.96E-1 1.65E-1
1
3P2 3.83E-2 3.25E-2 2.13E-2
0
3H 2.66E+0 1.21E+0 1.34E+0
6
3H 1.10E+0 9.84E-1 4.89E-1
5
3H 2.41E-1 5.33E-1 9.26E-2
4
3F2 1.47E+0 4.54E-1 1.07E+0
4
3F2 6.42E-1 1.91E-1 4.35E-1
3
3F2 2.11E-1 1.73E-1 1.57E-1
2
3G 1.11E+0 1.36E+0 1.10E+0
5
3G 1.24E+0 1.11E+0 4.28E-1
4
3G 4.52E-1 4.21E-1 1.09E-1
3

29. (Itheo-Iobs)/Iobs New Fe III model

30. • Collision strengths for forbidden transitions
are dominated by resonances.
• All previous calculations use LS-coupling
R-matrix, which does not include
relativistic effects in resonance positions
• Fully relativistic R-matrix methods are
needed

31. Photoionization of Fe+
 3p 6 3d 6 

 
 
3p 3d 4s  h   3p 6 3d 5 4s
6 6
 e
 
 3p 6 3d 5 nl 
 
 3p 6 3d 6 
 3p 5 3d 8  
   
 
  5 7    3p 6 3d 5 4s e
 3p 3d 4s  
  
 3p 6 3d 5 nl 
 

32. Top: LS cross section of Nahar & Pradhan (2002). Middle:
present DARC calculations. Lower: experiment
(Kjeldsen et al. (2002)

34. The Fe II problem
• We are carrying out fully relativistic
R-matrix calculations for Fe II
• We compare here with 75 lines measured
in the optical spectrum of Orion by
Mesa-Delgado et al. (2009).
• Density and temperature are known from
other species (ne=1.4x104 cm-3, T=9000K)

36. Spectral models for iron-peak ions
Sc Ti V Cr Mn Fe Co Ni
I
II B07 B06 M06 B10a B05 B04
III B10b B01
IV Z97 M05

37. Photoionization cross sections for
Iron-peak ions

38. Conclusions
• Atomic data underpins most astronomical
studies, from modeling microphysics processes,
to diagnostics of plasma conditions, to full
analysis of spectra.
• Atomic data for neutral and singly ionized
species are important in Op/UV astronomy.
• Though, these computations test the limits of
atomic methods.

39. Conclusions, cont.
• For effective collision strengths @ 104 K one
must a good representation of low energy
resonances, mostly formed in the inner-box
region
=> relativistic calculations must be performed
(DARC)
• When doing LS-calculations the larger the
expansion the worse the results

40. Conclusions, cont.
• New theoretical methods and computational
tools are needed to treat electron-electron
correlations.
• We have created a new open forum (blog) to
discuss atomic data issues in astronomy
http://astroatom.wordpress.com/