1. R-matrix calculations along iso-electronic sequences
Michael Witthoeft, Allan Whiteford, Nigel Badnell
University of Strathclyde

2. Introduction
Robust suite of R-matrix codes (LS, ICFT, Breit-Pauli, Dirac)
Increased availability of parallel computers +
Ability to efficiently calculate collision strengths along an iso-electronic sequence
Need:
an easier way to run an R-matrix calculation
to be able to quickly analyze the large amount of data

3. R-matrix Script
A flexible Perl script to automate an R-matrix calculation
works for serial or parallel machines
calculation sequence:
AUTOSCTRUCTURE (structure and high-energy limit points)
ICFT R-matrix calculation
produce adf04 file (fully commented)
supports radiation damping
no Auger damping yet

4. R-matrix Analysis Package (RAP)
RAP base package:
a set of Python routines that read and manipulate the R-matrix results
reads in:
adf04 files
AUTOSTRUCTURE output files (GF values)
TCCDW.DAT files (term coupling coefficients)
RAP GUI:
Graphical interface to the routines in the base package
Produce data files and plots of energies and effective collision strengths

5. F-like Sequence ICFT calculation with 87 terms and 195 levels.
contains the configurations
2s2 2p5 (two fine-structure levels)
2s 2p6
2s2 2p4 3l
2s 2p5 3l
2s2 2p4 4l
Scaling parameters for the structure are optimized for each individual ion.
All ions from Ne+ to Kr27+ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 36 30 31 32 33 34 35 Z
1 x 10-4
5 x 10-5
1 x 10-5
5 x 10-6

6. Structure

7. Energy Levels
Shown here are the energy levels for several ions along the sequence. We see that the levels scale as z2 for the higher-Z ions.

8. Energy Levels
Here are the energy levels for three ions split by configuration. Notice that the mixing between configurations decreases with increasing charge.

9. Energy of the fine-structure level compared to NIST
2s2 2p5 2P1/2

10. 2s2 2p4 3s 4P5/2 compared to NIST
This is representative of the other energy levels

11. GF value: 2s2 2p5 2P3/2 – 2s 2p6 2S1/2
relativistic Hartree-Fock calculation

12. GF value: 2s2 2p5 2P3/2 – 2s2 2p4 3s 2P3/2

13. GF value: 2s2 2p5 2P3/2 – 2s2 2p4 3d 2D5/2

14. Resonance Resolution

15. Si5+ Two energy meshes were used: 10-4 and 5x10-5.
A ratio plot gives a good overview of the convergence of the effective collision strengths with respect to energy mesh for a given temperature.
Only 1.2% of the transitions disagree by more than 10% between the two calculations.

16. Si5+ transitions from the ground term
The agreement for all of the these transitions is better than 10%.

17. Si5+
Here is another ratio plot, but now we are plotting as a function of transition energy.
The transitions on the right are the low-to-high transitions. The ones on the left are the high-to-high transitions.

18. Ti13+
2s2 2p5 2P3/2 - 2s2 2p4 3s 2S1/2

19. Comparisons

20. Fine-structure transition:
Present calculations compared against Berrington et al. (IP XXVIII).

21. Fine-structure transition: T = 104 z12 K

22. Fine-structure transition: T = 103 z12 K

23. 1-2 transition
Observe how the resonances move to lower scaled energy as Z increases.
The blue lines show 103 and 104 z12 K.

24. Fine-structure: Ne+

25. Fine-structure: Mg3+

26. Fine-structure: Si4+

27. Fine-structure: Fe17+

28. 2s2 2p5 2P3/2 – 2s 2p6 2S1/2
Ne+
Si5+
Ti13+
Fe17+

29. 2s2 2p5 2P3/2 – 2s2 2p4 3s 4P5/2
Ne+
Ti13+
Fe17+
Ni21+

30. Conclusions Complete F-like sequence has been calculated
Ne, Na, and Mg will be recalculated using observed energies
Sequences in progress: H-, He-, and Li-like (using radiation damping)
Next sequences will be the Ne- and Na-like