R-matrix calculations along iso-electronic sequences
Michael Witthoeft, Allan Whiteford, Nigel Badnell University of Strathclyde
Introduction
Robust suite of R-matrix codes (LS, ICFT, BreitPauli, 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
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
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
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+
5 x 10-6 1 x 10-5 5 x 10-5 1 x 10-4 Z 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Structure
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.
Energy Levels
Here are the energy levels for three ions split by configuration. Notice that the mixing between configurations decreases with increasing charge.
Energy of the fine-structure level compared to NIST
2s2 2p5 2P1/2
2s2 2p4 3s 4P5/2 compared to NIST This is representative of the other energy levels
GF value: 2s2 2p5 2P3/2 – 2s 2p6 2S1/2
GF value: 2s2 2p5 2P3/2 – 2s2 2p4 3s 2P3/2
GF value: 2s2 2p5 2P3/2 – 2s2 2p4 3d 2D5/2
Resonance Resolution
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.
Si5+
transitions from the ground term
The agreement for all of the these transitions is better than 10%.
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-tohigh transitions. The ones on the left are the high-to-high transitions.
Ti13+
2s2 2p5 2P3/2 - 2s2 2p4 3s 2S1/2
Comparisons
Fine-structure transition:
Present calculations compared against Berrington et al. (IP XXVIII).
Fine-structure transition: T = 104 z12 K
Fine-structure transition: T = 103 z12 K
1-2 transition Observe how the resonances move to lower scaled energy as Z increases.
The blue lines show 103 and 104 z12 K.
Fine-structure: Ne+
Fine-structure: Mg3+
Fine-structure: Si4+
Fine-structure: Fe17+
2s2 2p5 2P3/2 – 2s 2p6 2S1/2
Ne+
Si5+
Ti13+
Fe17+
2s2 2p5 2P3/2 – 2s2 2p4 3s 4P5/2
Ne+
Ti13+
Fe17+
Ni21+
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