R-matrix calculations along iso-electronic

sequences

Michael Witthoeft, Allan Whiteford, Nigel BadnellUniversity of Strathclyde

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

• 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 Script

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

R-matrix Analysis Package (RAP)

• 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+

F-like Sequence

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3630 31 32 33 34 35Z

1 x 10-4

5 x 10-5

1 x 10-5

5 x 10-6

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-to-high transitions. The ones on the left are the high-to-high transitions.

Ti13

+2s2 2p5 2P3/2 - 2s2 2p4 3s 2S1/2

Comparisons

Present calculations compared against Berrington et al. (IP XXVIII).

Fine-structure transition:

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 z1

2 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+

Ni21+Fe17+

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