Motivation
Atomic structure
Effective collision strengths
Conclusions
Validity of the ICFT R-matrix method: Be-like Al9+ a
case of study
L. Fernández-Menchero
University of Strathclyde. United Kingdom.
ADAS Workshop October 2015. Catania, Italy.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
1 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Contents
1
Motivation
2
Atomic structure
3
Effective collision strengths
4
Conclusions
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
2 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Contents
1
Motivation
2
Atomic structure
3
Effective collision strengths
4
Conclusions
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
3 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Motivation
Work on Be-like isoelectronic sequence. 238-level CI/CC expansion,
ICFT.
MZB-2014: L. Fernández-Menchero, G. Del Zanna, N. R. Badnell
2014, Astron. Astrophys., 566, A104.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
4 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Motivation
Work on Be-like isoelectronic sequence. 238-level CI/CC expansion,
ICFT.
MZB-2014: L. Fernández-Menchero, G. Del Zanna, N. R. Badnell
2014, Astron. Astrophys., 566, A104.
Previous work. 98-level CI/CC expansion, DARC.
AK-2014: K. M. Aggarwal, F. P. Keenan 2014, Mon. Not. R. Astr.
Soc., 438, 1223.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
4 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Motivation
Work on Be-like isoelectronic sequence. 238-level CI/CC expansion,
ICFT.
MZB-2014: L. Fernández-Menchero, G. Del Zanna, N. R. Badnell
2014, Astron. Astrophys., 566, A104.
Previous work. 98-level CI/CC expansion, DARC.
AK-2014: K. M. Aggarwal, F. P. Keenan 2014, Mon. Not. R. Astr.
Soc., 438, 1223.
Work MZB-2014 received a hard critique: DARC vs ICFT, resonance
resolution, energy range.
K. M. Aggarwal, F. P. Keenan 2015, Mon. Not. R. Astr. Soc., 447,
3849.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
4 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Motivation
Work on Be-like isoelectronic sequence. 238-level CI/CC expansion,
ICFT.
MZB-2014: L. Fernández-Menchero, G. Del Zanna, N. R. Badnell
2014, Astron. Astrophys., 566, A104.
Previous work. 98-level CI/CC expansion, DARC.
AK-2014: K. M. Aggarwal, F. P. Keenan 2014, Mon. Not. R. Astr.
Soc., 438, 1223.
Work MZB-2014 received a hard critique: DARC vs ICFT, resonance
resolution, energy range.
K. M. Aggarwal, F. P. Keenan 2015, Mon. Not. R. Astr. Soc., 447,
3849.
Reply: L. Fernández-Menchero, G. Del Zanna and N. R. Badnell
2015, Mon. Not. R. Astr. Soc., 450, 4174.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
4 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Motivation
238-level ICFT of MZB-2014 gives in general larger results for the
effective collision strengths Υ than 98-level DARC of AK-2014.
Electron exchange included by AK-2014 for more angular momenta
than MZB-2015: 2J = 81 vs 2J = 23.
Energy step length of AK-2014 slight finer than MZB-2014, depends
on ion.
AK-2014 goes further in scattering energy than MZB-2014: 12 times
versus 3 times the ionization potential plus interpolation up to
E = ∞ in Burgess–Tully domain.
DARC vs ICFT.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
5 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Motivation
238-level ICFT of MZB-2014 gives in general larger results for the
effective collision strengths Υ than 98-level DARC of AK-2014.
Electron exchange included by AK-2014 for more angular momenta
than MZB-2015: 2J = 81 vs 2J = 23.
Energy step length of AK-2014 slight finer than MZB-2014, depends
on ion.
AK-2014 goes further in scattering energy than MZB-2014: 12 times
versus 3 times the ionization potential plus interpolation up to
E = ∞ in Burgess–Tully domain.
DARC vs ICFT.
MZB-2014 has a much larger configuration interaction and close
coupling expansion than AK-2014: 238 levels vs 98 levels.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
5 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Contents
1
Motivation
2
Atomic structure
3
Effective collision strengths
4
Conclusions
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
6 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Atomic energies
238-level CI structure1 configurations 1s2 {2s2 , 2s2p, 2p2 }, 1s2 2{s, p} nl,
with n = 3 − 7 and l = s, p, d, f, g for n = 3 − 5 and
l = s, p, d for n = 6 − 7.
Total 130 terms, 238 levels.
98-level CI structure2 configurations 1s2 {2s2 , 2s2p, 2p2 }, 1s2 2{s, p} nl,
with n = 3 − 4 and l = s, p, d, f.
Total 54 terms, 98 levels.
1
L. Fernández-Menchero, G. Del Zanna and N. R. Badnell 2014, Astron.
Astrophys., 566, A104.
2 Present work (for test comparison).
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
7 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Atomic energies
Table: Al9+ target levels. All energies are in cm−1 .
i
1
2
3
4
5
6
7
8
9
10
Conf. Level
2s2 1 S0
2s 2p 3 Po0
2s 2p 3 Po1
2s 2p 3 Po2
2s 2p 1 Po1
2p2 3 P0
2p2 3 P1
2p2 3 P2
2p2 1 D2
2p2 1 S0
L. F. Menchero (Univ. Strathclyde)
ENIST
0.
155148.
156798.
160429.
300490.
404574.
406517.
409690.
449732.
553783.
E98
0.
155722.
157487.
161146.
309273.
408026.
409969.
413420.
458157.
567794.
( %)
( 0)
(0.4)
(0.4)
(0.4)
(2.9)
(0.9)
(0.8)
(0.9)
(1.9)
(2.5)
Validity of the ICFT R-matrix method
E238
0.
155539.
157404.
161278.
307209.
407826.
409888.
413526.
457831.
567267.
( %)
( 0)
(0.3)
(0.4)
(0.5)
(2.2)
(0.8)
(0.8)
(0.9)
(1.8)
(2.4)
ADAS Workshop 2015
8 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Atomic energies
Table: Al9+ target levels. All energies are in cm−1 .
i
88
89
90
91
92
93
94
95
96
97
98
Conf. Level
2p 4f 3 P3
2p 4f 3 P4
2p 4f 3 P5
2p 4f 3 D3
2p 4f 1 D4
2p 4f 3 D2
2p 4p 1 S0
2p 4f 3 D1
2p 4f 1 D2
2p 4d 1 Fo3
2p 4d 1 Po1
L. F. Menchero (Univ. Strathclyde)
ENIST
−
−
−
−
−
−
−
−
−
−
−
E98
2712961.
2713531.
2715225.
2716473.
2717105.
2717141.
2717922.
2718397.
2719895.
2722212.
2723448.
(%)
(−)
(−)
(−)
(−)
(−)
(−)
(−)
(−)
(−)
(−)
(−)
Validity of the ICFT R-matrix method
E238
2706897.
2707350.
2708632.
2710743.
2710218.
2711361.
2706869.
2712736.
2713991.
2715080.
2716711.
(%)
(−)
(−)
(−)
(−)
(−)
(−)
(−)
(−)
(−)
(−)
(−)
ADAS Workshop 2015
9 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Infinite energy point
2
10
n=4
n=3
n=2
1
10
0
238-level CI
10
75-80
-1
10
73-81
31-41
-2
10
-3
10
-4
10
-4
10
-3
10
-2
10
-1
10
98-level CI
0
10
1
10
2
10
Figure: Transition infinite energy points y∞ = ΩPWB
or 34 S for two different
∞
atomic structures: 98-level CI versus 238-level CI.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
10 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Contents
1
Motivation
2
Atomic structure
3
Effective collision strengths
Peak abundance temperature
Low temperature
High temperature
4
Conclusions
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
11 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Peak abundance temperature
Result comparison
2
2
10
10
n=4
n=3
n=2
1
10
n=4
n=3
n=2
1
10
75-80
0
238-level CI/CC
BP
10
-1
10
-2
10
-3
73-81
31-41
-1
10
-2
10
-3
10
10
-4
10
0
10
-4
-4
10
-3
10
-2
10
-1
10
ICFT
0
10
1
10
2
10
10
10
-4
-3
10
-2
10
-1
10
98-level CI/CC
0
10
1
10
2
10
Figure: Effective collision strengths for electron-impact excitation of the ion Al9+
at T = 106 K. Left: Breit–Pauli versus ICFT, 98 level CI/CC; right: 98-level
CI/CC versus 238-level CI/CC, ICFT.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
12 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Peak abundance temperature
Result comparison
Table:
Number of transitions in figures which differ by more than a certain relative error
δ = |ΥA − ΥB |/ΥB (or Υ → y∞ ), as a percentage.
Rel. error (%)
1
2
3
4
5
6
7
8
9
10
20
30
40
50
75
100
150
200
300
1000
Total
L. F. Menchero (Univ. Strathclyde)
y∞
98 vs 238 CI
3778
3600
3416
3266
3141
3022
2914
2804
2722
2644
2068
1643
1356
1163
846
707
538
443
336
187
4035
98 CI/CC Υ
BP vs ICFT
1336
803
500
350
260
206
158
127
106
82
22
9
4
2
2
2
1
0
0
0
4753
ICFT Υ
98 vs 238 CI/CC
4579
4400
4243
4077
3928
3798
3676
3569
3460
3357
2582
2090
1725
1449
1113
901
647
505
320
88
4753
Validity of the ICFT R-matrix method
ADAS Workshop 2015
13 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Peak abundance temperature
Result comparison
10
10
5
0
0
-5
-5
238-lev > 98-lev
-10
-15
238-lev > 98-lev
-10
-15
-20
-20
n=4
n=3
n=2
-25
-30
R = ϒ98/ϒ238
R = ϒ98/ϒ238
98-lev > 238-lev
98-lev > 238-lev
5
0
20
40
60
Lower level (i)
80
-25
100
-30
0
n=4
n=3
n=2
20
40
60
Upper level (i)
80
100
Figure: The ratio of effective collision strengths from 98- vs 238-level CI/CC
ICFT R-matrix calculations vs left: lower level and right: upper level index for all
inelastic transitions amongst the 98 lowest common levels of Al9+ at T = 106 K.
Positive values indicate Υ98 > Υ238 and negative values Υ238 > Υ98 .
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
14 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Peak abundance temperature
Result comparison
Comparing different relativistic formalism the differences are minimal.
Only a few spin-change transitions present differences, and they are
much smaller compared with CI/CC differences.
Comparing different atomic structures, differences in the results Υ are
, 43 S.
same order as differences in the atomic structure ΩPWB
∞
Υ for 238-level CI/CC expansion are in general larger than the ones
, 43 S was symmetrical.
for 98-level CI/CC expansion, while ΩPWB
∞
Differences are considerable larger for transitions to the n = 4 shell
than for the n = 2, 3 ones.
98-level CC expansion is not converged for the n = 4 atomic shell.
238-level CI expansion gives a much more accurate atomic structure
than 98-level.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
15 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Low temperature
Result comparison
2
10
n=4
n=3
n=2
1
238-level CI/CC
10
0
10
-1
10
-2
10
-3
10
-4
10
-4
10
-3
10
-2
10
-1
10
98-level CI/CC
0
10
1
10
2
10
Figure: Effective collision strengths for electron-impact excitation of the ion Al9+
at T = 2 × 104 K. 98-level CI/CC versus 238-level CI/CC, ICFT.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
16 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Low temperature
Result comparison
Differences between atomic structures much larger than at the peak
abundance temperature.
Position or resolution of resonances.
Both same step lengths and checked convergence. Resolution of the
resonances discarded.
Differences in position of the resonances due to atomic structure.
238-level CI expansion much more reliable than 98-level one, mainly
for levels in the n = 4 atomic shell.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
17 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
High temperature
Result comparison
Table: Comparison of effective collision strengths, Υ, at T = 2 × 107 K and the
reduced quantity y∞ at infinite temperature. A (B) denotes A × 10B .
DARC
i–j
T (K )
1–52
1–64
1–70
1–80
98-level CI/CC
2 × 107
3.01 (−2)
1.70 (−4)
5.29 (−6)
8.45 (−6)
ICFT
98-level CI/CC
2 × 107
3.20 (−2)
1.96 (−4)
4.23 (−6)
7.05 (−6)
∞
2.40 (−2)
1.01 (−4)
2.68 (−6)
−
238-level CI/CC
2 × 107
3.22 (−2)
9.40 (−5)
2.18 (−5)
1.09 (−5)
∞
2.64 (−2)
1.63 (−5)
2.18 (−5)
−
DARC: K. M. Aggarwal and F. P. Keenan 2014, Mon. Not. R. Astr. Soc., 438, 1223
98-level ICFT: present work
238-level ICFT: L. Fernández-Menchero, G. Del Zanna, N. R. Badnell 2014, Astron. Astrophys.,
566, A104.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
18 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
High temperature
Differences at high temperature
MZB-2014 calculated Ω up to three times the ionization potential and
interpolated in Burgess–Tully domain.
A. Burgess and J. A. Tully 1992. Astron. Astrophys., 254, 436–453.
AK-2014 calculated Ω up to twelve times the ionization potential and did
not perform any interpolation up to infinity.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
19 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
High temperature
2×10
1×10
-2
-2
-2
-2
00
0.2 0.4 0.6 0.8
Reduced energy
1 − 52
21
2s
S0 − 2s4p
1
4×10
3×10
2×10
1×10
-4
4×10
-4
-4
-4
00
0.2 0.4 0.6 0.8
Reduced energy
1 − 64
1
Po
1
21
2s
3×10
2×10
1×10
-5
-5
-5
-5
00
1
0.2 0.4 0.6 0.8
Reduced energy
1 − 70
S0 − 2p4s
1
Po
1
21
2s
1
Reduced collision strength
3×10
Collision strength
4×10
Reduced collision strength
Reduced collision strength
Burgess–Tully diagram
2×10
1×10
-4
-4
00
0.2 0.4 0.6 0.8
Reduced energy
1
1 − 80
3
S0 − 2p4p P0
2s2 1 S0 − 2p4f 1 F3
Figure: Reduced collision strengths versus energy from 238-level CI/CC ICFT
R-matrix calculations for selected transitions of Al9+ .
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
20 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
High temperature
Result comparison
Calculated Ω reached asymptotic form. Interpolation in Burgess–Tully
domain properly done.
Differences in the infinite energy point lead to differences in the Υ for
high temperature.
Infinite energy points more reliable for 238-level CI expansion than for
98-level CI expansion.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
21 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Contents
1
Motivation
2
Atomic structure
3
Effective collision strengths
4
Conclusions
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
22 / 24
Motivation
Atomic structure
Effective collision strengths
Conclusions
Conclusions
Three main error sources: atomic structure, close coupling expansion
and inclusion of relativistic effects.
Different atomic structures / CI expansions lead to large differences,
mainly at high temperature / energy.
A larger CC expansion improves strongly the results, mainly for the
higher excited terms / levels.
Method to consider the relativistic effects (ICFT, BP, DARC) does
not change meaningfully the results.
No calculation can guarantee the quality of the results for the last
terms / levels included in the close-coupling expansion.
Nothing special about Be-like Al9+ . Same conclusions can be applied
to other ions and sequences.
For example: Fe13+ : G. Del Zanna, N. R. Badnell, L.
Fernández-Menchero, G. Y. Liang, H. E. Mason and P. J. Storey
2015. Mon. Not. R. Astron. Soc. In press.
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
23 / 24
Motivation
Atomic structure
Effective collision strengths
MNRAS 450, 4174–4183 (2015)
Conclusions
doi:10.1093/mnras/stv887
Validity of the ICFT R-matrix method: Be-like Al 9+ a case study
L. Fernández-Menchero,1‹ G. Del Zanna2 and N. R. Badnell1
1 Department
2 Department
of Physics, University of Strathclyde, Glasgow G4 0NG, UK
of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
Accepted 2015 April 20. Received 2015 April 16; in original form 2015 March 16
Thank you for your attention
L. F. Menchero (Univ. Strathclyde)
Validity of the ICFT R-matrix method
ADAS Workshop 2015
24 / 24