Transcript Document

Distorted-wave cross sections of electronimpact excitation and ionization for heavyelement impurities in fusion reactors
Honglin Zhang, James Colgan, Christopher Fontes, and
Joseph Abdallah, Jr.
Los Alamos National Laboratory, NM, USA
Second Co-ordinated Meeting on
Atomic Data for Heavy Element Impurities in Fusion Reactor
IAEA, Vienna, Sept. 26 – 28, 2007
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Outline
• Review of the LANL atomic codes.
• Semi-relativistic distorted-wave calculations of electron-impact excitation transitions from
n = 1, 2 and 3 levels to n = 2, 3, and 4 levels in H-like through Mg-like silicon, chlorine
and argon ions.
• Semi-relativistic distorted-wave calculations of collisional ionization for the ground levels.
• Configuration-average collisional ionization among all configurations included in the
targets.
• Energy levels and electric-dipole transition probabilities or oscillator strengths.
• Time-dependent close-coupling method for calculating electron-impact ionization cross
sections for Si2+ and Si3+, from both the ground and first excited configurations;
comparisons with the distorted-wave results and with experiment.
• The fully relativistic calculations of K-shell ionization for neutral Mn, Fe, Ni and Cu, and
L-shell ionization of neutral W. These are compared with experiment.
• Fully relativistic distorted-wave collision strength results for 16 optically allowed Dn=0
transitions with n=2 in Be-like ions with Z= 26-92.
• Semi-relativistic and fully-relativistic calculations of transition probabilities and
wavelengths for XeII and XeIII.
Slide 1
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Review of Los Alamos Atomic Physics Codes
LTE
Structure +
Oscillator
strengths +
Slater integrals
Non-LTE
CATS/
RATS
ACE
Photoionization
Populations from
Saha equation
+ UTA’s + spectrum
Structure +
Oscillator
strengths +
Slater integrals
Collisional excitation
GIPPER
Photoionization/
Collisional ionization/
Auto-ionization
ATOMIC
Populations from
rate equations
+ UTA’s + spectrum
Slide 2
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Calculation for Si, Cl and Ar ions
• Fine-structure energy levels and transition probabilities or
oscillator strengths using CATS.
• Electron-impact excitation collision strengths using ACE.
• Electron-impact ionization cross sections for fine-structure
transitions from the ground level of each ion using
GIPPER.
• Electron-impact ionization cross sections for transitions
between all configurations with GIPPER.
• Photoionization cross sections and autoionization rates
between all configurations with GIPPER (we could do finestructure calculations for these if there is a need).
Slide 3
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Si, Cl and Ar ions: structure calculations
•
Mg-like ions: 283 levels from 33 configurations:
3s2, 3s3p, 3p2, 3s3d, 3p3d, 3d2, 3l4l‘, 3l5l’
•
Na-like ions: 21 levels from 12 configurations:
3s, 3p, 3d, 4l, 5l
•
Ne-like ions: 89 levels from 15 configurations:
2s22p6, 2s22p53l, 2s2p63l, 2s22p54l, 2s2p64l
•
F-like ions: 279 levels from 23 configurations:
2s22p5, 2s2p6, 2s22p43l, 2s2p53l, 2p63l, 2s22p44l, 2s2p54l, 2p64l
•
O-like ions: 554 levels from 24 configurations:
2s22p4, 2s2p5, 2p6, 2s22p33l, 2s2p43l, 2p53l, 2s22p34l, 2s2p44l, 2p54l
•
N-like ions: 668 levels from 24 configurations:
2s22p3, 2s2p4, 2p5, 2s22p23l, 2s2p33l, 2p43l, 2s22p24l, 2s2p34l, 2p44l
Slide 4
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Si, Cl and Ar ions: structure calculations (continued)
•
C-like ions: 564 levels from 24 configurations:
2s22p2, 2s2p3, 2p4, 2s22p3l, 2s2p23l, 2p33l, 2s22p4l, 2s2p24l, 2p34l
•
B-like ions: 291 levels from 24 configurations:
2s22p, 2s2p2, 2p3, 2s23l, 2s2p3l, 2p23l, 2s24l, 2s2p4l,2p24l
•
Be-like ions: 98 levels from 17 configurations:
2s2, 2s2p, 2p2, 2s3l, 2p3l, 2s4l, 2p4l
•
Li-like ions: 15 levels from 9 configurations:
1s22s, 1s22p, 1s23l, 1s24l
•
He-like ions: 31 levels from 10 configurations:
1s2, 1s2s, 1s2p, 1s3l, 1s4l
•
H-like ions: 16 levels from 10 configurations:
1s, 2s, 2p, 3l, 4l
Slide 5
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Mg-like ions: energies for the lowest levels
Level
E (eV)
Si 2+
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
3s2
1S
0
0.00000
Cl 5+
0.00000
Ar 6+
0.00000
3s3p 3P0
6.36027 12.02826 13.90651
3s3p 3P1
6.37323 12.09013 13.99706
3s3p 3P2
6.39942 12.21780 14.18570
3s3p 1P1
9.91609 18.11198 20.82083
3p2
1D
2
15.16632 28.47162 32.90299
3p2
3P
0
15.96102 29.12013 33.48995
3p2
3P
1
15.97474 29.18966 33.59496
3p2
3P
2
16.00150 29.32343 33.79650
3s3d 3D1 17.62964 34.66120 40.18754
3s3d 3D2 17.62999 34.66636 40.19681
3s3d 3D3 17.63050 34.67413 40.21071
3p2
1S
0
18.75465 33.98256 39.05255
Slide 6
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Mg-like Si: sample transition energies and oscillator strengths
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
l(a)
DE (eV)
i
j
gf
A
lifetime
1
3 1.9454E+03 6.3732E+00 2.6785E-05 1.5736E+04 6.3550E-05
1
5 1.2503E+03 9.9161E+00 1.7329E+00 2.4645E+09 4.0575E-10
1 18 5.6921E+02 2.1782E+01 2.4751E-05 1.6985E+05 5.8875E-06
1 20 5.6484E+02 2.1950E+01 2.9973E-02 2.0887E+08 4.7876E-09
1 36 4.6645E+02 2.6580E+01 1.2160E-07 1.2426E+03 8.0478E-04
1 38 4.6382E+02 2.6731E+01 3.7889E-04 3.9159E+06 2.5537E-07
1 40 4.6362E+02 2.6743E+01 2.1463E-02 2.2202E+08 4.5042E-09
1 43 4.6165E+02 2.6857E+01 4.5996E-06 4.7985E+04 2.0840E-05
1 46 4.4245E+02 2.8022E+01 3.7456E-06 4.2540E+04 2.3507E-05
1 60 4.3168E+02 2.8721E+01 1.7947E-03 2.1413E+07 4.6701E-08
1 61 4.2755E+02 2.8999E+01 3.3155E-04 4.0328E+06 2.4797E-07
1 93 3.5816E+02 3.4617E+01 1.2305E-07 2.1328E+03 4.6886E-04
1 95 3.5757E+02 3.4675E+01 1.9837E-06 3.4496E+04 2.8989E-05
1 100 3.5635E+02 3.4793E+01 1.7776E-05 3.1124E+05 3.2130E-06
1 124 3.3393E+02 3.7129E+01 1.2132E-05 2.4190E+05 4.1339E-06
1 133 3.3249E+02 3.7289E+01 8.3950E-06 1.6884E+05 5.9228E-06
Slide 7
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Comparison of oscillator strengths with MCDF for B-like ions
(from the ground level 2s22p 2P1/2)
•
The second entries are results by
Grant’s MCDF code.
–
For n=2-2 transitions:
Zhang & Sampson, ADNDT, 56, 41 (1994)
–
For n=2-3 transitions:
Zhang & Sampson, ADNDT, 58, 255 (1994)
•
Agreement is generally good.
•
For these ions, relativistic effects are
not important.
•
The differences are likely due to less CI
included in the MCDF calculations.
•
For other ions, situations are similar.
Slide 8
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Collision strength calculations for Si, Cl and Ar ions
• The present work covers the following transitions:
– n=1 – 2, 3, 4 levels in H- and He-like ions
15, 30 transitions
– n=2 – 2, 3, 4 levels in Li- through F-like ions
25, 378, 2276, 5534, 5368, 2186, 276 transitions
– n=2 - 3, 4 levels in Ne-like ions
88 transitions
– n=3 – 3, 4, 5 levels in Na- and Mg-like ions
37, 3140 transitions
• Nine final electron energies were used in the present
calculations:
E’ = 0.01-9. DEmax
Slide 9
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Comparison with RDW results
•
Comparison with the published RDW
data for Be- through Na-like Si, Cl and
Ar is generally good.
•
One example is shown in the figure for
B-like Si, Cl and Ar ; The RDW results
are from Zhang & Sampson, ADNDT, 56,
41 (1994).
•
The discrepancy for higher energies is
not due to the relativistic effects, but to
the CI effect.
•
The red curves represent another
calculation from CATS/ACE with only
three n=2 configurations, as in the
RDW calculation, which almost
overlap with the RDW curves.
•
The present collision strength data
appear to be quite accurate.
Slide 10
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Electron-impact ionization
• Electron-impact ionization cross sections for fine-structure
transitions from the ground level of each ion using
GIPPER.
• Electron-impact ionization cross sections for transitions
between all configurations with GIPPER.
• Fully relativistic ionization cross sections for neutral Mn,
Fe, Ni and Cu.
• These are compared with experiment and/or timedependent close-coupling (TDCC) calculations.
Slide 11
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Electron-impact ionization calculations
•
Electron-impact ionization of Si2+ (3s2). We
compare our DW calculations with
measurements of Djuric et al [PRA 47,
4786 (1993)].
•
We also use the non-perturbative timedependent close-coupling (TDCC) method
to check the accuracy of the DW
calculations.
•
The TDCC calculations are somewhat
lower than DW, and in better agreement
with experiment.
•
At around 125 eV, excitation-autoionization
makes a significant contribution to the
ionization cross section. We choose to
only present direct ionization cross
sections, since the data we submit will
include DW ionization from all
configurations, including autoionizing
configurations.
•
Since we have calculated excitation and
autoionization data, the excitationautoionization contribution can be added.
Si2+
Slide 12
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Electron-impact ionization calculations
•
Electron-impact ionization of Si3+ (3s).
We compare our DW calculations with
measurements of Crandall et al [PRA
25, 143 (1982)].
•
We again use the non-perturbative
TDCC method to check the accuracy of
the DW calculations.
•
For this case, the TDCC calculations are
only slightly lower than the DW; both are
in good agreement with experiment for
the direct ionization component.
•
For the higher Si ions, this good
agreement allows us to use only the DW
method to compute ionization cross
sections (which are computationally
much easier to obtain).
•
At above 100 eV, excitationautoionization dominates the cross
section.
Si3+
Slide 13
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Electron-impact ionization calculations
•
Electron-impact ionization of Si7+ (2s2
2p3). We compare our DW calculations
with measurements of Zeijlmans et al
[PRA 47, 2888 (1993)].
•
We present ionization from both the 2s
and 2p sub-shells. Good agreement with
experiment is found.
•
The ionization cross section data which
will be submitted to IAEA includes cross
sections for all Si, Cl, and Ar ions using
our DW method. The TDCC calculations
for Si2+ and Si3+ can also be used, as
they are generally more accurate for
near-neutral systems.
•
For the more highly charged ions, the
DW results appear to be in good
agreement with available experiment,
and should be of sufficient accuracy for
modeling purposes.
Si7+
Slide 14
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Electron-impact ionization calculations – K-shell
•
We also have been able to use a fully
relativistic DW approach (RDW) to
calculate K-shell ionization of heavy
neutral targets, to compare with the
experimental measurements of
Professor Luo’s group.
•
Even though the ionization
measurements are from a solid target,
DW (isolated atom) calculations appear
to work well.
•
Agreement with experiment is excellent.
•
Further semi-relativistic DW (SRDW)
calculations show that a fully relativistic
approach is necessary for these tightly
bound electrons to obtain good
agreement with experiment.
Mn K-shell
Slide 15
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Electron-impact ionization calculations – K-shell
• Similar conclusions can be drawn
from the other targets in our study,
in this case Fe.
Fe K-shell
• K-shell ionization cross sections
were calculated for Mn, Fe, Ni, and
Cu.
• These comparisons were recently
published [Colgan et al, PRA 73,
062711 (2006)].
• We look forward to investigating the
K-shell ionization of other heavy
targets of interest to this working
group.
Slide 16
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Electron-impact ionization calculations – L-shell
• The Luo group has also been able
to study ionization from the L-shell
of W.
W L-shell
• We again use our RDW method to
compute ionization from the 2s1/2
and 2p1/2 & 2p3/2 sub-shells. The
inset shows the individual shell
contributions.
• The agreement with experiment is
still quite good, although not as
spectacular as for the K-shell
studies.
• Differences here may be due to
interactions of the ejected electron
with bound electrons, which are only
approximately taken into account in
the RDW calculations.
Slide 17
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“Top-up”: semi-relativistic Coulomb-Bethe approximation vs. fully
relativistic Kummer transformation for high-Z ions
•
Coulomb-Bethe Approximation
l1
  
RDW
l
l 0
•


 l
l1
   lRDW 
CBe
l 0
l l11


CBe
l
l l11
Kummer Transformation
l1
l1
l 0
l 0
Ω   lRDW  (RPWB -  lRPWB )
•
The figure (shown in my June 2005
talk; for He-like ions) shows that the
SR CBe omits relativistic effects in the
continuum and is not accurate for high
energies.
•
We need to update the previously
published Dn=0 collision strengths for
Be- through O-like ions.
Slide 18
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New calculations for Be-like ions with RDW method
• 10 n=2 levels from 2s2, 2s2p and 2p2 configurations
• The previously published results were for
– Z=8-92
– 45 transitions
– for 6 final energies E’=0.03, 0.08, 0.2, 0.42, 0.8, 1.4 Z2eff Ryd, with Zeff=Z-2.5
• The new calculation covers
– Z=26-92
– the highest 3 energies E’=0.42, 0.8, 1.4
– 16 optically allowed transitions, where “top-up” contribution is large
• Comparison of new results with the published data shows
up to 38% increase in collision strengths.
Slide 19
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Structure calculations for XeII and XeIII
• To compare wavelengths and transition probabilities or fvalues with Dr. Cornille’s results, using lists of
configurations she provided
– XeII: 5s25p5, 5s25p45d, 5s25p46s, 5s25p46p
– XeIII: 5s25p4, 5s25p35d, 5s25p36s, 5s25p36p
• Semi-relativistic calculation with CATS
• Fully relativistic calculations with RATS
– Without Breit interaction
– With Breit interaction
Slide 20
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Future work
• Extend calculations for Si, Cl and Ar to near-neutral ions
and neutral atoms.
• Fine-structure photoionization cross sections and
autoionization rates, if needed.
• Heavier elements such as Fe, Ni and Xe.
• New relativistic collision strength calculations for B-, C-,
N-, O-like ions using the RDW method with the Kummer
transformation.
Slide 21
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