Operated by the Los Alamos National Security, LLC for the DOE/NNSA Distorted-wave cross sections of electron- impact excitation and ionization for heavy-

Operated by the Los Alamos National Security, LLC for the DOE/NNSA

Distorted-wave cross sections of electron-impact excitation and ionization for heavy-

element 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

Slide 2


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 n=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 3


CATS/RATS

ACE

GIPPER

ATOMIC

LTE Non-LTEStructure +Oscillator strengths +Slater integrals

Structure +Oscillator strengths +Slater integrals

Collisional excitation

PhotoionizationPhotoionization/Collisional ionization/Auto-ionization

Populations fromSaha equation+ UTA’s + spectrum

Populations fromrate equations+ UTA’s + spectrum

Review of Los Alamos Atomic Physics Codes

Slide 4


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 fine-structure calculations for these if there is a need).

Slide 5


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:


Slide 6


Si, Cl and Ar ions: structure calculations (continued)

• C-like ions: 564 levels from 24 configurations:


• 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 7


Mg-like ions: energies for the lowest levels

Level E (eV)

Si 2+ Cl 5+ Ar 6+

1. 3s2 1S0 0.00000 0.00000 0.00000

2. 3s3p 3P0 6.36027 12.02826 13.90651

3. 3s3p 3P1 6.37323 12.09013 13.99706

4. 3s3p 3P2 6.39942 12.21780 14.18570

5. 3s3p 1P1 9.91609 18.11198 20.82083

6. 3p2 1D2 15.16632 28.47162 32.90299

7. 3p2 3P0 15.96102 29.12013 33.48995

8. 3p2 3P1 15.97474 29.18966 33.59496

9. 3p2 3P2 16.00150 29.32343 33.79650

10. 3s3d 3D1 17.62964 34.66120 40.18754

11. 3s3d 3D2 17.62999 34.66636 40.19681

12. 3s3d 3D3 17.63050 34.67413 40.21071

13. 3p2 1S0 18.75465 33.98256 39.05255

Slide 8


Mg-like Si: sample transition energies and oscillator strengths

i j (a) E (eV) gf A lifetime

1. 1 3 1.9454E+03 6.3732E+00 2.6785E-05 1.5736E+04 6.3550E-05

2. 1 5 1.2503E+03 9.9161E+00 1.7329E+00 2.4645E+09 4.0575E-10

3. 1 18 5.6921E+02 2.1782E+01 2.4751E-05 1.6985E+05 5.8875E-06

4. 1 20 5.6484E+02 2.1950E+01 2.9973E-02 2.0887E+08 4.7876E-09

5. 1 36 4.6645E+02 2.6580E+01 1.2160E-07 1.2426E+03 8.0478E-04

6. 1 38 4.6382E+02 2.6731E+01 3.7889E-04 3.9159E+06 2.5537E-07

7. 1 40 4.6362E+02 2.6743E+01 2.1463E-02 2.2202E+08 4.5042E-09

8. 1 43 4.6165E+02 2.6857E+01 4.5996E-06 4.7985E+04 2.0840E-05

9. 1 46 4.4245E+02 2.8022E+01 3.7456E-06 4.2540E+04 2.3507E-05

10. 1 60 4.3168E+02 2.8721E+01 1.7947E-03 2.1413E+07 4.6701E-08

11. 1 61 4.2755E+02 2.8999E+01 3.3155E-04 4.0328E+06 2.4797E-07

12. 1 93 3.5816E+02 3.4617E+01 1.2305E-07 2.1328E+03 4.6886E-04

13. 1 95 3.5757E+02 3.4675E+01 1.9837E-06 3.4496E+04 2.8989E-05

14. 1 100 3.5635E+02 3.4793E+01 1.7776E-05 3.1124E+05 3.2130E-06

15. 1 124 3.3393E+02 3.7129E+01 1.2132E-05 2.4190E+05 4.1339E-06

16. 1 133 3.3249E+02 3.7289E+01 8.3950E-06 1.6884E+05 5.9228E-06

Slide 9


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 10


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’ = 0.019. Emax

Slide 11


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 12


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 time- dependent close-coupling (TDCC) calculations.

Slide 13


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 time-dependent 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 excitation-autoionization contribution can be added.

Si2+

Slide 14



• 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, excitation-autoionization dominates the cross section.

Si3+

Slide 15



• 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 16


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 17


Electron-impact ionization calculations – K-shell

• Similar conclusions can be drawn from the other targets in our study, in this case Fe.

• 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.

Fe K-shell

Slide 18


Electron-impact ionization calculations – L-shell

• The Luo group has also been able to study ionization from the L-shell of W.

• 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.

W L-shell

Slide 19


“Top-up”: semi-relativistic Coulomb-Bethe approximation vs. fully relativistic Kummer transformation for high-Z ions

• Coulomb-Bethe Approximation

• Kummer Transformation

• 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 n=0 collision strengths for Be- through O-like ions.

1

CBe

0

RDW

1

1

lll

l

ll

)(Ω11

0

RPWBRPWB

0

RDW

l

ll

l

ll

1

CBe

0

RDW

1

1

lll

l

ll

Slide 20


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=892– 45 transitions– for 6 final energies E’=0.03, 0.08, 0.2, 0.42, 0.8, 1.4 Z2

eff Ryd, with Zeff=Z2.5

• The new calculation covers– Z=2692 – 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 21


Structure calculations for XeII and XeIII

• To compare wavelengths and transition probabilities or f-values 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 22


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.

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Operated by the Los Alamos National Security, LLC for the DOE/NNSA Distorted-wave cross sections of electron- impact excitation and ionization for heavy-