Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

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ELECTRON IMPACT EXCITATION OF H-LIKE, He-LIKE and Li-LIKE IONS WITH Z 30 KANTI M. AGGARWAL Astrophysics Research Centre Queen’s University Belfast BELFAST BT7 1NN Northern Ireland, UK 15 December 2011

description

Talk given by KM Aggarwal at 3d CDAMOP, 14-16 December 2011, Delhi University, Delhi, India.

Transcript of Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

Page 1: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

ELECTRON IMPACT EXCITATION OF H-LIKE,He-LIKE and Li-LIKE IONS WITH Z ≤ 30

KANTI M. AGGARWAL

Astrophysics Research Centre

Queen’s University Belfast

BELFAST BT7 1NN

Northern Ireland, UK

15 December 2011

Page 2: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

ATOMIC PARAMETERS

• ENERGY LEVELSEj − Ei = hνij = hc/λij

• RADIATIVE RATES (A, s−1),OSCILLATOR STRENGTHS (f, dimensionless),LINE STRENGTHS (S, a.u.)

fi,j =mc

8π2e2λ2jiωj

ωiAji = 1.49 × 10−16 λ2

ij(ωj/ωi)Aji

E1: Aji =2.0261×1018

ωjλ3

jiS and fij =

303.75λjiωi

S,

E2: Aji =1.1199×1018

ωjλ5

jiS and fij =

167.89λ3

jiωiS,

M1: Aji =2.6974×1013

ωjλ3

jiS and fij =

4.044×10−3

λjiωiS,

M2: Aji =1.4910×1013

ωjλ5

jiS and fij =

2.236×10−3

λ3

jiωiS.

λ is in A.

• LIFE-TIMEτj =

1∑iAji

• COLLISION STRENGTHS (CROSS SECTIONS)Ωij(E) = ki

2ωiσij(πa02)

Page 3: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

• EFFECTIVE COLLISION STRENGTHS (RATE COEFFICIENTS)

Υ(Te) =∫∞

0 Ωe−Ej/kTed(Ej/kTe)

qij =8.63×10−6

ωiTe1/2 e−Eij/kTeΥij cm3/s

qji =8.63×10−6

ωjTe1/2 Υij cm

3/s

• LINE INTENSITY RATIO

Iji =AjiNjNA,ZNAhνjin

1+NHe

L4π ergs cm−2 s−1 sr−1

R = I(λij)I(λmn)

= Aji

Anm

λmn

λij

Nj

Nn

Page 4: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

APPLICATIONS

1. Astrophysical Plasmas (Te ≤ 50,000 K)

2. Solar Plasmas (Te ∼ 106 K)

3. Lasing Plasmas (Te ∼ 107 K)

4. Fusion Plasmas (Te ∼ 108 K)

Page 5: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

PROGRAMS

Structure Codes:

CIV3, SS, AS, MBPT, MCHF, MCDF, GRASP, FAC

Scattering Codes:

R-matrix: RM, BPRM, RMPS, DARC

DW: UCL, HULLAC, FAC

Page 6: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

Table 1. Energy levels (in Ryd) of Na XI.

Index Configuration/Level NIST GRASP1 GRASP2 FAC1 FAC2

1 1s 2S1/2 0.00000 0.00000 0.00000 0.00000 0.000002 2p 2Po

1/2 90.86686 90.88443 90.86916 90.86789 90.86789

3 2s 2S1/2 90.86894 90.88443 90.87122 90.86983 90.869834 2p 2Po

3/2 90.91589 90.93335 90.91819 90.91692 90.91692

5 3s 2S1/2 107.71206 107.72938 107.71475 107.71306 107.713066 3p 2Po

1/2 107.71144 107.72938 107.71414 107.71247 107.71247

7 3d 2D3/2 107.72595 107.74387 107.72865 107.72697 107.726978 3p 2Po

3/2 107.72597 107.74387 107.72868 107.72700 107.72700

9 3d 2D5/2 107.73078 107.74870 107.73347 107.73180 107.7318010 4p 2Po

1/2 113.60505 113.62312 113.60789 113.60608 113.60608

11 4s 2S1/2 113.60531 113.62312 113.60815 113.60632 113.6063212 4d 2D3/2 113.61117 113.62923 113.61401 113.61220 113.6122013 4p 2Po

3/2 113.61118 113.62923 113.61402 113.61221 113.61221

14 4d 2D5/2 113.61321 113.63126 113.61605 113.61423 113.6142315 4f 2Fo

5/2 113.61320 113.63126 113.61605 113.61423 113.61423

16 4f 2Fo7/2 113.61422 113.63228 113.61707 113.61525 113.61525

17 5s 2S1/2 116.33223 116.35023 116.33514 116.33325 116.3332518 5p 2Po

1/2 116.33210 116.35023 116.33501 116.33313 116.33313

19 5p 2Po3/2 116.33524 116.35336 116.33814 116.33627 116.33627

20 5d 2D3/2 116.33523 116.35336 116.33814 116.33626 116.3362621 5f 2Fo

5/2 116.33627 116.35440 116.33918 116.33730 116.33730

22 5d 2D5/2 116.33627 116.35440 116.33918 116.33730 116.3373023 5g 2G7/2 116.33679 116.35492 116.33970 116.33782 116.3378224 5f 2Fo

7/2 116.33679 116.35492 116.33970 116.33782 116.33782

25 5g 2G9/2 116.33710 116.35523 116.34001 116.33813 116.33813

NIST: http://physics.nist.gov/PhysRefData

GRASP1: Energies from the grasp code with 25 level calculations without Breit and QED effects

GRASP2: Energies from the grasp code with 25 level calculations with Breit and QED effects

FAC1: Energies from the fac code with 25 level calculations

FAC2: Energies from the fac code with 49 level calculations

Page 7: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

Table 1. Energy levels (in Ryd) of Ca XIX.

Index Configuration/Level NIST GRASP1 GRASP2 FAC1 AS1 1s2 1S0 0.0000 0.00000 0.00000 0.00000 0.000002 1s2s 3S1 283.7882 283.88812 283.57452 283.68921 284.114263 1s2p 3Po

0285.3436 285.39578 285.13821 285.28061 285.59393

4 1s2p 3Po

1285.4185 285.51672 285.20807 285.35190 285.71835

5 1s2s 1S0 285.4858 285.58511 285.31180 285.43976 285.811406 1s2p 3Po

2285.7404 285.85834 285.53394 285.67554 286.06924

7 1s2p 1Po

1286.8106 286.95300 286.62332 286.79581 287.20172

8 1s3s 3S1 335.9927 336.09799 335.77313 335.90472 336.346539 1s3p 3Po

0336.4222 336.51401 336.20422 336.33923 336.75189

10 1s3p 3Po

1336.4422 336.54880 336.22516 336.36057 336.78650

11 1s3s 1S0 336.4392 336.54910 336.23611 336.36319 336.7808812 1s3p 3Po

2336.5387 336.65027 336.32224 336.45746 336.88831

13 1s3d 3D1 336.88208 336.55698 336.68375 337.1230814 1s3d 3D2 336.88699 336.55630 336.68341 337.1284815 1s3d 3D3 336.92514 336.59476 336.72141 337.1683716 1s3d 1D2 336.93552 336.60849 336.73608 337.1798417 1s3p 1Po

1336.8303 336.94742 336.61896 336.75745 337.18771

18 1s4s 3S1 354.0334 354.14233 353.81509 353.93887 354.3908419 1s4p 3Po

0354.2116 354.31351 353.99234 354.10986 354.55695

20 1s4s 1S0 354.2143 354.32648 354.00433 354.12442 354.5632921 1s4p 3Po

1354.2200 354.32803 354.00119 354.11896 354.57098

22 1s4p 3Po

2354.2608 354.37082 354.04221 354.16010 354.61301

23 1s4d 3D1 354.46585 354.13852 354.26810 354.7082824 1s4d 3D2 354.46835 354.13873 354.26846 354.7109725 1s4d 3D3 354.48404 354.15448 354.28387 354.7272926 1s4f 3Fo

2354.48959 354.16129 354.28183 354.73273

27 1s4f 3Fo

3354.48965 354.16022 354.28073 354.73279

28 1s4d 1D2 354.48981 354.16159 354.29150 354.7335829 1s4p 1Po

1354.3797 354.49289 354.16425 354.28232 354.73386

30 1s4f 3Fo

4354.49866 354.16934 354.28983 354.74225

31 1s4f 1Fo

3354.49872 354.17023 354.29071 354.74234

32 1s5s 3S1 362.3324 362.44150 362.11343 362.23334 362.68939.........49 1s5g 1G4 362.62524 362.29642 362.41629 362.86871

NIST: http://nist.gov/pml/data/asd.cfm

GRASP1: Energies from the grasp code with 49 level calculations without Breit and QED effects

GRASP2: Energies from the grasp code with 49 level calculations with Breit and QED effects

FAC1: Energies from the fac code with 49 level calculations

AS: Energies from the as code with 49 level calculations

Page 8: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

Table 1. Experimental and theoretical energy levels (in Ryd) for Ni XXVI.

Index Configuration Level NIST GRASP1 GRASP2 FAC BPRM

1 1s22s 2S1/2 0.00000 0.00000 0.00000 0.00000 0.000002 1s22p 2Po

1/2 3.89178 3.90376 3.90511 3.91952 3.885013 1s22p 2Po

3/2 5.50927 5.57232 5.52065 5.53194 5.701004 1s23s 2S1/2 99.02019 99.07935 99.00668 99.01307 99.158615 1s23p 2Po

1/2 100.09931 100.16271 100.09123 100.09864 100.219906 1s23p 2Po

3/2 100.57828 100.65613 100.56940 100.57562 100.758007 1s23d 2D3/2 100.98671 101.07256 100.97398 100.97593 101.146008 1s23d 2D5/2 101.13798 101.22420 101.12491 101.12655 101.310309 1s24s 2S 1/2 133.13657 133.22189 133.13351 133.12926 132.58530

10 1s24p 2Po1/2 133.58956 133.66806 133.58003 133.57172 133.58981

11 1s24p 2Po3/2 133.79150 133.87576 133.78142 133.77240 133.82431

12 1s24d 2D3/2 133.96346 134.04854 133.94948 133.95422 134.1630113 1s24d 2D5/2 134.02734 134.11261 134.01317 134.01749 134.2328014 1s24f 2Fo

5/2 134.12195 134.02229 134.01509 134.2388015 1s24f 2Fo

7/2 134.15372 134.05408 134.04684 134.2732116 1s25s 2S1/2 148.80599 148.89410 148.80017 148.79221 148.2722017 1s25p 2Po

1/2 149.03718 149.11978 149.02602 149.01685 149.1666118 1s25p 2Po

3/2 149.14052 149.22594 149.12897 149.11909 149.2831119 1s25d 2D3/2 149.22836 149.31369 149.21437 149.21584 149.4147020 1s25d 2D5/2 149.26108 149.34651 149.24698 149.24818 149.4505021 1s25f 2Fo

5/2 149.35176 149.25212 149.24463 149.4540122 1s25f 2Fo

7/2 149.36804 149.26840 149.26088 149.4716023 1s25g 2G7/2 149.36813 149.26849 149.26057 149.4707024 1s25g 2G9/2 149.37788 149.27824 149.27032 149.48120

NIST: http://www.nist.gov/pml/data/asd.cfmGRASP1: Present results from the grasp code without the Breit and QED effectsGRASP2: Present results from the grasp code with the Breit and QED effectsFAC: Present results from the fac codeBPRM: Nahar (2002)

Page 9: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

Table 3. Comparison of radiative rates (A- values, s−1) for some transitions of Ti XX.

i j A (GRASP) A (FAC) A (BPRM) f (GRASP)1 2 1.4907+09 1.4990+09 1.4030+09 2.1176−021 3 2.5447+09 2.5500+09 2.5930+09 5.0977−021 5 3.5749+12 3.6310+12 3.6770+12 1.2474−011 6 3.4911+12 3.5540+12 3.5830+12 2.4228−011 10 1.5800+12 1.6500+12 1.3880+12 3.1126−021 11 1.5542+12 1.6270+12 1.3630+12 6.1127−021 17 8.1676+11 9.1200+11 7.4220+11 1.2949−021 18 8.0541+11 9.0220+11 7.3070+11 2.5518−022 7 8.8657+12 8.9040+12 8.8800+12 6.7361−012 12 2.8917+12 2.9410+12 2.8480+12 1.2229−012 19 1.3340+12 1.4250+12 1.3250+12 4.5170−023 8 1.0533+13 1.0590+13 1.0540+13 6.1113−013 13 3.4188+12 3.4810+12 3.3630+12 1.0998−013 20 1.5731+12 1.6780+12 1.5610+12 4.0469−027 11 6.2633+09 6.3600+09 1.7550+12⋆ 2.0804−037 14 2.0665+12 2.0650+12 2.0740+12 1.0132+007 18 2.6896+09 2.9250+09 1.2150+06⋆ 4.1388−049 10 4.5265+07 2.9160+08 4.9417−029 11 8.0239+07 4.2270+08 1.1998−019 17 1.0936+11 1.1230+11 1.0170+11 1.5227−019 18 1.0607+11 1.0900+11 9.7840+10 2.9315−0110 12 7.4663+06 2.0560+07 4.7484−0210 19 1.9329+11 1.9710+11 1.9160+11 5.6630−0111 13 3.8843+06 1.2340+07 3.2363−0211 20 2.3314+11 2.3760+11 2.3150+11 5.1892−0112 14 1.6307+04 1.8750+04 3.6407−0312 18 3.3472+09 3.4160+09 1.8630+11⋆ 5.1952−0312 21 3.8650+11 3.8550+11 3.8590+11 8.8399−0113 14 1.4472+01 7.7210+00 4.0115−0516 17 1.4704+07 8.2050+07 6.2748−0216 18 2.6185+07 1.2070+08⋆ 1.5249−0117 19 2.6949+06 5.7560+06 6.6087−0218 20 1.3974+06 3.2770+06 4.4991−0220 21 9.2274+00 5.0810+00 8.0693−05

GRASP: Present results from the grasp codeFAC: Present results from the fac codeRMBP: Nahar (2002)

Differences are up to three orders of magnitude.

Page 10: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

0 200 400 600

0

50

100

Ω

Ej (Ryd)

5g7/2 – 5f7/2

3p3/2 – 3d5/2

(b)

(a)

0 2000 4000 6000

0

5

10

5g7/2 – 5f7/2

3p3/2 – 3d5/2

Ej (Ryd)

Ω

fig.3

Figure 3: Comparison of collision strengths (Ω) with scattered energy (Ej) for the 3p3/2 - 3d5/2 and 5g7/2 - 5f7/2 transitions of

(a) O VIII and (b) Ni XXVIII. Continuous and broken curves are from CB and circles and stars are from FAC.

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Page 11: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

104 105 106 107 1080

50

100

5g7/2 – 5f7/2

3p3/2 – 3d5/2

Te (K)

(a)

104 105 106 107 1080

2

4

6

5g7/2 – 5f7/2

3p3/2 – 3d5/2

Te (K)

(b)

Eff

ecti

ve

coll

isio

n s

tren

gth

fig. 4

Figure 4: Comparison of effective collision strengths (Υ) for the 3p3/2 - 3d5/2 and 5g7/2 - 5f7/2 transitions of (a) O VIII and (b)

Ni XXVIII. Continuous and broken curves are from CB and FAC, respectively.

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Page 12: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

Figure 2: Comparison of collision strengths from our calculations from darc (continuous curves) and

fac (broken curves) for the 2–6 (circles: 1s2s 3S1 - 1s2p 3Po

2), 4–14 (triangles: 1s2p 3Po

1 - 1s3d 3D2),

and 10–24 (stars: 1s3p 3Po

1 - 1s4d 3D2) allowed transitions of Cl XVI.

Figure 3: Comparison of collision strengths from our calculations from darc (continuous curves) and

fac (broken curves) for the 2–8 (circles: 1s2s 3S1 - 1s3s 3S1), 2–15 (triangles: 1s2s 3S1 - 1s3d 3D3), and

4–10 (stars: 1s2p 3Po

1 - 1s3p 3Po

1) forbidden transitions of Cl XVI.

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Page 13: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

Figure 6: Comparison of collision strengths from our calculations from darc (continuous curves) and fac

(broken curves) for the 23–35 (circles: 4d 3D1 – 5p 3Po

2), 25–33 (triangles: 4d 3D3 – 5p 3Po

0), and 25–34 (stars:

4d 3D3 – 5p 3Po

1) transitions of Mg XI.

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Page 14: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

Figure 7: Collision strengths for the 1s2 1S0 - 1s2s 3S1 (1–2) transition of Mg XI.

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Page 15: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

Figure 11: Comparison of effective collision strengths for the 13–14 (circles: 1s3d 3D1 – 1s3d 3D2), 14–15

(triangles: 1s3d 3D2 – 1s3d 3D3), and 15–16 (stars: 1s3d 3D3 – 1s3d 1D2) transitions of S XV. Continuous

and dotted curves are from the present darc and earlier R- matrix codes [20], respectively.

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Page 16: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

Figure 12: Comparison of effective collision strengths for the 19–46 (circles: 1s4p 3Po

0 – 1s5g 3G4), 26–36

(triangles: 1s4f 3Fo

2– 1s5p 3Po

2), and 29–34 (stars: 1s4f 3Fo

4– 1s5p 3Po

1) transitions of S XV. Continuous and

dotted curves are from the present darc and earlier R- matrix codes [20], respectively.

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Page 17: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

Figure 10: Comparison of effective collision strengths for the 7–8 (circles: 3d 2D3/2 – 3d2D5/2), 12–13 (triangles: 4d

2D3/2 –

4d 2D5/2), and 14–15 (stars: 4f2Fo

5/2 – 4f2Fo

7/2) transitions of Fe XXIV. Continuous and broken curves are from the present

DARC and earlier BPRM codes [25], respectively.

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Page 18: Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30

SUMMARY

H-like ions

Calculations have been reported for many H-like ions, but results areparticularly required for ions of 19 ≤ Z ≤ 23 and Z ≥ 29.

He-like ions

Calculations have been reported for He-like ions up to Z = 21, butwork is in progress for ions of Z ≥ 22.

Li-like ions

Calculations have been reported for Li-like ions up to Z = 28. Results

from BPRM calculations are also available for ions up to Z = 36, but

calculations from DARC will be helpful for assessing accuracy and

establishing reliability.