ELECTRON IMPACT EXCITATION OF H-LIKE,   He-LIKE and Li-LIKE IONS WITH Z ≤ 30             KANTI M. AGGARWAL            Astr...
ATOMIC PARAMETERS• ENERGY LEVELS    Ej − Ei = hνij = hc/λij• RADIATIVE RATES (A, s−1 ),  OSCILLATOR STRENGTHS (f, dimensio...
• EFFECTIVE COLLISION STRENGTHS (RATE COEFFICIENTS)                      −Ej /kTeΥ(Te ) =         0 Ωe                 ∞  ...
APPLICATIONS1. Astrophysical Plasmas (Te ≤ 50,000 K)2. Solar Plasmas (Te ∼ 106 K)3. Lasing Plasmas (Te ∼ 107 K)4. Fusion P...
PROGRAMSStructure Codes:CIV3, SS, AS, MBPT, MCHF, MCDF, GRASP, FACScattering Codes:R-matrix: RM, BPRM, RMPS, DARCDW: UCL, ...
Table 1. Energy levels (in Ryd) of Na XI.    Index    Configuration/Level         NIST     GRASP1       GRASP2          FAC...
Table 1. Energy levels (in Ryd) of Ca XIX. Index    Configuration/Level        NIST     GRASP1       GRASP2          FAC1  ...
Table 1. Experimental and theoretical energy levels (in Ryd) for Ni XXVI.    Index    Configuration    Level         NIST  ...
Table 3. Comparison of radiative rates (A- values, s−1 ) for some transitions of Ti XX.     i    j    A (GRASP)        A (...
fig.3              (a)   100                                          3p3/2 – 3d5/2Ω      50                              ...
fig. 4                                      (a)                               100                                         ...
Figure 2: Comparison of collision strengths from our calculations from darc (continuous curves) andfac (broken curves) for...
Figure 6: Comparison of collision strengths from our calculations from darc (continuous curves) and fac(broken curves) for...
Figure 7: Collision strengths for the 1s2 1 S0 - 1s2s 3 S1 (1–2) transition of Mg XI.                                     ...
Figure 11: Comparison of effective collision strengths for the 13–14 (circles: 1s3d 3 D1 – 1s3d 3 D2 ), 14–15(triangles: 1s...
Figure 12: Comparison of effective collision strengths for the 19–46 (circles: 1s4p 3 Po – 1s5g 3 G4 ), 26–36              ...
Figure 10: Comparison of effective collision strengths for the 7–8 (circles: 3d 2 D3/2 – 3d 2 D5/2 ), 12–13 (triangles: 4d...
SUMMARYH-like ionsCalculations have been reported for many H-like ions, but results areparticularly required for ions of 1...
Upcoming SlideShare
Loading in …5
×

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

845 views
760 views

Published on

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

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
845
On SlideShare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
5
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

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

  1. 1. 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
  2. 2. ATOMIC PARAMETERS• ENERGY LEVELS Ej − Ei = hνij = hc/λij• RADIATIVE RATES (A, s−1 ), OSCILLATOR STRENGTHS (f, dimensionless), LINE STRENGTHS (S, a.u.) mc 2 ωjfi,j = 8π 2 e2 λji ωi Aji = 1.49 × 10−16 λ2 (ωj /ωi )Aji ij 2.0261×1018 303.75E1: Aji = ωj λ3 S and fij = λji ωi S, ji 1.1199×1018E2: Aji = ωj λ5 S and fij = 167.89 S, λ3 ω i ji ji 2.6974×1013 4.044×10−3M1: Aji = ωj λ3 S and fij = λji ωi S, ji 1.4910×1013 fij = 2.236×10 −3M2: Aji = ωj λ5 S and 3 ω λji i S. jiλ is in ˚. A• LIFE-TIME τj = 1Aji i• COLLISION STRENGTHS (CROSS SECTIONS) Ωij (E) = ki 2 ωi σij (πa0 2 )
  3. 3. • EFFECTIVE COLLISION STRENGTHS (RATE COEFFICIENTS) −Ej /kTeΥ(Te ) = 0 Ωe ∞ d(Ej /kTe ) 8.63×10−6 −Eij /kTeqij = ωi Te 1/2 e Υij cm3 /sqji = 8.63×10 Υij cm3 /s −6 ω T 1/2 j e• LINE INTENSITY RATIO n LIji =Aji Nj NA,Z NA hνji 1+NHe 4π ergs cm−2 s−1 sr−1 I(λij ) Aji λmn NjR= I(λmn ) = Anm λij Nn
  4. 4. APPLICATIONS1. Astrophysical Plasmas (Te ≤ 50,000 K)2. Solar Plasmas (Te ∼ 106 K)3. Lasing Plasmas (Te ∼ 107 K)4. Fusion Plasmas (Te ∼ 108 K)
  5. 5. PROGRAMSStructure Codes:CIV3, SS, AS, MBPT, MCHF, MCDF, GRASP, FACScattering Codes:R-matrix: RM, BPRM, RMPS, DARCDW: UCL, HULLAC, FAC
  6. 6. Table 1. Energy levels (in Ryd) of Na XI. Index Configuration/Level NIST GRASP1 GRASP2 FAC1 FAC2 2 1 1s S1/2 0.00000 0.00000 0.00000 0.00000 0.00000 2 2p 2 Po 1/2 90.86686 90.88443 90.86916 90.86789 90.86789 2 3 2s S1/2 90.86894 90.88443 90.87122 90.86983 90.86983 2 o 4 2p P3/2 90.91589 90.93335 90.91819 90.91692 90.91692 2 5 3s S1/2 107.71206 107.72938 107.71475 107.71306 107.71306 2 o 6 3p P1/2 107.71144 107.72938 107.71414 107.71247 107.71247 2 7 3d D3/2 107.72595 107.74387 107.72865 107.72697 107.72697 2 o 8 3p P3/2 107.72597 107.74387 107.72868 107.72700 107.72700 2 9 3d D5/2 107.73078 107.74870 107.73347 107.73180 107.73180 2 o 10 4p P1/2 113.60505 113.62312 113.60789 113.60608 113.60608 2 11 4s S1/2 113.60531 113.62312 113.60815 113.60632 113.60632 2 12 4d D3/2 113.61117 113.62923 113.61401 113.61220 113.61220 2 o 13 4p P3/2 113.61118 113.62923 113.61402 113.61221 113.61221 2 14 4d D5/2 113.61321 113.63126 113.61605 113.61423 113.61423 2 o 15 4f F5/2 113.61320 113.63126 113.61605 113.61423 113.61423 2 o 16 4f F7/2 113.61422 113.63228 113.61707 113.61525 113.61525 2 17 5s S1/2 116.33223 116.35023 116.33514 116.33325 116.33325 2 o 18 5p P1/2 116.33210 116.35023 116.33501 116.33313 116.33313 2 o 19 5p P3/2 116.33524 116.35336 116.33814 116.33627 116.33627 2 20 5d D3/2 116.33523 116.35336 116.33814 116.33626 116.33626 2 o 21 5f F5/2 116.33627 116.35440 116.33918 116.33730 116.33730 2 22 5d D5/2 116.33627 116.35440 116.33918 116.33730 116.33730 2 23 5g G7/2 116.33679 116.35492 116.33970 116.33782 116.33782 2 o 24 5f F7/2 116.33679 116.35492 116.33970 116.33782 116.33782 2 25 5g G9/2 116.33710 116.35523 116.34001 116.33813 116.33813NIST: http://physics.nist.gov/PhysRefDataGRASP1: Energies from the grasp code with 25 level calculations without Breit and QED effectsGRASP2: Energies from the grasp code with 25 level calculations with Breit and QED effectsFAC1: Energies from the fac code with 25 level calculationsFAC2: Energies from the fac code with 49 level calculations
  7. 7. Table 1. Energy levels (in Ryd) of Ca XIX. Index Configuration/Level NIST GRASP1 GRASP2 FAC1 AS 1 1s2 1 S0 0.0000 0.00000 0.00000 0.00000 0.00000 3 2 1s2s S1 283.7882 283.88812 283.57452 283.68921 284.11426 3 1s2p 3 Po0 285.3436 285.39578 285.13821 285.28061 285.59393 4 1s2p 3 Po1 285.4185 285.51672 285.20807 285.35190 285.71835 5 1s2s 1 S0 285.4858 285.58511 285.31180 285.43976 285.81140 6 1s2p 3 Po2 285.7404 285.85834 285.53394 285.67554 286.06924 7 1s2p 1 Po1 286.8106 286.95300 286.62332 286.79581 287.20172 8 1s3s 3 S1 335.9927 336.09799 335.77313 335.90472 336.34653 9 1s3p 3 Po0 336.4222 336.51401 336.20422 336.33923 336.75189 10 1s3p 3 Po1 336.4422 336.54880 336.22516 336.36057 336.78650 11 1s3s 1 S0 336.4392 336.54910 336.23611 336.36319 336.78088 12 1s3p 3 Po2 336.5387 336.65027 336.32224 336.45746 336.88831 13 1s3d 3 D1 336.88208 336.55698 336.68375 337.12308 14 1s3d 3 D2 336.88699 336.55630 336.68341 337.12848 15 1s3d 3 D3 336.92514 336.59476 336.72141 337.16837 16 1s3d 1 D2 336.93552 336.60849 336.73608 337.17984 17 1s3p 1 Po1 336.8303 336.94742 336.61896 336.75745 337.18771 18 1s4s 3 S1 354.0334 354.14233 353.81509 353.93887 354.39084 19 1s4p 3 Po0 354.2116 354.31351 353.99234 354.10986 354.55695 20 1s4s 1 S0 354.2143 354.32648 354.00433 354.12442 354.56329 21 1s4p 3 Po1 354.2200 354.32803 354.00119 354.11896 354.57098 22 1s4p 3 Po2 354.2608 354.37082 354.04221 354.16010 354.61301 23 1s4d 3 D1 354.46585 354.13852 354.26810 354.70828 24 1s4d 3 D2 354.46835 354.13873 354.26846 354.71097 25 1s4d 3 D3 354.48404 354.15448 354.28387 354.72729 26 1s4f 3 Fo2 354.48959 354.16129 354.28183 354.73273 27 1s4f 3 Fo3 354.48965 354.16022 354.28073 354.73279 28 1s4d 1 D2 354.48981 354.16159 354.29150 354.73358 29 1s4p 1 Po1 354.3797 354.49289 354.16425 354.28232 354.73386 30 1s4f 3 Fo4 354.49866 354.16934 354.28983 354.74225 31 1s4f 1 Fo3 354.49872 354.17023 354.29071 354.74234 32 1s5s 3 S1 362.3324 362.44150 362.11343 362.23334 362.68939 ... ... ... 1 49 1s5g G4 362.62524 362.29642 362.41629 362.86871NIST: http://nist.gov/pml/data/asd.cfmGRASP1: Energies from the grasp code with 49 level calculations without Breit and QED effectsGRASP2: Energies from the grasp code with 49 level calculations with Breit and QED effectsFAC1: Energies from the fac code with 49 level calculationsAS: Energies from the as code with 49 level calculations
  8. 8. Table 1. Experimental and theoretical energy levels (in Ryd) for Ni XXVI. Index Configuration Level NIST GRASP1 GRASP2 FAC BPRM 1 1s2 2s 2 S1/2 0.00000 0.00000 0.00000 0.00000 0.00000 2 1s2 2p 2 Po 1/2 3.89178 3.90376 3.90511 3.91952 3.88501 2 o 3 1s2 2p P 3/2 5.50927 5.57232 5.52065 5.53194 5.70100 4 1s2 3s 2 S1/2 99.02019 99.07935 99.00668 99.01307 99.15861 2 o 5 1s2 3p P 1/2 100.09931 100.16271 100.09123 100.09864 100.21990 2 o 6 1s2 3p P 3/2 100.57828 100.65613 100.56940 100.57562 100.75800 7 1s2 3d 2 D3/2 100.98671 101.07256 100.97398 100.97593 101.14600 8 1s2 3d 2 D5/2 101.13798 101.22420 101.12491 101.12655 101.31030 9 1s2 4s 2 S 1/2 133.13657 133.22189 133.13351 133.12926 132.58530 2 o 10 1s2 4p P 1/2 133.58956 133.66806 133.58003 133.57172 133.58981 2 o 11 1s2 4p P 3/2 133.79150 133.87576 133.78142 133.77240 133.82431 12 1s2 4d 2 D3/2 133.96346 134.04854 133.94948 133.95422 134.16301 13 1s2 4d 2 D5/2 134.02734 134.11261 134.01317 134.01749 134.23280 2 o 14 1s2 4f F 5/2 134.12195 134.02229 134.01509 134.23880 2 o 15 1s2 4f F 7/2 134.15372 134.05408 134.04684 134.27321 16 1s2 5s 2 S1/2 148.80599 148.89410 148.80017 148.79221 148.27220 2 o 17 1s2 5p P 1/2 149.03718 149.11978 149.02602 149.01685 149.16661 2 o 18 1s2 5p P 3/2 149.14052 149.22594 149.12897 149.11909 149.28311 19 1s2 5d 2 D3/2 149.22836 149.31369 149.21437 149.21584 149.41470 20 1s2 5d 2 D5/2 149.26108 149.34651 149.24698 149.24818 149.45050 2 o 21 1s2 5f F 5/2 149.35176 149.25212 149.24463 149.45401 2 o 22 1s2 5f F 7/2 149.36804 149.26840 149.26088 149.47160 23 1s2 5g 2 G7/2 149.36813 149.26849 149.26057 149.47070 24 1s2 5g 2 G9/2 149.37788 149.27824 149.27032 149.48120NIST: 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)
  9. 9. 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 2.1176−02 1 3 2.5447+09 2.5500+09 2.5930+09 5.0977−02 1 5 3.5749+12 3.6310+12 3.6770+12 1.2474−01 1 6 3.4911+12 3.5540+12 3.5830+12 2.4228−01 1 10 1.5800+12 1.6500+12 1.3880+12 3.1126−02 1 11 1.5542+12 1.6270+12 1.3630+12 6.1127−02 1 17 8.1676+11 9.1200+11 7.4220+11 1.2949−02 1 18 8.0541+11 9.0220+11 7.3070+11 2.5518−02 2 7 8.8657+12 8.9040+12 8.8800+12 6.7361−01 2 12 2.8917+12 2.9410+12 2.8480+12 1.2229−01 2 19 1.3340+12 1.4250+12 1.3250+12 4.5170−02 3 8 1.0533+13 1.0590+13 1.0540+13 6.1113−01 3 13 3.4188+12 3.4810+12 3.3630+12 1.0998−01 3 20 1.5731+12 1.6780+12 1.5610+12 4.0469−02 7 11 6.2633+09 6.3600+09 1.7550+12⋆ 2.0804−03 7 14 2.0665+12 2.0650+12 2.0740+12 1.0132+00 7 18 2.6896+09 2.9250+09 1.2150+06⋆ 4.1388−04 9 10 4.5265+07 2.9160+08 4.9417−02 9 11 8.0239+07 4.2270+08 1.1998−01 9 17 1.0936+11 1.1230+11 1.0170+11 1.5227−01 9 18 1.0607+11 1.0900+11 9.7840+10 2.9315−01 10 12 7.4663+06 2.0560+07 4.7484−02 10 19 1.9329+11 1.9710+11 1.9160+11 5.6630−01 11 13 3.8843+06 1.2340+07 3.2363−02 11 20 2.3314+11 2.3760+11 2.3150+11 5.1892−01 12 14 1.6307+04 1.8750+04 3.6407−03 12 18 3.3472+09 3.4160+09 1.8630+11⋆ 5.1952−03 12 21 3.8650+11 3.8550+11 3.8590+11 8.8399−01 13 14 1.4472+01 7.7210+00 4.0115−05 16 17 1.4704+07 8.2050+07 6.2748−02 16 18 2.6185+07 1.2070+08⋆ 1.5249−01 17 19 2.6949+06 5.7560+06 6.6087−02 18 20 1.3974+06 3.2770+06 4.4991−02 20 21 9.2274+00 5.0810+00 8.0693−05GRASP: Present results from the grasp codeFAC: Present results from the fac codeRMBP: Nahar (2002) Differences are up to three orders of magnitude.
  10. 10. fig.3 (a) 100 3p3/2 – 3d5/2Ω 50 5g7/2 – 5f7/2 0 0 200 400 600 Ej (Ryd) 10 (b) 3p3/2 – 3d5/2Ω 5 5g7/2 – 5f7/2 0 0 2000 4000 6000 Ej (Ryd)Figure 3: Comparison of collision strengths (Ω) with scattered energy (E j ) 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. 13
  11. 11. fig. 4 (a) 100 3p3/2 – 3d5/2 50Effective collision strength 5g7/2 – 5f7/2 0 104 105 106 107 108 Te (K) 6 (b) 4 3p3/2 – 3d5/2 2 5g7/2 – 5f7/2 0 104 105 106 107 108 Te (K)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. 14
  12. 12. Figure 2: Comparison of collision strengths from our calculations from darc (continuous curves) andfac (broken curves) for the 2–6 (circles: 1s2s 3 S1 - 1s2p 3 Po ), 4–14 (triangles: 1s2p 3 Po - 1s3d 3 D2 ), 2 1and 10–24 (stars: 1s3p 3 Po - 1s4d 3 D2 ) allowed transitions of Cl XVI. 1Figure 3: Comparison of collision strengths from our calculations from darc (continuous curves) andfac (broken curves) for the 2–8 (circles: 1s2s 3 S1 - 1s3s 3 S1 ), 2–15 (triangles: 1s2s 3 S1 - 1s3d 3 D3 ), and4–10 (stars: 1s2p 3 Po - 1s3p 3 Po ) forbidden transitions of Cl XVI. 1 1 12
  13. 13. Figure 6: Comparison of collision strengths from our calculations from darc (continuous curves) and fac(broken curves) for the 23–35 (circles: 4d 3 D1 – 5p 3 Po ), 25–33 (triangles: 4d 3 D3 – 5p 3 Po ), and 25–34 (stars: 2 04d 3 D3 – 5p 3 Po ) transitions of Mg XI. 1 18
  14. 14. Figure 7: Collision strengths for the 1s2 1 S0 - 1s2s 3 S1 (1–2) transition of Mg XI. 19
  15. 15. Figure 11: Comparison of effective collision strengths for the 13–14 (circles: 1s3d 3 D1 – 1s3d 3 D2 ), 14–15(triangles: 1s3d 3 D2 – 1s3d 3 D3 ), and 15–16 (stars: 1s3d 3 D3 – 1s3d 1 D2 ) transitions of S XV. Continuousand dotted curves are from the present darc and earlier R- matrix codes [20], respectively. 23
  16. 16. Figure 12: Comparison of effective collision strengths for the 19–46 (circles: 1s4p 3 Po – 1s5g 3 G4 ), 26–36 0(triangles: 1s4f 3 Fo – 1s5p 3 Po ), and 29–34 (stars: 1s4f 3 Fo – 1s5p 3 P1 ) transitions of S XV. Continuous and 2 2 4 odotted curves are from the present darc and earlier R- matrix codes [20], respectively. 24
  17. 17. Figure 10: Comparison of effective collision strengths for the 7–8 (circles: 3d 2 D3/2 – 3d 2 D5/2 ), 12–13 (triangles: 4d 2 D3/2 –4d 2 D5/2 ), and 14–15 (stars: 4f 2 Fo – 4f 2 Fo ) transitions of Fe XXIV. Continuous and broken curves are from the present 5/2 7/2DARC and earlier BPRM codes [25], respectively. 22
  18. 18. SUMMARYH-like ionsCalculations have been reported for many H-like ions, but results areparticularly required for ions of 19 ≤ Z ≤ 23 and Z ≥ 29.He-like ionsCalculations have been reported for He-like ions up to Z = 21, butwork is in progress for ions of Z ≥ 22.Li-like ionsCalculations have been reported for Li-like ions up to Z = 28. Resultsfrom BPRM calculations are also available for ions up to Z = 36, butcalculations from DARC will be helpful for assessing accuracy andestablishing reliability.

×