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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
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 ωj
fi,j =   8π 2 e2 λji ωi Aji   = 1.49 × 10−16 λ2 (ωj /ωi )Aji
                                              ij

               2.0261×1018                                303.75
E1:       Aji =    ωj λ3          S       and       fij =  λji ωi S,
                       ji
               1.1199×1018
E2:       Aji = ωj λ5             S       and       fij = 167.89 S,
                                                           λ3 ω i
                       ji                                   ji
                2.6974×1013                                4.044×10−3
M1:       Aji = ωj λ3              S      and        fij = λji ωi         S,
                        ji
                1.4910×1013
                                                     fij = 2.236×10
                                                                     −3
M2:       Aji = ωj λ5              S      and                    3 ω
                                                               λji i      S.
                        ji




λ is in ˚.
        A


• LIFE-TIME
     τj = 1Aji
                  i




• COLLISION STRENGTHS (CROSS SECTIONS)
    Ωij (E) = ki 2 ωi σij (πa0 2 )
• EFFECTIVE COLLISION STRENGTHS (RATE COEFFICIENTS)

                      −Ej /kTe
Υ(Te ) =         0 Ωe
                 ∞
                               d(Ej /kTe )

         8.63×10−6 −Eij /kTe
qij =      ωi Te 1/2
                     e       Υij         cm3 /s


qji = 8.63×10 Υij cm3 /s
                   −6

        ω T 1/2
           j e




• LINE INTENSITY RATIO

                           n   L
Iji =Aji Nj NA,Z NA hνji 1+NHe 4π             ergs cm−2 s−1 sr−1


         I(λij )        Aji λmn Nj
R=      I(λmn )    =    Anm λij Nn
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)
PROGRAMS




Structure Codes:
CIV3, SS, AS, MBPT, MCHF, MCDF, GRASP, FAC



Scattering Codes:
R-matrix: RM, BPRM, RMPS, DARC
DW: UCL, HULLAC, FAC
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    116.33813


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
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   362.86871

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
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   149.48120



NIST: http://www.nist.gov/pml/data/asd.cfm
GRASP1: Present results from the grasp code without the Breit and QED effects
GRASP2: Present results from the grasp code with the Breit and QED effects
FAC: Present results from the fac code
BPRM: Nahar (2002)
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     8.0693−05

GRASP: Present results from the grasp code
FAC: Present results from the fac code
RMBP: Nahar (2002)




                        Differences are up to three orders of magnitude.
fig.3
              (a)
   100
                                          3p3/2 – 3d5/2
Ω




      50
                                      5g7/2 – 5f7/2


        0
              0                200        400                           600
                                 Ej (Ryd)
      10
              (b)
                                                    3p3/2 – 3d5/2
Ω




        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
fig. 4

                                      (a)
                               100
                                            3p3/2 – 3d5/2



                                50
Effective 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
Figure 2: Comparison of collision strengths from our calculations from darc (continuous curves) and
fac (broken curves) for the 2–6 (circles: 1s2s 3 S1 - 1s2p 3 Po ), 4–14 (triangles: 1s2p 3 Po - 1s3d 3 D2 ),
                                                              2                             1

and 10–24 (stars: 1s3p 3 Po - 1s4d 3 D2 ) allowed transitions of Cl XVI.
                          1




Figure 3: Comparison of collision strengths from our calculations from darc (continuous curves) and
fac (broken curves) for the 2–8 (circles: 1s2s 3 S1 - 1s3s 3 S1 ), 2–15 (triangles: 1s2s 3 S1 - 1s3d 3 D3 ), and
4–10 (stars: 1s2p 3 Po - 1s3p 3 Po ) forbidden transitions of Cl XVI.
                     1           1


                                                      12
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                                      0
4d 3 D3 – 5p 3 Po ) transitions of Mg XI.
                1




                                                         18
Figure 7: Collision strengths for the 1s2 1 S0 - 1s2s 3 S1 (1–2) transition of Mg XI.




                                         19
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. Continuous
and dotted curves are from the present darc and earlier R- matrix codes [20], respectively.




                                                     23
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
                                                                           o

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




                                                       24
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       7/2
DARC and earlier BPRM codes [25], respectively.




                                                                22
SUMMARY



H-like ions
Calculations have been reported for many H-like ions, but results are
particularly 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, but
work 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.

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

  • 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. 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 ωj fi,j = 8π 2 e2 λji ωi Aji = 1.49 × 10−16 λ2 (ωj /ωi )Aji ij 2.0261×1018 303.75 E1: Aji = ωj λ3 S and fij = λji ωi S, ji 1.1199×1018 E2: Aji = ωj λ5 S and fij = 167.89 S, λ3 ω i ji ji 2.6974×1013 4.044×10−3 M1: Aji = ωj λ3 S and fij = λji ωi S, ji 1.4910×1013 fij = 2.236×10 −3 M2: Aji = ωj λ5 S and 3 ω λji i S. ji λ is in ˚. A • LIFE-TIME τj = 1Aji i • COLLISION STRENGTHS (CROSS SECTIONS) Ωij (E) = ki 2 ωi σij (πa0 2 )
  • 3. • EFFECTIVE COLLISION STRENGTHS (RATE COEFFICIENTS) −Ej /kTe Υ(Te ) = 0 Ωe ∞ d(Ej /kTe ) 8.63×10−6 −Eij /kTe qij = ωi Te 1/2 e Υij cm3 /s qji = 8.63×10 Υij cm3 /s −6 ω T 1/2 j e • LINE INTENSITY RATIO n L Iji =Aji Nj NA,Z NA hνji 1+NHe 4π ergs cm−2 s−1 sr−1 I(λij ) Aji λmn Nj R= I(λmn ) = Anm λij Nn
  • 4. 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)
  • 5. PROGRAMS Structure Codes: CIV3, SS, AS, MBPT, MCHF, MCDF, GRASP, FAC Scattering Codes: R-matrix: RM, BPRM, RMPS, DARC DW: UCL, HULLAC, FAC
  • 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 116.33813 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
  • 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 362.86871 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
  • 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 149.48120 NIST: http://www.nist.gov/pml/data/asd.cfm GRASP1: Present results from the grasp code without the Breit and QED effects GRASP2: Present results from the grasp code with the Breit and QED effects FAC: Present results from the fac code BPRM: Nahar (2002)
  • 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 8.0693−05 GRASP: Present results from the grasp code FAC: Present results from the fac code RMBP: Nahar (2002) Differences are up to three orders of magnitude.
  • 10. fig.3 (a) 100 3p3/2 – 3d5/2 Ω 50 5g7/2 – 5f7/2 0 0 200 400 600 Ej (Ryd) 10 (b) 3p3/2 – 3d5/2 Ω 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. fig. 4 (a) 100 3p3/2 – 3d5/2 50 Effective 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. Figure 2: Comparison of collision strengths from our calculations from darc (continuous curves) and fac (broken curves) for the 2–6 (circles: 1s2s 3 S1 - 1s2p 3 Po ), 4–14 (triangles: 1s2p 3 Po - 1s3d 3 D2 ), 2 1 and 10–24 (stars: 1s3p 3 Po - 1s4d 3 D2 ) allowed transitions of Cl XVI. 1 Figure 3: Comparison of collision strengths from our calculations from darc (continuous curves) and fac (broken curves) for the 2–8 (circles: 1s2s 3 S1 - 1s3s 3 S1 ), 2–15 (triangles: 1s2s 3 S1 - 1s3d 3 D3 ), and 4–10 (stars: 1s2p 3 Po - 1s3p 3 Po ) forbidden transitions of Cl XVI. 1 1 12
  • 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 0 4d 3 D3 – 5p 3 Po ) transitions of Mg XI. 1 18
  • 14. Figure 7: Collision strengths for the 1s2 1 S0 - 1s2s 3 S1 (1–2) transition of Mg XI. 19
  • 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. Continuous and dotted curves are from the present darc and earlier R- matrix codes [20], respectively. 23
  • 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 o dotted curves are from the present darc and earlier R- matrix codes [20], respectively. 24
  • 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 7/2 DARC and earlier BPRM codes [25], respectively. 22
  • 18. SUMMARY H-like ions Calculations have been reported for many H-like ions, but results are particularly 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, but work 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.