2. Atomic calculations

The target expansion for the present calculations, used earlier in Paper XVII (Nahar & Pradhan 1996) for the radiative work for Fe III, consists of 49 LS-terms dominated by the configurations , and . The 140 fine structure levels of these 49 terms, and their observed energies (Sugar & Corliss 1985), are listed in Table 1 (click here). This table also provides the key to the level indices used to identify the transitions in tabulating the maxwellian-averaged collision strengths.

 

i Term J Energy i Term J Energy

1 5/2 0.00000 54 9/2 1.42360

2 11/2 0.29384 55 7/2 1.42270

3 9/2 0.29427 56 5/2 1.42200

4 7/2 0.29439 57 3/2 1.42170

5 5/2 0.29435 58 11/2 1.45200

6 5/2 0.32126 59 9/2 1.45100

7 3/2 0.32198 60 7/2 1.44900

8 1/2 0.32265 61 5/2 1.44650

9 7/2 0.35338 62 3/2 1.47230

10 5/2 0.35480 63 1/2 1.45820

11 3/2 0.35483 64 11/2 1.46510

12 1/2 0.35445 65 9/2 1.46090

13 13/2 0.42912 66 7/2 1.47710

14 11/2 0.42901 67 5/2 1.47690

15 5/2 0.45146 68 9/2 1.50720

16 3/2 0.45610 69 7/2 1.50310

17 7/2 0.46834 70 7/2 1.50810

18 5/2 0.47538 71 5/2 1.50910

19 9/2 0.47952 72 3/2 1.51020

20 7/2 0.48020 73 1/2 1.51090

21 5/2 0.48150 74 9/2 1.52830

22 3/2 0.48149 75 7/2 1.52910

23 11/2 0.51367 76 13/2 1.53570

24 9/2 0.51084 77 11/2 1.53610

25 9/2 0.52599 78 1/2 1.55580

26 7/2 0.52314 79 5/2 1.56140

27 7/2 0.55819 80 3/2 1.56260

28 5/2 0.55730 81 5/2 1.61300

29 1/2 0.60800 82 3/2 1.61360

30 5/2 0.67555 83 7/2 1.66910

31 3/2 0.67522 84 5/2 1.66910

32 9/2 0.75539 85 11/2 1.73390

33 7/2 0.75542 86 9/2 1.72700

34 3/2 0.91234 87 7/2 1.72140

35 1/2 0.91242 88 5/2 1.71710

36 5/2 0.98637 89 3/2 1.71400

37 3/2 0.98652 90 1/2 1.71210

38 9/2 1.17520 91 7/2 1.73350

39 7/2 1.17140 92 5/2 1.73150

40 5/2 1.16820 93 3/2 1.73040

41 3/2 1.16580 94 5/2 1.73120

42 1/2 1.16430 95 3/2 1.73880

43 7/2 1.26520 96 1/2 1.74360

44 5/2 1.26060 97 9/2 1.73430

45 3/2 1.25710 98 7/2 1.73530

46 1/2 1.25480 99 5/2 1.73540

47 5/2 1.41930 100 3/2 1.73510

48 3/2 1.40770 101 5/2 1.76380

49 1/2 1.40020 102 3/2 1.74680

50 13/2 1.41000 103 1/2 1.74070

51 11/2 1.40800

52 9/2 1.40630

53 7/2 1.40500

Table 1: The 140 fine structure levels corresponding to the 49 LS terms included in the calculations and their observed energies (Ry) in Fe IV (Sugar & Corliss 1985)

 

 

i Term J Energy i Term J Energy

104 9/2 1.76590 123 13/2 1.94250

105 7/2 1.76230 124 11/2 1.93840

106 5/2 1.75510 125 9/2 1.93530

107 3/2 1.76120 126 7/2 1.93310

108 1/2 1.75980 127 7/2 1.96120

109 3/2 1.78480 128 5/2 1.95300

110 1/2 1.79410 129 3/2 1.94510

111 7/2 1.78730 130 1/2 1.93930

112 5/2 1.78810 131 11/2 1.96840

113 9/2 1.79380 132 9/2 1.96270

114 7/2 1.79110 133 7/2 1.95950

115 5/2 1.78910 134 5/2 1.95760

116 3/2 1.78780 135 15/2 1.97630

117 9/2 1.83330 136 13/2 1.97170

118 7/2 1.83360 137 11/2 1.96660

119 7/2 1.84630 138 9/2 1.96060

120 5/2 1.84380 139 9/2 1.97220

121 3/2 1.84150 140 7/2 1.96940

122 1/2 1.84000

Table 1: continued

In the present work, as in our earlier Papers III, VI and XVIII, the reactance matrix (the K-matrix) is first calculated and used to evaluate the collision strengths. In the NR algebraic recoupling approach, the K-matrices are obtained as usual by the different stages of the R-matrix package (Berrington etal. 1995) in LS coupling. The K-matrices are subsequently transformed from LS coupling to pair coupling (Eissner etal. 1974), using the STGFJ code (Luo & Pradhan 1990; Zhang & Pradhan 1995a), which is an extension of the asymptotic region code, STGF, of the R-matrix codes (Hummer etal.
1993). The collision strengths were calculated for a large number of electron energies ranging from 0 to 15 rydbergs. The energy range is carefully chosen in order to obtain detailed collision strengths in the region where they are dominated by resonances, as well as in an extended region where resonances are not important or have not been included, but which are necessary to obtain accurate maxwellian-averaged rate coefficients, particularly for dipole allowed transitions.

In order to delineate the resonance structures, an effective quantum number mesh (-mesh) was used to obtain the collision strengths at 5604 energy points in the range E = 0 - 1.789 rydbergs. The -mesh ensures equal sampling of resonances in each interval , where and is the energy of the particular target threshold to which the resonance series converges. In the energy region E > 1.789 rydbergs, the collision strengths were calculated for 20 additional energies up to 15 rydbergs. It is impractical to carry through the calculation of collision strengths at an even larger number of energies, as the number of scattering channels increases across higher target thresholds. The calculations are therefore optimised to obtain extensive delineation of resonances for the collision strengths for forbidden transitions in the low energy region that contributes predominantly to the maxwellian rate coefficient. For the optically allowed transitions, the dominant contribution arises from higher partial waves and in higher energy regions since ); here, however, resonances are relatively less important.

We include partial wave contributions from total angular momenta of the electron plus target system J = 0 - 11 (where J = L + S; L and S are total orbital and spin angular momenta). The corresponding SL's, for both even and odd parities, are



These should be sufficient to ensure convergence for the non-optically allowed transitions. As in the Fe II (Paper III) and Fe III (Paper XVIII) work, the Coulomb-Bethe approximation was employed to account for the large contributions to the collision strengths for optically allowed transitions at energies greater than 1.789 rydbergs. The electric dipole line strengths required for the Coulomb-Bethe approximation were derived from the Opacity Project database TOPbase (Cunto etal.\ 1992). The oscillator strengths in the TOPbase were transformed to line strengths in LS coupling and then algebraically recoupled to obtain fine structure values using a code by Sultana Nahar.