A 180-level BPRM calculation was used for the resonance energy region (up to 9.95 Ryd), with a maximum of 1104 channels in each partial wave. In order for this calculation to be computational feasable, the number of continuum terms was the minimum required to span this energy range: only five per channel, resulting in collisional Hamiltonian matrices of maximum order 6164. The purpose of this calculation was to obtain accurate collision strengths in the low-energy resonance region, and since resonances are important only for low partial waves the expansion was truncated at J=6.

A 31-level BPRM calculation was used to top-up both the energy and the partial-wave expansion, in order to calculate converged collision strengths to a high enough energy for collision rates to be obtained over a realistic temperature range. The 31-level calculation had only 158 channels, so 30 continuum terms per channel could be included and the partial-waves calculated up to J=56, enabling converged collision strengths to be calculated for the transitions 3s²3p⁵-3s3p⁶, 3s²3p⁵-3s²3p⁴3d and 3s3p⁶-3s²3p⁴3d (i.e. up to the lowest 31 levels), and the energy range extended from 9.95 to 600 Ryd.

Table 1 lists the energies of the lowest 31 levels calculated from the wavefunction used in the 181-level BPRM calculation, and compares with NIST reference data. Table 2 compares the oscillator strengths obtained using the 181-level BPRM wavefunction with those of Bhatia & Doshek (1995). The oscillator strengths from the two calculations are qualitatively similar but not in very good agreement. However, our results are much closer to a recent experiment by Träbert (1996) for the lifetime and branching ratio of the 3s3p⁶ ²S $^{\rm e}_{1/2}$ level (Table 3).

Table 1: The lowest 31 energy levels (Ryd) for Fe X. For reference, level 32 (3s3p⁵3d) is calculated at 6.284 Ryd. 180 levels were actually included in the calculation (see Fig. 1). "Expt'' is reference data from Sugar & Corliss (1985)
i State J Present Expt

1 $3{\rm s}^{2}3{\rm p}^5$ $^2{\rm P}^{\rm o}$ 3/2 .0000 .0000

2 $3{\rm s}^{2}3{\rm p}^5$ $^2{\rm P}^{\rm o}$ 1/2 .1346 .1429

3 $3{\rm s}3p^6$ $^2S^{\rm e}$ 1/2 2.631 2.636

4 $3{\rm p}^43{\rm d}$ $^4{\rm D}^{\rm e}$ 5/2 3.581 3.542

5 $3{\rm p}^43{\rm d}$ $^4{\rm D}^{\rm e}$ 7/2 3.582 3.542

6 $3{\rm p}^43{\rm d}$ $^4{\rm D}^{\rm e}$ 3/2 3.591 3.554

7 $3{\rm p}^43{\rm d}$ $^4{\rm D}^{\rm e}$ 1/2 3.603 3.568

8 $3{\rm p}^43{\rm d}$ $^4{\rm F}^{\rm e}$ 9/2 3.863 3.806

9 $3{\rm p}^43{\rm d}$ $^2{\rm P}^{\rm e}$ 1/2 3.875

10 $3{\rm p}^43{\rm d}$ $^4{\rm F}^{\rm e}$ 7/2 3.906 3.853

11 $3{\rm p}^43{\rm d}$ $^4{\rm F}^{\rm e}$ 5/2 3.938 3.889

12 $3{\rm p}^43{\rm d}$ $^4{\rm F}^{\rm e}$ 3/2 3.947 3.903

13 $3{\rm p}^43{\rm d}$ $^2{\rm P}^{\rm e}$ 3/2 3.952 3.936

14 $3{\rm p}^43{\rm d}$ $^4{\rm P}^{\rm e}$ 1/2 4.014 3.962

15 $3{\rm p}^43{\rm d}$ $^2{\rm D}^{\rm e}$ 3/2 4.015 3.961

16 $3{\rm p}^43{\rm d}$ $^4{\rm P}^{\rm e}$ 3/2 4.057

17 $3{\rm p}^43{\rm d}$ $^4{\rm P}^{\rm e}$ 5/2 4.079 4.026

18 $3{\rm p}^43{\rm d}$ $^2{\rm F}^{\rm e}$ 7/2 4.081 4.017

19 $3{\rm p}^43{\rm d}$ $^2{\rm D}^{\rm e}$ 5/2 4.097

20 $3{\rm p}^43{\rm d}$ $^2{\rm G}^{\rm e}$ 9/2 4.172 4.108

21 $3{\rm p}^43{\rm d}$ $^2{\rm G}^{\rm e}$ 7/2 4.173 4.111

22 $3{\rm p}^43{\rm d}$ $^2{\rm F}^{\rm e}$ 5/2 4.195 4.126

23 $3{\rm p}^43{\rm d}$ $^2{\rm F}^{\rm e}$ 5/2 4.460

24 $3{\rm p}^43{\rm d}$ $^2{\rm F}^{\rm e}$ 7/2 4.495 4.429

25 $3{\rm p}^43{\rm d}$ $^2{\rm D}^{\rm e}$ 3/2 4.735 4.664

26 $3{\rm p}^43{\rm d}$ $^2{\rm D}^{\rm e}$ 5/2 4.774

27 $3{\rm p}^43{\rm d}$ $^2{\rm S}^{\rm e}$ 1/2 5.059 4.938

28 $3{\rm p}^43{\rm d}$ $^2{\rm P}^{\rm e}$ 3/2 5.255 5.141

29 $3{\rm p}^43{\rm d}$ $^2{\rm P}^{\rm e}$ 1/2 5.307 5.194

30 $3{\rm p}^43{\rm d}$ $^2{\rm D}^{\rm e}$ 5/2 5.351 5.221

31 $3{\rm p}^43{\rm d}$ $^2{\rm D}^{\rm e}$ 3/2 5.466 5.342

**Table 1:** The lowest 31 energy levels (Ryd) for Fe X. For reference, level 32 (3s3p⁵3d) is calculated at 6.284 Ryd. 180 levels were actually included in the calculation (see Fig. 1). "Expt'' is reference data from Sugar & Corliss (1985)
i	State	J	Present	Expt
1	$3{\rm s}^{2}3{\rm p}^5$	$^2{\rm P}^{\rm o}$ 3/2	.0000	.0000
2	$3{\rm s}^{2}3{\rm p}^5$	$^2{\rm P}^{\rm o}$ 1/2	.1346	.1429
3	$3{\rm s}3p^6$	$^2S^{\rm e}$ 1/2	2.631	2.636
4	$3{\rm p}^43{\rm d}$	$^4{\rm D}^{\rm e}$ 5/2	3.581	3.542
5	$3{\rm p}^43{\rm d}$	$^4{\rm D}^{\rm e}$ 7/2	3.582	3.542
6	$3{\rm p}^43{\rm d}$	$^4{\rm D}^{\rm e}$ 3/2	3.591	3.554
7	$3{\rm p}^43{\rm d}$	$^4{\rm D}^{\rm e}$ 1/2	3.603	3.568
8	$3{\rm p}^43{\rm d}$	$^4{\rm F}^{\rm e}$ 9/2	3.863	3.806
9	$3{\rm p}^43{\rm d}$	$^2{\rm P}^{\rm e}$ 1/2	3.875
10	$3{\rm p}^43{\rm d}$	$^4{\rm F}^{\rm e}$ 7/2	3.906	3.853
11	$3{\rm p}^43{\rm d}$	$^4{\rm F}^{\rm e}$ 5/2	3.938	3.889
12	$3{\rm p}^43{\rm d}$	$^4{\rm F}^{\rm e}$ 3/2	3.947	3.903
13	$3{\rm p}^43{\rm d}$	$^2{\rm P}^{\rm e}$ 3/2	3.952	3.936
14	$3{\rm p}^43{\rm d}$	$^4{\rm P}^{\rm e}$ 1/2	4.014	3.962
15	$3{\rm p}^43{\rm d}$	$^2{\rm D}^{\rm e}$ 3/2	4.015	3.961
16	$3{\rm p}^43{\rm d}$	$^4{\rm P}^{\rm e}$ 3/2	4.057
17	$3{\rm p}^43{\rm d}$	$^4{\rm P}^{\rm e}$ 5/2	4.079	4.026
18	$3{\rm p}^43{\rm d}$	$^2{\rm F}^{\rm e}$ 7/2	4.081	4.017
19	$3{\rm p}^43{\rm d}$	$^2{\rm D}^{\rm e}$ 5/2	4.097
20	$3{\rm p}^43{\rm d}$	$^2{\rm G}^{\rm e}$ 9/2	4.172	4.108
21	$3{\rm p}^43{\rm d}$	$^2{\rm G}^{\rm e}$ 7/2	4.173	4.111
22	$3{\rm p}^43{\rm d}$	$^2{\rm F}^{\rm e}$ 5/2	4.195	4.126
23	$3{\rm p}^43{\rm d}$	$^2{\rm F}^{\rm e}$ 5/2	4.460
24	$3{\rm p}^43{\rm d}$	$^2{\rm F}^{\rm e}$ 7/2	4.495	4.429
25	$3{\rm p}^43{\rm d}$	$^2{\rm D}^{\rm e}$ 3/2	4.735	4.664
26	$3{\rm p}^43{\rm d}$	$^2{\rm D}^{\rm e}$ 5/2	4.774
27	$3{\rm p}^43{\rm d}$	$^2{\rm S}^{\rm e}$ 1/2	5.059	4.938
28	$3{\rm p}^43{\rm d}$	$^2{\rm P}^{\rm e}$ 3/2	5.255	5.141
29	$3{\rm p}^43{\rm d}$	$^2{\rm P}^{\rm e}$ 1/2	5.307	5.194
30	$3{\rm p}^43{\rm d}$	$^2{\rm D}^{\rm e}$ 5/2	5.351	5.221
31	$3{\rm p}^43{\rm d}$	$^2{\rm D}^{\rm e}$ 3/2	5.466	5.342

Table 2: gf-values for transitions from the 3p⁵ ²P $^{\rm o}_{3/2,1/2}$ ground levels to the the 3s3p⁶ and 3p⁴3d levels for Fe X. BD = gf calculated by Bhatia & Doshek (1995); Present = gf calculated from the same wavefunction as used in the present 181-level BPRM collision calculation; A = present calculated A-value, s^-1. The level indexing (i,i') is defined in Table 1
i-i' J_i' BD Present A, s^-1

1-3 1/2 0.0716 0.1027 2.854E9

1-4 5/2 0.71E-4 2.08E-4 3.504E6

1-6 3/2 2.06E-4 2.02E-4 5.281E6

1-7 1/2 9.14E-5 5.59E-5 2.926E6

1-9 1/2 2.68E-3 8.12E-4 4.954E7

1-11 5/2 1.24E-3 1.49E-3 3.031E7

1-12 3/2 19.7E-3 9.03E-3 2.783E8

1-13 3/2 5.65E-5 2.10E-3 6.651E7

1-14 1/2 2.25E-3 3.56E-3 2.325E8

1-15 3/2 9.56E-3 4.85E-3 1.557E8

1-16 3/2 28.2E-4 4.17E-4 1.397E7

1-17 5/2 6.40E-3 4.64E-3 1.017E8

1-19 5/2 15.9E-3 3.67E-3 8.114E7

1-22 5/2 11.1E-4 6.82E-4 1.579E7

1-23 5/2 3.66E-3 4.60E-3 1.206E8

1-25 3/2 0.0131 0.0100 4.441E8

1-26 5/2 0.58E-3 2.45E-3 7.356E7

1-27 1/2 1.940 1.312 1.338E11

1-28 3/2 3.788 2.817 1.542E11

1-29 1/2 0.1863 0.3693 4.260E10

1-30 5/2 6.462 5.128 1.941E11

1-31 3/2 0.283 0.1710 1.013E10

2-3 1/2 0.0365 0.0513 1.285E9

2-6 3/2 31.9E-6 2.93E-6 7.094E4

2-7 1/2 13.6E-5 7.75E-5 3.757E6

2-9 1/2 72.0E-3 3.62E-3 2.055E8

2-12 3/2 7.51E-3 3.96E-3 1.137E8

2-13 3/2 4.16E-4 3.95E-4 1.169E7

2-14 1/2 6.77E-4 7.17E-4 4.382E7

2-15 3/2 8.56E-3 3.31E-3 9.929E7

2-16 3/2 15.9E-5 6.84E-5 2.149E6

2-25 3/2 11.7E-3 7.62E-3 3.193E8

2-27 1/2 0.2115 0.4553 4.403E10

2-28 3/2 0.2402 0.1052 5.468E9

2-29 1/2 1.833 1.091 1.196E11

2-31 3/2 4.004 3.213 1.810E11

**Table 2:** gf-values for transitions from the 3p⁵ ²P $^{\rm o}_{3/2,1/2}$ ground levels to the the 3s3p⁶ and 3p⁴3d levels for Fe X. BD = gf calculated by Bhatia & Doshek (1995); Present = gf calculated from the same wavefunction as used in the present 181-level BPRM collision calculation; A = present calculated A-value, s^-1. The level indexing (i,i') is defined in Table 1
i-i'	J_i'	BD	Present	A, s^-1
1-3	1/2	0.0716	0.1027	2.854E9
1-4	5/2	0.71E-4	2.08E-4	3.504E6
1-6	3/2	2.06E-4	2.02E-4	5.281E6
1-7	1/2	9.14E-5	5.59E-5	2.926E6
1-9	1/2	2.68E-3	8.12E-4	4.954E7
1-11	5/2	1.24E-3	1.49E-3	3.031E7
1-12	3/2	19.7E-3	9.03E-3	2.783E8
1-13	3/2	5.65E-5	2.10E-3	6.651E7
1-14	1/2	2.25E-3	3.56E-3	2.325E8
1-15	3/2	9.56E-3	4.85E-3	1.557E8
1-16	3/2	28.2E-4	4.17E-4	1.397E7
1-17	5/2	6.40E-3	4.64E-3	1.017E8
1-19	5/2	15.9E-3	3.67E-3	8.114E7
1-22	5/2	11.1E-4	6.82E-4	1.579E7
1-23	5/2	3.66E-3	4.60E-3	1.206E8
1-25	3/2	0.0131	0.0100	4.441E8
1-26	5/2	0.58E-3	2.45E-3	7.356E7
1-27	1/2	1.940	1.312	1.338E11
1-28	3/2	3.788	2.817	1.542E11
1-29	1/2	0.1863	0.3693	4.260E10
1-30	5/2	6.462	5.128	1.941E11
1-31	3/2	0.283	0.1710	1.013E10
2-3	1/2	0.0365	0.0513	1.285E9
2-6	3/2	31.9E-6	2.93E-6	7.094E4
2-7	1/2	13.6E-5	7.75E-5	3.757E6
2-9	1/2	72.0E-3	3.62E-3	2.055E8
2-12	3/2	7.51E-3	3.96E-3	1.137E8
2-13	3/2	4.16E-4	3.95E-4	1.169E7
2-14	1/2	6.77E-4	7.17E-4	4.382E7
2-15	3/2	8.56E-3	3.31E-3	9.929E7
2-16	3/2	15.9E-5	6.84E-5	2.149E6
2-25	3/2	11.7E-3	7.62E-3	3.193E8
2-27	1/2	0.2115	0.4553	4.403E10
2-28	3/2	0.2402	0.1052	5.468E9
2-29	1/2	1.833	1.091	1.196E11
2-31	3/2	4.004	3.213	1.810E11

Table 3: Predictions and measurement (Träbert 1996) on the line doublet 3s²3p⁵ ²P $^{\rm o}_{3/2,1/2}$ - 3s3p⁶ ²S $^{\rm e}_{1/2}$ for Fe X. BD = calculated from Bhatia & Doshek (1995); Present = calculated from the same wavefunction as used in the present 181-level BPRM collision calculation
BD Present Measured

Lifetime ps. 344 242 $270\pm20$

Branch ratio 2.17 2.22 $2.4\pm0.3$

**Table 3:** Predictions and measurement (Träbert 1996) on the line doublet 3s²3p⁵ ²P $^{\rm o}_{3/2,1/2}$ - 3s3p⁶ ²S $^{\rm e}_{1/2}$ for Fe X. BD = calculated from Bhatia & Doshek (1995); Present = calculated from the same wavefunction as used in the present 181-level BPRM collision calculation
	BD	Present	Measured
Lifetime ps.	344	242	$270\pm20$
Branch ratio	2.17	2.22	$2.4\pm0.3$

Table 4: A comparison of collision strengths for Fe X fine structure transitions as a function of electron impact energy (Ryd). The level indexing (i,i') is defined in Table 1; the numbers on the same line as the transition are collision strengths from the present calculation and the ones below labelled BD are from Bhatia & Doschek (1995) for the same transition
i-i' 18.0 27.0 36.0 45.0

1-3 .356 .363 .361 .361

BD .421 .441 .461 .479

2-3 .186 .188 .188 .188

BD .226 .239 .252 .262

1-4 .044 .028 .020 .015

BD .039 .026 .018 .013

2-4 .014 .0085 .0060 .0045

BD .012 .0079 .0056 .0042

3-4 .0020 .0013 .0010 .0008

BD .0020 .0013 .0009 .0007

1-5 .0662 .0423 .0293 .0213

BD .0593 .0383 .0265 .0193

$\displaystyle 3{\rm d}(r)$	=	$\displaystyle 141.9677864\exp(-8.0582535r)r^3$
		$\displaystyle +58.2199125\exp(-4.3181676r)r^3$
$\displaystyle 4{\rm f}(r)$	=	$\displaystyle 183.85325\exp(-5.175)r^4.$

i-i'	18.0	27.0	36.0	45.0
1-3	.356	.363	.361	.361
BD	.421	.441	.461	.479
2-3	.186	.188	.188	.188
BD	.226	.239	.252	.262
1-4	.044	.028	.020	.015
BD	.039	.026	.018	.013
2-4	.014	.0085	.0060	.0045
BD	.012	.0079	.0056	.0042
3-4	.0020	.0013	.0010	.0008
BD	.0020	.0013	.0009	.0007
1-5	.0662	.0423	.0293	.0213
BD	.0593	.0383	.0265	.0193

2 The calculation