2 Atomic calculations

The EIE calculations are described in detail in CP99a,b, and compared with previous works. Below, we briefly summarise the qualitative aspects of those results. The next subsection discusses in detail the present calculations for the forbidden and allowed A-values for Fe VI.

2.1 Electron impact excitation of Fe VI

With the exception of two calculations two decades ago, there were no other calculations until the recent work reported in CP99a,b. It is difficult to consider the relativistic effects together with the electron correlation effects in this complex atomic system, and the coupled channel calculations necessary for such studies are very computer intensive. The two previous sources for the excitation rates of Fe VI are the non-relativistic close coupling (CC) calculations by Garstang et al. (1978) and the distorted-wave (DW) calculations by Nussbaumer & Storey (1978). Although the Garstang et al. (1978) calculations were in the CC approximation, they used a very small basis set and did not obtain the resonance structures; their results are given only for the averaged values. The Nussbaumer & Storey (1978) calculations were in the DW approximations that does not enable a treatment of resonances. Therefore neither set of calculations included resonances or the coupling effects due to higher configurations. Owing primarily to these factors we find that the earlier excitation rates of Nussbaumer and Storey are lower by up to factors of three or more when compared to the new Fe VI rates presented in CP99b.

2.2 Radiative transition probabilities

The target expansions in the present work are based on the 34-term wave function expansion for Fe VI developed by Bautista (1996) using the SUPERSTRUCTURE program in the non-relativistic calculations for photoionization cross sections of Fe V. The SUPERSTRUCTURE calculations for Fe VI were extended to include relativistic fine structure using the Breit-Pauli Hamiltonian (Eissner et al. 1974; Eissner 1998). The designations for the 80 levels (34 LS terms) dominated by the configurations ${\rm 3d^3}$, ${\rm 3d^24s}$ and ${\rm 3d^24p}$and their observed energies (Sugar & Corliss 1985), are shown in Table 1.

 

Table 1: The 80 fine structure levels corresponding to the 34 LS terms included in the calculations and their observed energies (Ry) in Fe VI (Sugar & Corliss 1985)

i	Term		2J	Energy		i	Term		2J	Energy
1	3d3	4F	3	0.0		41	3d2(3F)4p	4F$^{\circ}$	5	3.101443
2			5	0.004659		42			7	3.110750
3			7	0.010829		43			9	3.120492
4			9	0.018231		44	3d2(3F)4p	2F$^{\circ}$	5	3.121742
5	3d3	4P	1	0.170756		45			7	3.131189
6			3	0.172612		46	3d2(3F)4p	4D$^{\circ}$	1	3.131290
7			5	0.178707		47			3	3.127568
8	3d3	2G	7	0.187870		48			5	3.137250
9			9	0.194237		49			7	3.147723
10	3d3	2P	1	0.241445		50	3d2(3F)4p	2D$^{\circ}$	3	3.140706
11			3	0.238888		51			5	3.152138
12	3d3	$^2{\rm D}2$	3	0.260877		52	3d2(3F)4p	2G$^{\circ}$	7	3.179977
13			5	0.259568		53			9	3.189597
14	3d3	2H	9	0.261755		54	3d2(3P)4p	2S$^{\circ}$	1	3.205891
15			11	0.266116		55	3d2(3P)4p	4S$^{\circ}$	3	3.240986
16	3d3	2F	5	0.424684		56	3d2(1D)4p	2P$^{\circ}$	1	3.272354
17			7	0.421163		57			3	3.260106
18	3d3	2D1	3	0.656558		58	3d2(1D)4p	2F$^{\circ}$	5	3.265386
19			5	0.653448		59			7	3.279505
20	3d2(3F)4s	4F	3	2.386075		60	3d2(3P)4p	4D$^{\circ}$	1	3.275057
21			5	2.390877		61			3	3.278569
22			7	2.397871		62			5	3.287005
23			9	2.406823		63			7	3.301248
24	3d2(3F)4s	2F	5	2.452586		64	3d2(1D)4p	2D$^{\circ}$	3	3.297495
25			7	2.466551		65			5	3.304281
26	3d2(1D)4s	2D	3	2.562646		66	3d2(3P)4p	4P$^{\circ}$	1	3.316518
27			5	2.559763		67			3	3.320593
28	3d2(3P)4s	4P	1	2.565008		68			5	3.330627
29			3	2.570092		69	3d2(1G)4p	2G$^{\circ}$	7	3.326827
30			5	2.578448		70			9	3.328555
31	3d2(3P)4s	2P	1	2.623713		71	3d2(3P)4p	2D$^{\circ}$	3	3.376592
32			3	2.630266		72			5	3.376970
33	3d2(1G)4s	2G	7	2.663908		73	3d2(1G)4p	2H$^{\circ}$	9	3.390785
34			9	2.663752		74			11	3.405461
35	3d2(1S)4s	2S	1	3.065870		75	3d2(3P)4p	2P$^{\circ}$	1	3.408944
36	3d2(3F)4p	4G$^{\circ}$	5	3.082420		76			3	3.412018
37			7	3.093542		77	3d2(1G)4p	2F$^{\circ}$	5	3.454410
38			9	3.106829		78			7	3.444151
39			11	3.123191		79	3d2(1S)4p	2P$^{\circ}$	1	3.719860
40	3d2(3F)4p	4F$^{\circ}$	3	3.094115		80			3	3.739745

These observed energies were used in the Hamiltonian diagonalization to obtain the R-matrix surface amplitudes in stage STGH (Berrington et al. 1995). This table also provides the key to the level indices for transitions in tabulating dipole-allowed and forbidden transition probabilities and the Maxwellian-averaged collision strengths from CP99a,b. Examining the new Breit-Pauli SUPERSTRUCTURE calculations we deduce that the computed energy values for levels 7 and 13; levels 11 and 12 in Table 1 of CP99a should be reversed given the level designations, respectively. An indication of the accuracy of the target eigenfunctions may be obtained from the calculated energy levels in Table 1 of CP99a, and from the computed length and velocity oscillator strengths for some of the dipole fine structure transitions given in their Table 2.

 

Table 2: Partial Table 2 (complete table available electronically from CDS). Weighted dipole allowed E1 oscillator strengths $gf_{\rm L}$, $gf_{\rm V}$ in the length and velocity formulations, and the Einstein A-coefficients $A_{\rm L}$ in the length formulation

i	j	$gf_{\rm L}$	$gf_{\rm V}$	$A_{\rm L}$	i	j	$gf_{\rm L}$	$gf_{\rm V}$	$A_{\rm L}$
36	1	9.34e-02	9.68e-02	1.19e+09	80	2	9.64e-06	9.10e-06	2.70e+05
40	1	4.64e-01	4.68e-01	8.92e+09	36	3	2.91e-04	2.88e-04	3.68e+06
41	1	9.82e-02	9.85e-02	1.26e+09	37	3	2.14e-04	2.67e-04	2.04e+06
44	1	2.43e-03	2.50e-03	3.17e+07	38	3	1.75e-01	1.80e-01	1.34e+09
46	1	2.57e-01	2.55e-01	1.01e+10	41	3	1.05e-01	1.05e-01	1.34e+09
47	1	2.88e-02	2.89e-02	5.66e+08	42	3	9.02e-01	9.05e-01	8.71e+09
48	1	8.98e-04	8.83e-04	1.18e+07	43	3	8.20e-02	8.14e-02	6.37e+08
50	1	5.48e-02	5.40e-02	1.09e+09	44	3	8.66e-02	8.58e-02	1.12e+09
51	1	2.56e-03	2.50e-03	3.40e+07	45	3	2.86e-02	2.91e-02	2.80e+08
54	1	1.82e-06	1.86e-06	7.49e+04	48	3	5.06e-01	5.01e-01	6.62e+09
55	1	1.90e-08	1.54e-08	4.01e+02	49	3	3.99e-02	3.90e-02	3.95e+08
56	1	5.62e-03	5.89e-03	2.42e+08	51	3	8.14e-02	8.18e-02	1.07e+09
57	1	1.22e-04	1.29e-04	2.61e+06	52	3	6.25e-04	5.87e-04	6.30e+06
58	1	1.12e-04	1.09e-04	1.59e+06	53	3	1.30e-03	1.17e-03	1.06e+07
60	1	6.74e-02	7.11e-02	2.90e+09	58	3	1.12e-02	1.16e-02	1.58e+08
61	1	2.92e-02	3.06e-02	6.29e+08	59	3	6.04e-03	6.33e-03	6.48e+07
62	1	2.05e-03	2.14e-03	2.97e+07	62	3	1.71e-01	1.77e-01	2.45e+09
64	1	4.64e-04	4.80e-04	1.01e+07	63	3	2.73e-02	2.80e-02	2.97e+08
65	1	5.92e-05	5.99e-05	8.65e+05	65	3	3.28e-03	3.35e-03	4.77e+07
66	1	2.69e-05	2.67e-05	1.19e+06	68	3	1.32e-04	1.28e-04	1.95e+06
67	1	2.30e-05	2.23e-05	5.09e+05	69	3	9.30e-05	8.67e-05	1.03e+06
68	1	9.37e-07	8.67e-07	1.39e+04	70	3	1.45e-06	1.80e-07	1.28e+04
71	1	1.64e-04	1.37e-04	3.74e+06	72	3	2.46e-04	1.83e-04	3.74e+06
72	1	2.17e-05	1.86e-05	3.32e+05	73	3	2.64e-06	2.50e-06	2.42e+04
75	1	2.27e-05	1.54e-05	1.06e+06	77	3	1.38e-05	1.58e-05	2.19e+05
76	1	1.93e-06	1.28e-06	4.50e+04	78	3	7.28e-07	8.26e-07	8.62e+03
77	1	1.51e-05	1.87e-05	2.42e+05	37	4	8.83e-04	8.95e-04	8.38e+06
79	1	1.30e-05	1.26e-05	7.22e+05	38	4	1.59e-03	1.52e-03	1.22e+07
80	1	2.25e-06	2.15e-06	6.33e+04	39	4	1.86e-01	1.90e-01	1.20e+09
36	2	2.29e-03	2.47e-03	2.90e+07	42	4	7.97e-02	8.01e-02	7.66e+08
37	2	1.36e-01	1.41e-01	1.31e+09	43	4	1.29e+0	1.29e+0	1.00e+10
40	2	8.40e-02	8.49e-02	1.61e+09	45	4	3.29e-01	3.28e-01	3.20e+09
41	2	6.24e-01	6.27e-01	8.01e+09	49	4	6.18e-01	6.10e-01	6.07e+09
42	2	1.20e-01	1.19e-01	1.16e+09	52	4	8.53e-05	8.03e-05	8.57e+05
44	2	5.67e-03	5.86e-03	7.37e+07	53	4	4.35e-03	4.02e-03	3.52e+07
45	2	3.71e-03	3.76e-03	3.64e+07	59	4	5.10e-02	5.22e-02	5.45e+08
47	2	3.04e-01	3.01e-01	5.96e+09	63	4	2.30e-01	2.36e-01	2.49e+09
48	2	6.17e-02	6.10e-02	8.10e+08	69	4	3.62e-04	3.81e-04	3.97e+06
49	2	3.61e-04	3.41e-04	3.58e+06	70	4	5.33e-05	4.02e-05	4.70e+05
50	2	1.34e-01	1.34e-01	2.65e+09	73	4	2.09e-07	8.11e-08	1.91e+03
51	2	2.82e-02	2.79e-02	3.74e+08	74	4	1.18e-05	1.07e-05	9.04e+04
52	2	5.53e-04	4.96e-04	5.60e+06	78	4	1.12e-04	1.21e-04	1.32e+06
55	2	4.58e-07	4.10e-07	9.63e+03	40	5	8.03e-04	7.85e-04	1.38e+07
57	2	5.81e-04	6.07e-04	1.24e+07	46	5	1.14e-01	1.09e-01	4.03e+09
58	2	2.26e-03	2.43e-03	3.21e+07	47	5	8.80e-02	8.41e-02	1.54e+09
59	2	2.86e-04	2.88e-04	3.08e+06	50	5	2.53e-02	2.40e-02	4.48e+08
61	2	1.17e-01	1.22e-01	2.51e+09	54	5	1.56e-03	1.57e-03	5.78e+07
62	2	3.70e-02	3.84e-02	5.33e+08	55	5	1.66e-01	1.67e-01	3.15e+09
63	2	1.42e-03	1.47e-03	1.55e+07	56	5	1.88e-03	1.90e-03	7.28e+07
64	2	8.48e-04	8.65e-04	1.85e+07	57	5	5.31e-03	5.48e-03	1.02e+08
65	2	9.55e-04	9.84e-04	1.39e+07	60	5	2.36e-02	2.32e-02	9.15e+08
67	2	1.22e-04	1.21e-04	2.70e+06	61	5	2.81e-02	2.77e-02	5.46e+08
68	2	1.99e-05	1.81e-05	2.94e+05	64	5	1.97e-03	1.97e-03	3.88e+07
69	2	3.84e-06	2.14e-06	4.26e+04	66	5	1.95e-02	1.95e-02	7.75e+08
71	2	7.81e-05	5.55e-05	1.78e+06	67	5	8.78e-02	8.79e-02	1.75e+09
72	2	1.82e-04	1.48e-04	2.77e+06	71	5	2.20e-04	2.10e-04	4.55e+06
76	2	1.63e-05	1.15e-05	3.81e+05	75	5	3.78e-04	3.79e-04	1.59e+07
77	2	1.80e-06	1.96e-06	2.87e+04	76	5	4.32e-05	2.90e-05	9.11e+05
78	2	1.07e-05	1.33e-05	1.27e+05	79	5	2.11e-05	1.94e-05	1.07e+06

The agreement between the length and velocity oscillator strengths is generally about 10%, an acceptable level of accuracy for a complex iron ion.

2.2.1 Dipole allowed fine-structure transitions

The weighted oscillator strength gf or the Einstein A-coefficient for a dipole allowed fine-structure transition is proportional to the generalised line strength (Seaton 1987) defined, in either length form or velocity form, by the equations

$$% S_{\rm L}\ =\ \mid <\Psi_j\mid\sum^{N+1}_{k=1}z_k\mid\Psi_i>\mid ^2$$ (1)

and

$$% S_{\rm V}=\omega^{-2}\mid\left<\Psi_j\mid\sum^{N+1}_{k=1} \frac{\partial}{\partial z_k}\mid\Psi_i\right >\mid ^2$$ (2)

where $\omega$ is the incident photon energy in Ry, and $\Psi_i$ and $\Psi_j$are the wave functions representing the initial and final states, respectively.

Using the transition energy, E_ij, between the initial and final states, g_if_ij and A_ji for this transition can be obtained from S as

$$% g_if_{ij}=\frac{E_{ij}}3S$$ (3)

and

$$% A_{ji}({\rm a.u.})\! = \! \frac 12\alpha ^3\frac{g_i}{g_j}E_{ij}^2f_{ij} \! =\! 2.6774\,\, 10^9(E_j-E_i)^3S^{E1}_{ij}/g_j$$ (4)

where $\alpha=1/137.036$ is the fine structure constant in a.u., and g_i, g_j are the statistical weights of the initial and final states, respectively. In terms of c.g.s unit of time,

$$% A_{ji}({\rm s}^{-1})=\frac {A_{ji}({\rm a.u.})}{\tau _0}$$ (5)

where $\tau _0=2.4191^{-17}~{\rm s}$ is the atomic unit of time.

We can use experimental transition energy $E_{ij}^{\rm exp}$ to obtain refined $g_if^{\rm e}_{ij}$ and $A^{\rm e}_{ji}$ values through

$$% g_if^{\rm e}_{ij}=g_if_{ij}\frac{E_{ij}^{\rm exp}}{E_{ij}^{\rm cal}}$$ (6)

$$% A^{\rm e}_{ji}=A_{ji}\left(\frac{E_{ij}^{\rm exp}}{E_{ij}^{\rm cal}}\right)^3.$$ (7)

Computed $gf_{\rm L}$ and $gf_{\rm V}$ values, in both the length and the velocity formulations, for 867 E1 (dipole allowed and intercombination) transitions within the first 80 fine structure levels are tabulated in Table 2 (a partial table is given in the text; the complete Table 2 is available electronically from the CDS library). Transition probabilities $A_{\rm L}$ are also given in the length formulation, which is generally more accurate than the velocity formulation in the present calculations. Experimental level energies are used to improve the accuracy of the calculated gf and A-values. All of these E1 transition probabilities of Fe VI were incorporated in the calculation of line ratios when accounting for the FLE effect by the UV continuum radiation field (details below).

2.2.2 Forbidden electric quadrupole (E2) and magnetic dipole (M1) transitions

The Breit-Pauli mode of the SUPERSTRUCTURE code was also used to calculate the E2 and the M1transitions in Fe VI. The configuration expansion was adapted from that used to optimise the lowest 34 LS terms by Bautista (1996). The spectroscopic configurations, the correlation configurations and the scaling parameters $\lambda _{nl}$ for the Thomas-Fermi-Dirac-Amaldi type potential of orbital nl are listed in Tables 3 and 4 of CP99a. Much effort was devoted to choosing the correlation configurations to optimise the target wavefunctions, within the constraint of computational constraints associated with large memory requirements for many of the ${\rm 3p}$ open shell configurations. The primary criteria in this selection are the level of agreement with the observed values for (a) the level energies and fine structure splittings within the lowest LS terms, and (b) the f-values for a number of the low lying dipole allowed transitions. Another practical criterion is that the calculated A-values should be relatively stable with minor changes in scaling parameters.

Like the procedure used in the calculation of the dipole allowed and intercombination E1 gf-values, the experimental level energies are also used to improve the accuracy of the computed E2 and M1 transition probabilities A^E2 and A^M1, given as

$$% g_jA^{E2}_{ji}=2.6733\,\, 10^3(E_j-E_i)^5S^{E2}(i,j) ({\rm s}^{-1})$$ (8)

and

$$% g_jA^{M1}_{ji}=3.5644\,\, 10^4(E_j-E_i)^3S^{M1}(i,j) ({\rm s}^{-1}).$$ (9)

The computed A^E2 and A^M1 for all 130 transitions among the first 19 levels are given in Table 3.

 

Table 3: Comparison of the electric quadrupole (E2) and magnetic dipole (M1) transition probabilities between the first 19 levels of Fe VI in ${\rm s}^{-1}$among the present calculation by SUPERSTRUCTURE, calculation by Garstang et al. (1978) and calculation by Nussbaumer & Storey (1978)

Transition		Present		Garstang et al.		NS
i	j	E2	M1	E2	M1	E2	M1
2	1	5.13e-11	5.76e-3	0.0	5.7e-3	4.97-11	5.74-3
5	1	6.04e-2	2.01e-4	8.3e-2	8.0e-5	5.97-2	3.31-4
6	1	1.27e-2	3.40e-3	1.7e-2	1.2e-3	1.26e-2	4.05e-3
7	1	7.15e-4	2.15e-4	1.0e-3	9.0e-5	7.04e-4	2.66e-4
8	1	1.90e-5	0.0	1.4e-5	0.0	1.66-5
10	1	1.99e-3	1.54e-3	7.0e-3	7.3e-4	1.54e-3	1.99e-3
11	1	6.88e-4	3.70e-1	2.8e-3	1.19e-1	5.40e-4	3.56e-1
12	1	3.84e-4	3.77e-1	6.6e-4	4.01e-1	2.67e-4	3.86e-1
13	1	5.71e-7	4.97e-2	2.8e-6	3.36e-2	9.53e-7	4.34e-2
16	1	4.62e-3	1.97e-1			4.53e-3	2.23e-1
17	1	6.60e-4	0.0			6.55e-4
18	1	3.69e-3	8.60e-2			4.14e-3	1.26e-1
19	1	6.35e-4	4.97e-3			6.30e-4	9.44e-3
3	2	2.03e-10	1.34e-2	0.0	1.3e-2	1.99e-10	1.34e-2
4	2	6.46e-10	0.0
5	2	3.47e-2	0.0	4.85e-2	0.0	3.42e-2
6	2	3.35e-2	1.97e-3	4.59e-2	6e-4	3.32e-2	1.78e-3
7	2	5.69e-3	9.87e-4	7.9e-3	4.2e-4	5.63e-3	1.36e-3
8	2	1.63e-6	2.04e-1	1.6e-5	1.73e-1	1.74e-6	2.44e-1
9	2	6.00e-6	0.0	2e-6	0.0	4.71e-6
10	2	3.19e-3	0.0	1.5e-3	0.0	2.75e-3
11	2	3.39e-3	5.98e-1	6.4e-3	1.84e-1	2.78e-3	5.75e-1
12	2	7.96e-4	7.82e-1	1.2e-3	7.1e-1	5.37e-4	7.30e-1
13	2	2.95e-5	1.44e-1	2.1e-7	9.5e-2	2.79e-5	1.39e-1
14	2	2.59e-5	0.0	2.5e-5	0.0	2.70e-5
16	2	9.77e-4	2.73e-2			1.09e-3	3.08e-2
17	2	1.90e-3	8.39e-2			1.70e-3	1.01e-1
18	2	2.77e-6	1.81e-1			1.21e-5	2.51e-1
19	2	2.05e-3	1.53e-2			2.11e-3	2.39e-2
4	3	3.66e-10	1.44e-2	0.0	1.4e-2	3.59e-10	1.45e-2
6	3	3.86e-2	0.0	5.4e-2	0.0	3.84e-2
7	3	2.12e-2	2.39e-3	2.94e-2	9e-4	2.11e-2	2.63e-3
8	3	1.83e-5	2.19e-1	1.2e-5	1.85e-1	2.02e-5	2.61e-1
9	3	2.02e-6	2.20e-1	3.1e-5	1.86e-1	1.96e-6	2.51e-1
11	3	4.95e-3	0.0	6.1e-3	0.0	4.14e-3
12	3	2.18e-3	0.0	5.3e-4	0.0	1.71e-3
13	3	3.82e-4	1.12e+0	5e-5	7.29e-1	3.41e-4	1.07e+0
14	3	6.41e-5	2.20e-3	1.6e-5	4.3e-3	7.12e-5	4.12e-3
15	3	1.83e-5	0.0	5.0e-5	0.0	1.94e-5
16	3	9.55e-4	3.57e-2			1.06e-3	3.78e-2
17	3	4.11e-4	1.49e-2			5.97e-4	1.70e-2
18	3	1.30e-2	0.0			1.57e-2
19	3	4.04e-3	1.64e-1			4.94e-3	2.45e-1
7	4	5.28e-2	0.0	7.3e-2	0.0	5.23e-2
8	4	4.06e-6	1.26e-2	8.2e-6	1.1e-2	4.29e-6	1.34e-2
9	4	7.96e-5	5.39e-1	7.8e-5	4.55e-1	8.62e-5	6.24e-1
13	4	7.74e-4	0.0	5.1e-4	0.0	6.12e-4
14	4	5.55e-6	3.35e-3	2.3e-5	7.8e-3	4.63e-6	6.86e-3
15	4	1.56e-4	6.73e-4	1.9e-4	5.7e-4	1.68e-4	1.01e-3
16	4	1.60e-4	0.0			2.04e-4
17	4	4.27e-3	2.17e-1			5.01e-3	2.56e-1
19	4	5.55e-2	0.0			6.41e-2
6	5	6.56e-13	1.86e-4	0.0	1.85e-4	6.64e-13	1.87e-4
7	5	5.71e-9	0.0
10	5	0.0	4.42e-1	0.0	3.3e-1		3.76e-1
11	5	6.09e-7	1.10e-1	2e-7	8.1e-2	4.88e-7	9.29e-2
12	5	3.67e-7	2.08e-2	1.26e-5	1.3e-3	1.71e-7	1.52e-2
13	5	3.22e-7	0.0	5.7e-6	0.0	2.84e-7
16	5	8.51e-4	0.0			5.80e-4

 

Table 3: continued

Transition		Present		Garstang et al.		NS
i	j	E2	M1	E2	M1	E2	M1
18	5	3.83e-2	1.26e-1			2.99e-2	1.37e-1
19	5	9.70e-3	0.0			7.16e-3
7	6	2.08e-9	4.70e-3	0.0	4.6e-3	2.09e-9	4.73e-3
10	6	1.46e-7	9.14e-6	1.5e-6	3.6e-5	2.21e-7	1.76e-5
11	6	3.61e-9	2.56e-1	9.5e-6	1.7e-1	1.69e-8	2.13e-1
12	6	1.00e-5	1.02e-2	5.4e-6	7.4e-4	8.43e-6	6.67e-3
13	6	7.01e-7	2.19e-3	5.4e-5	1.8e-3	5.06e-7	2.27e-3
16	6	1.30e-6	5.25e-4			2.13e-8	1.04e-3
17	6	3.04e-3	0.0			2.15e-3
18	6	1.05e-1	4.73e-1			8.08e-2	5.20e-1
19	6	1.02e-1	2.20e-1			7.71e-2	2.41e-1
8	7	4.85e-13	1.12e-10
10	7	2.97e-6	0.0	1.0e-5	0.0	2.45e-6
11	7	5.13e-6	1.14e-1	1.5e-5	1.19e-1	4.17e-6	1.00e-1
12	7	1.31e-6	2.19e-1	3.6e-6	7.4e-2	9.72e-7	1.76e-1
13	7	5.45e-6	7.98e-2	3.7e-6	4.3e-2	4.33e-6	6.71e-2
14	7	1.76e-9	0.0
16	7	7.10e-5	2.32e-3			6.11e-5	5.47e-3
17	7	3.12e-4	2.11e-4			2.69e-4	4.95e-4
18	7	8.14e-4	1.06e-1			7.99e-4	1.23e-1
19	7	1.49e-3	1.30e+0			1.18e-3	1.41e+0
9	8	1.41e-12	4.03e-3	0.0	4e-3	1.71e-13	4.01e-3
11	8	1.12e-5	0.0	4.9e-6	0.0	7.85e-6
12	8	6.73e-5	0.0	9.3e-5	0.0	5.13e-5
13	8	5.80e-6	2.08e-6	9.6e-6	9e-6	3.89e-6	1.06e-5
14	8	1.82e-4	8.33e-2	1.9e-4	1.38e-1	1.59e-4	1.24e-1
15	8	5.32e-6	0.0	1.7e-5	0.0	4.28e-6
16	8	1.47e-1	1.35e-1			1.49e-1	1.49e-1
17	8	1.24e-2	2.29e-1			1.24e-2	2.53e-1
18	8	1.25e+01	0.0			1.18e+1
19	8	9.45e-1	1.99e-3			9.07e-1	2.23e-3
13	9	5.83e-5	0.0	5.9e-5	0.0	4.08e-5
14	9	2.32e-5	1.43e-1	0.0	2.35e-1	2.53e-5	2.11e-1
15	9	1.35e-4	7.84e-2	2.2e-4	1.29e-1	1.13e-4	1.16e-1
16	9	7.32e-5	0.0			2.06e-5
17	9	1.24e-1	1.07e-1			1.26e-1	1.17e-1
19	9	1.07e+1	0.0			1.00e+1
11	10	1.32e-12	2.19e-4	0.0	3.2e-4	1.21e-12	2.30e-4
12	10	3.15e-7	4.08e-2	4.0e-7	1.18e-2	2.94e-7	3.80e-2
13	10	7.59e-8	0.0	1e-7	0.0
16	10	1.63e-2	0.0			1.41e-2
18	10	1.54e+0	5.98e-3			1.43e+0	2.21e-3
19	10	6.28e-1	0.0			5.87e-1
12	11	5.15e-8	1.04e-1	3e-7	6.56e-2	5.89e-8	1.02e-1
13	11	8.66e-8	5.96e-2	8e-7	2.6e-2	1.10e-7	5.56e-2
16	11	1.05e-2	6.60e-3			1.07e-2	8.08e-3
17	11	2.26e-2	0.0			2.13e-2
18	11	2.11e+0	2.14e-2			2.08e+0	1.08e-2
19	11	6.72e-1	2.98e-1			6.63e-1	3.47e-1
13	12	7.95e-13	2.54e-5	0.0	3.4e-5	6.88e-13	2.70e-5
16	12	2.19e-2	5.41e-3			2.30e-2	7.71e-3
17	12	9.32e-4	0.0			4.44e-4
18	12	5.98e-2	9.58e-3			2.56e-2	3.81e-3
19	12	1.58e+0	2.69e-1			1.46e+0	3.09e-1
14	13	6.89e-15	0.0
16	13	7.25e-3	2.75e-2			7.66e-3	3.63e-2
17	13	2.92e-2	1.02e-2			3.10e-2	1.36e-2
18	13	2.73e-1	7.48e-1			2.96e-1	8.64e-1
19	13	5.79e-1	4.77e-3			6.22e-1	4.80e-3
15	14	5.22e-11	1.33e-3	0.0	1.3e-3	5.33e-11	1.32e-3
16	14	7.02e-2	0.0			6.78e-2
17	14	1.20e-3	5.00e-4			8.85e-4	8.13e-4

 

Table 3: continued

Transition		Present		Garstang et al.		NS
i	j	E2	M1	E2	M1	E2	M1
19	14	1.19e-1	0.0			1.50e-1
17	15	5.18e-2	0.0			4.99e-2
17	16	3.12e-12	8.88e-4			2.88e-12	8.86e-4
18	16	5.14e-1	3.95e-1			4.67e-1	3.72e-1
19	16	9.09e-2	6.41e-1			8.26e-2	6.01e-1
18	17	1.05e-1	0.0			9.67e-2
19	17	5.24e-1	3.73e-1			4.75e-1	3.50e-1
19	18	7.24e-11	6.42e-4			6.68e-11	6.41e-4

The results calculated by Garstang et al. (1978) and by Nussbaumer & Storey (1978) are also given for comparison, where available. For 70 transitions in Table 3 the A^E2 are much smaller than the A^M1, by up to several orders of magnitude for some transitions. While for the other 60 transitions, A^E2 are greater than the A^M1. The computed A^E2 and A^M1 for all the other 1101 transitions within the first 80 levels are given in Table 4 (a partial table is given in the text; the complete Table 4 is available electronically from the CDS library).

 

Table 4: Partial Table 4 (complete table available from CDS). Electric quadrupole (E2) and magnetic dipole (M1) transition probabilities between the first 80 levels of Fe VI in s^-1in the present calculation by SUPERSTRUCTURE

i	j	E2	M1	i	j	E2	M1	i	j	E2	M1	i	j	E2	M1
20	1	4.12e+4	6.84e-6	30	5	9.36e+3	0.0	26	10	8.54e+3	5.52e-5	33	14	6.87e+4	2.90e-3
21	1	2.68e+4	2.50e-5	31	5	0.0	2.86e-2	27	10	3.32e+3	0.0	34	14	1.68e+3	5.30e-3
22	1	2.51e+3	0.0	32	5	1.12e+2	6.88e-3	28	10	0.0	2.53e-4	22	15	1.19e+2	0.0
24	1	2.63e-1	7.50e-4	35	5	0.0	1.97e-4	29	10	8.11e+3	4.29e-6	23	15	1.49e+1	9.31e-7
25	1	3.57e-2	0.0	20	6	4.29e+3	3.09e-8	30	10	4.02e+3	0.0	25	15	5.88e+4	0.0
26	1	4.13e+3	8.11e-4	21	6	8.71e+3	1.42e-6	31	10	0.0	2.34e-4	33	15	2.31e+3	0.0
27	1	1.48e+2	7.62e-5	22	6	9.26e+3	0.0	32	10	1.07e+4	7.71e-5	34	15	6.46e+4	2.90e-3
28	1	4.20e+4	1.93e-6	24	6	1.64e+2	1.77e-7	35	10	0.0	3.08e-2	20	16	7.74e+0	1.87e-3
29	1	4.24e+3	9.91e-4	25	6	8.96e+1	0.0	20	11	2.65e+1	1.39e-4	21	16	2.15e+0	2.14e-4
30	1	2.52e+2	6.16e-5	26	6	1.03e+4	2.65e-4	21	11	7.38e+1	1.50e-4	22	16	1.96e+0	3.00e-4
31	1	3.18e+0	8.46e-6	27	6	1.35e+4	7.67e-4	22	11	1.33e+2	0.0	23	16	1.27e-1	0.0
32	1	8.58e-1	1.28e-8	28	6	5.62e+3	2.54e-3	24	11	1.74e+4	1.13e-4	24	16	4.36e+3	7.11e-6
33	1	1.58e+0	0.0	29	6	7.95e+3	4.01e-4	25	11	1.47e+3	0.0	25	16	4.18e+2	2.74e-3
35	1	1.71e+1	4.03e-8	30	6	1.09e+4	2.04e-3	26	11	9.61e+2	3.38e-4	26	16	5.33e+3	2.20e-4
20	2	3.94e+4	6.70e-5	31	6	1.01e+3	5.91e-6	27	11	1.21e+4	6.87e-4	27	16	1.29e+3	4.16e-4
21	2	2.23e+4	2.14e-6	32	6	2.00e+2	1.28e-2	28	11	1.44e+2	4.15e-5	28	16	3.22e+1	0.0
22	2	2.64e+4	5.43e-5	33	6	5.07e+0	0.0	29	11	5.10e+1	1.27e-4	29	16	4.78e+3	2.44e-4
23	2	1.58e+3	0.0	35	6	6.08e+1	5.35e-4	30	11	1.44e+4	6.58e-5	30	16	7.93e+2	2.95e-4
24	2	8.11e+1	1.59e-4	20	7	3.03e+2	1.62e-7	31	11	3.62e+4	1.53e-3	31	16	7.47e+4	0.0
25	2	8.71e+0	2.89e-4	21	7	1.82e+3	2.99e-8	32	11	8.82e+2	4.32e-3	32	16	1.05e+4	7.40e-6
26	2	1.35e+4	1.68e-3	22	7	6.14e+3	1.67e-6	33	11	7.35e+2	0.0	33	16	1.99e+4	2.94e-3
27	2	1.46e+3	1.66e-4	23	7	1.57e+4	0.0	35	11	1.35e+4	7.76e-3	34	16	1.63e+3	0.0
28	2	2.79e+4	0.0	24	7	1.35e+0	3.52e-7	20	12	1.05e+1	1.84e-4	35	16	1.65e+0	0.0
29	2	1.20e+4	1.59e-3	25	7	2.62e+1	1.38e-7	21	12	2.02e+1	1.89e-4	20	17	1.57e+0	0.0
30	2	2.16e+3	1.62e-4	26	7	1.97e+4	2.31e-3	22	12	1.15e+1	0.0	21	17	8.39e+0	4.87e-4
31	2	5.90e+1	0.0	27	7	7.67e+3	3.71e-4	24	12	4.20e+3	1.12e-4	22	17	4.52e+0	1.60e-4
32	2	1.83e+0	9.06e-6	28	7	5.16e+4	0.0	25	12	9.66e+3	0.0	23	17	2.32e+0	9.69e-4
33	2	9.02e-1	4.30e-4	29	7	1.67e+4	1.33e-3	26	12	1.58e+4	3.10e-4	24	17	8.42e+2	4.30e-3
34	2	4.37e-1	0.0	30	7	8.72e+3	1.20e-4	27	12	6.28e+2	2.44e-4	25	17	5.30e+3	2.47e-6
35	2	1.07e+1	0.0	31	7	4.13e+1	0.0	28	12	2.46e+0	8.28e-4	26	17	1.34e+3	0.0
20	3	4.85e+3	0.0	32	7	7.14e+1	2.29e-2	29	12	1.98e+4	1.02e-3	27	17	7.05e+3	1.73e-4
21	3	3.42e+4	7.43e-5	33	7	1.15e+0	1.19e-8	30	12	1.14e+3	1.46e-7	29	17	2.32e+3	0.0
22	3	3.42e+4	4.87e-7	34	7	1.33e+1	0.0	31	12	8.56e+2	1.40e-3	30	17	4.42e+3	1.16e-4
23	3	1.92e+4	5.77e-5	35	7	1.03e+2	0.0	32	12	2.18e+4	1.60e-3	32	17	6.00e+4	0.0
24	3	1.39e+1	7.62e-5	20	8	3.60e+1	0.0	33	12	1.08e+3	0.0	33	17	2.56e+3	6.63e-3
25	3	1.12e+2	5.86e-5	21	8	2.84e+1	6.92e-7	35	12	1.73e+4	7.24e-3	34	17	2.11e+4	3.02e-3
26	3	1.85e+4	0.0	22	8	3.39e+1	3.79e-6	20	13	4.21e-2	5.84e-5	20	18	9.03e-2	6.88e-5
27	3	6.86e+3	1.79e-3	23	8	4.37e+0	2.34e-7	21	13	6.17e-3	7.29e-5	21	18	1.49e+0	7.92e-5
29	3	1.70e+4	0.0	24	8	5.13e+4	1.57e-3	22	13	2.83e+0	4.27e-4	22	18	1.79e-1	0.0
30	3	9.20e+3	1.12e-3	25	8	5.08e+3	2.61e-3	23	13	3.95e+1	0.0	24	18	1.91e+3	5.14e-4
32	3	5.14e+1	0.0	26	8	2.18e+4	0.0	24	13	3.25e+3	4.91e-4	25	18	3.05e+2	0.0
33	3	3.68e+0	5.18e-4	27	8	2.78e+3	6.25e-6	25	13	1.95e+4	2.33e-4	26	18	2.74e-1	1.55e-7
34	3	1.39e-1	4.18e-4	29	8	2.42e+4	0.0	26	13	5.49e+3	1.78e-3	27	18	2.07e+1	1.74e-3
21	4	2.56e+3	0.0	30	8	1.98e+3	3.17e-6	27	13	1.80e+4	1.47e-3	28	18	1.00e-1	1.11e-6
22	4	2.33e+4	3.83e-5	32	8	1.50e+2	0.0	28	13	1.86e+2	0.0	29	18	1.03e+1	1.57e-6
23	4	6.63e+4	3.92e-7	33	8	2.98e+4	3.66e-9	29	13	7.66e+3	8.91e-6	30	18	6.96e+0	1.15e-3
24	4	6.64e+0	0.0	34	8	2.61e+3	3.57e-6	30	13	1.38e+4	2.22e-3	31	18	1.75e+4	2.77e-6
25	4	1.56e+1	9.41e-4	21	9	5.39e+1	0.0	31	13	6.57e+3	0.0	32	18	9.36e+3	2.45e-6
27	4	2.07e+4	0.0	22	9	1.80e+1	6.01e-6	32	13	1.20e+4	1.77e-3	33	18	7.33e+3	0.0
30	4	2.88e+4	0.0	23	9	5.95e+1	1.57e-7	33	13	1.55e+2	2.46e-6	35	18	4.70e+4	5.07e-8
33	4	7.33e-1	2.94e-5	24	9	1.07e+4	0.0	34	13	2.05e+3	0.0	20	19	6.10e-2	1.49e-5
34	4	1.21e+1	1.19e-3	25	9	4.87e+4	1.31e-3	35	13	4.51e+4	0.0	21	19	8.13e-1	5.63e-6
20	5	1.07e+4	1.55e-7	27	9	2.20e+4	0.0	21	14	1.09e+2	0.0	22	19	2.28e+0	6.04e-5
21	5	4.78e+3	0.0	30	9	1.72e+4	0.0	22	14	2.36e+1	6.08e-7	23	19	3.46e-2	0.0
24	5	2.55e+1	0.0	33	9	8.36e+2	8.76e-5	23	14	2.01e+0	2.23e-6	24	19	4.45e+2	1.69e-3
26	5	9.80e+2	2.75e-4	34	9	3.35e+4	1.05e-4	24	14	5.53e+4	0.0	25	19	2.46e+3	8.39e-4
27	5	8.16e+3	0.0	20	10	3.97e+1	1.06e-7	25	14	5.14e+3	7.81e-6	26	19	3.22e+1	1.91e-3
28	5	0.0	2.17e-5	21	10	2.69e+1	0.0	27	14	8.39e+2	0.0	27	19	6.67e+0	9.49e-6
29	5	2.04e+3	1.39e-3	24	10	6.36e+3	0.0	30	14	5.22e+2	0.0	28	19	8.86e+0	0.0

There are no other calculations in literature for these transitions for comparisons. There are many cases where one of the two transition probabilities is negligible, usually the A^E2. But the case of Fe VI is somewhat different from that of Fe III (Nahar & Pradhan 1996), where the A^E2 are greater than A^M1 for nearly half the total number of transitions, especially those with large excitation energies.