4 Results and discussion

We have obtained nearly 1.5 10⁶ oscillator strengths for bound-bound transitions in Fe V. To our knowledge there are no previous ab initio relativistic calculations for transition probabilities for Fe V. The previous Opacity Project data consists of approximately 30000 LS transitions. Therefore the new dataset of nearly 1.5 10⁶oscillator strengths should significantly enhance the database, and the range and precision of related applications, some of which we discuss later.

We divide the discussion of energies and oscillator strengths in the subsections below.

4.1 Fine-structure levels from the BPRM calculations

A total of 3 865 fine-structure bound levels of Fe V have been obtained for $J\pi$ symmetries, 0 $\leq J \leq$ 8 even and odd parities. These belong to symmetries 2S+1 = 5, 3, 1, 0 $\leq L \leq$ 9, with $n \leq 10$ and 0 $\leq l \leq$ 9. The BPRM calculations initially yield only the energies and the total symmetry, $J\pi$, of the levels. Through an identification procedure based on the analysis of quantum defects and percentage channel contributions for each level in the region outside the R-matrix boundary (described in Nahar & Pradhan 2000), the levels are assigned with possible designation of $C_{\rm t}(S_{\rm t}L_{\rm t})J_{\rm t}\pi_{\rm t}nlJ(SL)\pi$, which specifies the core or target configuration, LS term and parity, and total angular momentum; the principal and orbital angular momenta, nl, of the outer or the valence electron; the total angular momentum, J, and the possible LS term and parity, $SL\pi$, of the (N+1)-electron bound level. Table 1a presents a few partial sets of energy levels from the complete set available electronically.

Computed order of levels according to $J\pi$

Examples of fine structure energy levels are presented in sets of $J\pi$ in Table 1a where their assigned identifications are given. N_J is the total number of energy levels for the symmetry $J\pi$ (e.g. there are 80 levels with $J\pi$ = $0^{\rm e}$, although the table presents only 25 of them). The effective quantum number, $\nu~=~z/\sqrt(E-E_{\rm t})$ where $E_{\rm t}$ is the energy of the target state, is also given for each level. The $\nu$ is not given for any equivalent electron level as it is undefined. In the core configuration, the first digit after each orbital specifies the occupancy number. The second digit, in some cases, refers to the seniority of the core term (e.g. in "3d32", "3d3" refers to the core configuration and "2" refers to the seniority number of the associated core term). An unidentifiable level is often assigned with a possible equivalent electron level. In Table 1a, one level of $J\pi$ = $0^\circ$ is assigned to the equivalent electron configuration, 3p⁵3d⁵. The assignment is based on two factors: (a) the calculated $\nu$ of the level does not match with that of any valence electon, and (b) the wavefunction is represented by a number of channels of similar percentage weights, i.e., no dominant channel. The configuration 3p⁵3d³ corresponds to a large number of LS terms. However, the level can not be identified with any particular term through quantum defect analysis. Hence it is designated as ⁰S, indicating an undetermined spectroscopic term.

4.1.2 Energy order of levels

In Table 1b a limited selection of energy levels is presented in a format different from that in Table 1a. Here they are listed in ascending energy order regardless of $J\pi$ values, and are grouped together within the same configuration to show the correspondence between the sets of J-levels and the LS terms. This format provides a check of completeness of sets of energy levels in terms of LS terms, and also determines the missing levels. Levels grouped in such a manner also show closely spaced energies, consistent with the fact that they are fine-structure components with a given LS term designation. The title of each set in Table 1b lists all possible LS terms that can be formed from the core or target term, and outer or the valence electron angular momentum. "Nlv'' is the total number of J-levels that correspond to the set of LS terms. The spin multiplicity (2S+1) and parity ($\pi$) are given next. The J values for each term is given within parentheses next to the corresponding L. At the end of the set of levels, "Nlv(c)'' is the total number of J-levels obtained in the calculations. Hence, if Nlv = Nlv(c) for a set of levels of the same configuration the set is designated as "complete''.

Most sets of fine-structure components between LS multiplets are found to be complete. High lying energy levels often belong to incomplete sets. The possible LS terms for each level is specified in the last column. It is seen that a level may possibly belong to several LS terms. In the absence any other criteriion, the proper term for the level may be assumed by applying Hund's rule: with levels of the same spin multiplicity, the highest L-level is

  

Table 1: a). Identified fine-strucuture energy levels of Fe V. N_J = total number of levels for the symmetry $J\pi$

 

Table 1: b). Ordered and identified fine-structure energy levels of Fe V. Nlv = total number of levels expected for the possible LS terms listed, and Nlv(c) = number of levels calculated. $SL\pi$lists the possible LS terms for each level (see text for details)

$C_{\rm t}$	$S_{\rm t}L_{\rm t}\pi_{\rm t}$	$J_{\rm t}$	nl	J	E(cal)	$\nu$	$SL\pi$
Nlv =  5, 5,e:	F ( 5 4 3 2 1 )
3d3	(4Fe)	3/2	4s	1	-3.73515E+00	2.59	5  F e
3d3	(4Fe)	5/2	4s	2	-3.73238E+00	2.59	5  F e
3d3	(4Fe)	5/2	4s	3	-3.72820E+00	2.59	5  F e
3d3	(4Fe)	7/2	4s	4	-3.72275E+00	2.59	5  F e
3d3	(4Fe)	9/2	4s	5	-3.71610E+00	2.59	5  F e
Ncal =  5: set complete
Nlv =  3, 3,e:	F ( 4 3 2 )
3d3	(4Fe)	3/2	4s	2	-3.63808E+00	2.62	3  F e
3d3	(4Fe)	7/2	4s	3	-3.63107E+00	2.62	3  F e
3d3	(4Fe)	9/2	4s	4	-3.62225E+00	2.62	3  F e
Ncal = 3: set complete
Nlv = 3, 1,o:	P ( 1 ) D ( 2 ) F ( 3 )
3d3 1	(2De)	3/2	4p	2	-2.45812E+00	2.83	1  D o
3d3 1	(2De)	5/2	4p	3	-2.40581E+00	2.86	1  F o
3d3 1	(2De)	5/2	4p	1	-2.33944E+00	2.89	1  P o
Ncal = 3: set complete
Nlv = 23, 5,e:	P ( 3 2 1 ) D ( 4 3 2 1 0 ) F ( 5 4 3 2 1 ) G ( 6 5 4 3 2 ) H ( 7 6 5 4 3)
3d3	(4Fe)	3/2	4d	3	-2.37021E+00	3.25	5  PDFGH e
3d3	(4Fe)	5/2	4d	4	-2.36647E+00	3.25	5  DFGH e
3d3	(4Fe)	5/2	4d	5	-2.36189E+00	3.25	5  FGH e
3d3	(4Fe)	3/2	4d	1	-2.35988E+00	3.25	5  PDF e
3d3	(4Fe)	7/2	4d	6	-2.35651E+00	3.25	5  GH e
3d3	(4Fe)	5/2	4d	2	-2.35541E+00	3.26	5  PDFG e
3d3	(4Fe)	9/2	4d	7	-2.35041E+00	3.25	5  H e
3d3	(4Fe)	5/2	4d	1	-2.34932E+00	3.26	5  PDF e
3d3	(4Fe)	9/2	4d	3	-2.34736E+00	3.25	5  PDFGH e
3d3	(4Fe)	9/2	4d	3	-2.34736E+00	3.25	5  PDFGH e
3d3	(4Fe)	7/2	4d	2	-2.34633E+00	3.26	5  PDFG e
3d3	(4Fe)	3/2	4d	2	-2.34397E+00	3.27	5  PDFG e
3d3	(4Fe)	7/2	4d	4	-2.34329E+00	3.26	5  DFGH e
3d3	(4Fe)	5/2	4d	3	-2.34092E+00	3.26	5  PDFGH e
3d3	(4Fe)	9/2	4d	3	-2.33989E+00	3.26	5  PDFGH e
3d3	(4Fe)	9/2	4d	5	-2.33822E+00	3.26	5  FGH e
3d3	(4Fe)	7/2	4d	5	-2.33234E+00	3.27	5  FGH e
3d3	(4Fe)	9/2	4d	6	-2.32699E+00	3.26	5  GH e
3d3	(4Fe)	3/2	4d	4	-2.28772E+00	3.31	5  DFGH e
3d3	(4Fe)	3/2	4d	0	-2.28673E+00	3.31	5  D e
3d3	(4Fe)	7/2	4d	1	-2.28265E+00	3.30	5  PDF e
3d3	(4Fe)	9/2	4d	2	-2.27468E+00	3.30	5  PDFG e
3d3	(4Fe)	7/2	4d	3	-2.26346E+00	3.31	5  PDFGH e
3d3	(4Fe)	9/2	4d	4	-2.25835E+00	3.31	5  DFGH e
Ncal = 23: set complete
Nlv = 3, 1,e:	P ( 1 ) D ( 2 ) F ( 3 )
3d3	(2Pe)	3/2	4d	1	-2.08815E+00	3.26	1  P e
3d3	(2Pe)	1/2	4d	2	-1.95699E+00	3.41	1  D e
3d3	(2Pe)	3/2	4d	3	-1.94667E+00	3.38	1  F e
Ncal = 3: set complete
Nlv = 15, 3,e:	P ( 2 1 0 ) D ( 3 2 1 ) F ( 4 3 2 ) G ( 5 4 3 ) H ( 6 5 4 )
3d3	(4Fe)	3/2	4d	1	-2.35634E+00	3.26	3  PD e
3d3	(4Fe)	5/2	4d	2	-2.35219E+00	3.25	3  PDF e
3d3	(4Fe)	7/2	4d	3	-2.34872E+00	3.25	3  DFG e
3d3	(4Fe)	5/2	4d	4	-2.33701E+00	3.27	3  FGH e
3d3	(4Fe)	5/2	4d	5	-2.28113E+00	3.31	3  GH e
3d3	(4Fe)	3/2	4d	3	-2.28060E+00	3.31	3  DFG e
3d3	(4Fe)	7/2	4d	4	-2.27417E+00	3.31	3  FGH e
3d3	(4Fe)	9/2	4d	6	-2.27323E+00	3.30	3  H e
3d3	(4Fe)	3/2	4d	2	-2.26789E+00	3.32	3  PDF e
3d3	(4Fe)	7/2	4d	5	-2.26632E+00	3.31	3  GH e
3d3	(4Fe)	5/2	4d	0	-2.24585E+00	3.33	3  P e
3d3	(4Fe)	5/2	4d	1	-2.24483E+00	3.33	3  PD e
3d3	(4Fe)	7/2	4d	2	-2.24278E+00	3.33	3  PDF e
3d3	(4Fe)	7/2	4d	3	-2.23973E+00	3.33	3  DFG e
3d3	(4Fe)	9/2	4d	4	-2.23571E+00	3.33	3  FGH e

 

Table 1: continued

$C_{\rm t}$	$S_{\rm t}L_{\rm t}\pi_{\rm t}$	$J_{\rm t}$	nl	J	E(cal)	$\nu$	$SL\pi$
Ncal = 15: set complete
Nlv = 13,  3,e:	S ( 1 ) P ( 2 1 0 ) D ( 3 2 1 ) F ( 4 3 2 ) G ( 5 4 3 )
3d3 2	(2De)	5/2	5d	1	-1.05446E+00	4.36	3 SPD e
3d3 2	(2De)	5/2	5d	5	-1.04247E+00	4.38	3 G e
3d3 2	(2De)	3/2	5d	3	-1.04179E+00	4.38	3 DFG e
3d3 2	(2De)	3/2	5d	1	-1.03332E+00	4.40	3 SPD e
3d3 2	(2De)	5/2	5d	4	-1.03014E+00	4.40	3 FG e
3d3 2	(2De)	5/2	5d	2	-1.02889E+00	4.40	3 PDF e
3d3 2	(2De)	3/2	5d	0	-1.02130E+00	4.42	3 P e
3d3 2	(2De)	5/2	5d	1	-1.01682E+00	4.43	3 SPD e
3d3 2	(2De)	5/2	5d	3	-1.01420E+00	4.43	3 DFG e
3d3 2	(2De)	3/2	5d	2	-1.00936E+00	4.44	3 PDF e
3d3 2	(2De)	3/2	5d	2	-9.92578E-01	4.47	3 PDF e
3d3 2	(2De)	5/2	5d	3	-9.81500E-01	4.49	3 DFG e
Ncal = 12  , Nlv =  13: set incomplete, level missing: 4

usually the lowest. For example, of the two J = 4 levels with terms ³(F,G) in the second set, the first or the lower level could be ³G while the second or the higher one could be ³F. It may be noted that this criterion is violated for a number of cases in Fe V due to strong CI. In Table 1b, the upper sets of low energies are complete. The two lower sets are incomplete where a few levels are missing. The missing levels are detected by the program PRCBPID.

4.1.3 Comparison with observed energies

Only a limited number of observed energy levels of Fe V are available (Sugar & Corliss 1985). All 179 observed levels were identified in a straightforward manner by the program PRCBPID. The present results are found to agree to about 1% with the observed energies for most of the levels (Table III, Nahar & Pradhan 2000). In Table 2, a comparison is presented for the 3d⁴ levels. The experimentally observed levels are also the lowest calculated levels in Fe V. The additional information in Table 2 is the level index, I_J, next to the J-values. As the BPRM levels are designated with $J\pi$ values only, the level index shows the energy position, in ascending order, of the level in the $J\pi$ symmetry. It is necessary to use the level indices to make the correspondence among the calculated and the observed levels for later use.

Although the LS term designation in general meets consistency checks, it is possible that there is some uncertainty in the designations. The spin multiplicities of the ion are obtained by the addition of the angular momentum 1/2 of the outer electron to the total spin, $S_{\rm t}$, of the target. The higher multiplicity corresponds to the addition of +1/2, and the lower one to the subtraction of -1/2. Typically the level with higher multiplicity lies lower. Due to the large number of different channels representing the levels of a $J\pi$ symmetry, it is possible that this angular addition might have been interchanged for some cases where the channels themselves are incorrectly identified. Therefore, for example, a triplet could be represented by a singlet and vice versa. This can affect the Ldesignation since a singlet can be assigned only to one single total L, whereas a triplet can be assigned to a few possible L values. For such cases, the LS multiplets may not represent the correct transitions.

We emphasize, however, that the present calculations are all in intermediate coupling and the LS coupling designations attempted in this work are carried out only to complete the full spectroscopic identification that may be of interest for (a) specialized users such as experimentalists, and (b) as a record of all possible information (some of which may be uncertain) that can be derived from the BPRM calculations for bound levels.

4.2 E1 oscillators strengths from the BPRM calculations

The bound-bound transitions among the 3865 fine-structure levels of Fe V have resulted in 1.46 10⁶ oscillator strengths for dipole-allowed and intercombination transitions.

4.2.1 Calculated f-values for the allowed transitions

Table 3 presents a partial set, in the format adopted, from the complete file of oscillator strengths. The two numbers at the beginning of the table are the nuclear charge (i.e. Z = 26) and the number of electrons ( $N_{{\rm elc}}$ = 22) for Fe V. Below this line are the sets of transitions of a pair of symmetries $J\pi~-~J'\pi'$. The first line of each set contains values of 2J, parity $\pi$ (=0 for even and =1 for odd), 2J' and $\pi'$. Hence in Table 3, the set of transitions given are among $J=0^{\rm e}~-~J=1^\circ$. The line following the transition symmetries specifies the number of bound levels, N_Ji and N_Jj, of the symmetries among which the transitions occur. This line is followed by $N_{Ji}\times N_{Jj}$transitions. The first two columns are the level indices, I_i and I_j (as mentioned above) for the energy indices of the levels, and the third and the fourth columns are their energies, E_i and E_j, in Rydberg units. The fifth and sixth columns are gf_Land gf_V, where f_L and f_V are the oscillator strengths in length and velocity forms, and g = 2J+1 (J is the total angular momentum of the lower level). For the gf-values that are negative the lower level is i(absorption) and for the positive ones the lower level is j (emission). The last column gives the transition probability, $A_{ji}({\rm s}^{-1})$. To obtain the identification of the levels, Table 1a should be referrred to following I_i and I_j. For example, the second transition of Table 3 corresponds to the intercombination transition 3d⁴(⁵D $^{\rm e})(I_i=1) \rightarrow$3d³(⁴F$^{\rm e})$4p(³D $^\circ)(I_j=3)$.

4.2.2 f-values with experimental energies

As the observed energies are much more precisely known that the calculated ones, the f and A-values can be reprocessed with the observed energies for some improvement in accuracy. Using the energy independent BPRM line strength, S (Eq. 7), the f-value can be obtained as,

$$f_{ij} = S(i,j,{\rm BPRM}){E_{ji}({\rm obs})\over (3g_{i})}.$$ (13)

Transitions among all observed levels have been so reprocessed. This recalculated subset consists of 3737 dipole-allowed and intercombination transitions among the 179 observed levels (a relatively small part of the present transition probabilities dataset). The calculated energy level indices corresponding to the observed levels for each $J\pi$ are listed in Table 4.

 

 

Table 2: Comparison of calculated BPRM energies, $E_{\rm c}$, with the observed ones (Sugar & Corliss 1985), $E_{\rm o}$, of Fe V. I_J is the level index for the energy position in symmetry $J\pi$

Level		J	IJ	$E_{\rm c}$(Ry)	$E_{\rm o}$(Ry)
3d4	5D	4	1	5.5493	5.5015
3d4	5D	3	1	5.5542	5.5058
3d4	5D	2	1	5.5580	5.5094
3d4	5D	1	1	5.5607	5.5119
3d4	5D	0	1	5.5621	5.5132
3d42	3P	2	2	5.3247	5.2720
3d42	3P	1	2	5.3389	5.2856
3d42	3P	0	2	5.3471	5.2940
3d4	3H	6	1	5.3074	5.2805
3d4	3H	5	1	5.3111	5.2833
3d4	3H	4	2	5.3143	5.2860
3d42	3F	4	3	5.3043	5.2674
3d42	3F	3	2	5.3064	5.2686
3d42	3F	2	3	5.3076	5.2693
3d4	3G	5	2	5.2581	5.2359
3d4	3G	4	4	5.2614	5.2384
3d4	3G	3	3	5.2651	5.2415
3d42	1G	4	5	5.2006	5.1798
3d4	3D	3	4	5.1950	5.1794
3d4	3D	2	4	5.1945	5.1782
3d4	3D	1	3	5.1928	5.1767
3d4	1I	6	2	5.1852	5.1713
3d42	1S	0	3	5.1700	5.1520
3d42	1D	2	5	5.1353	5.0913
3d4	1F	3	5	5.0476	5.0326
3d41	3P	2	6	4.9756	4.9495
3d41	3P	1	4	4.9663	4.9398
3d41	3P	0	4	4.9616	4.9352
3d41	3F	4	6	4.9719	4.9460
3d41	3F	3	6	4.9706	4.9449
3d41	3F	2	7	4.9712	4.9453
3d41	1G	4	7	4.8830	4.8636
3d41	1D	2	8	4.6609	4.6581
3d41	1S	0	5	4.4302	4.4093

A sample set of f- and A-values from the reprocessed transitions are presented in Table 5a in $J\pi-J'\pi'$ order. Each transition is given with complete identification. The level index, I_i, for each energy level is given next to the J-value for easy linkage to the energy and f-files. In all calculations where large number of transitions are used, the reprocessed f- and A-values should replace those in the complete file (containing 1.46 10⁶ transitions). For example, the f- and A-values for the first transition $J=0^{\rm e}(I_i=1)\rightarrow J=1^\circ(I_j=1)$ in Table 3 should be replaced by those for the first transition in Table 5a. The overall replacement of transitions can be carried out easily using the level energy index set in Table 4.

4.2.3 Spectroscopic designation and completeness

The reprocessed transitions are further ordered in terms of their configurations for a completeness check, and to obtain the LS multiplet designations. A partial set is presented in Table 5b (the complete table is available electronically). The completeness depends on the observed set of fine-structure levels since transitions have been reprocessed only for the observed levels. The LS multiplets are useful for various comparisons with existing values where fine-structure transitions can not be resolved.

Figure 1: Comparison between the length and the velocity forms of f-values for $(J=2)^{\rm e}-(J=3)^3$ transitions in Fe V

 

 

Table 3: Transition probabilities for Fe V (see text for explanation)

26    22
0    0         2    1
80	236	$E_i({\rm Ry})$	$E_j({\rm Ry})$	gfL	gfV	$A_{ji}({\rm s}^{-1})$
1	1	-5.56210E+00	-3.14950E+00	-2.212E-01	-1.800E-01	3.447E+09
1	2	-5.56210E+00	-3.14082E+00	-5.660E-03	-4.178E-03	8.884E+07
1	3	-5.56210E+00	-3.13088E+00	-5.894E-02	-4.843E-02	9.328E+08
1	4	-5.56210E+00	-2.99367E+00	-8.675E-02	-7.425E-02	1.532E+09
1	5	-5.56210E+00	-2.97465E+00	-4.542E-03	-4.060E-03	8.142E+07
1	6	-5.56210E+00	-2.96345E+00	-8.619E-05	-1.086E-04	1.558E+06
1	7	-5.56210E+00	-2.93263E+00	-1.059E-03	-8.938E-04	1.961E+07
1	8	-5.56210E+00	-2.90308E+00	-1.333E-08	-3.023E-07	2.524E+02
1	9	-5.56210E+00	-2.88417E+00	-2.099E-06	-9.150E-07	4.031E+04
1	10	-5.56210E+00	-2.87902E+00	-1.268E-03	-9.286E-04	2.444E+07
1	11	-5.56210E+00	-2.86205E+00	-4.284E-06	-4.003E-06	8.362E+04
1	12	-5.56210E+00	-2.84777E+00	-4.484E-06	-5.049E-06	8.845E+04
1	13	-5.56210E+00	-2.83128E+00	-3.114E-05	-2.131E-05	6.217E+05
1	14	-5.56210E+00	-2.78217E+00	-2.470E-06	-1.789E-06	5.111E+04
1	15	-5.56210E+00	-2.77047E+00	-6.248E-05	-4.283E-05	1.304E+06
1	16	-5.56210E+00	-2.65585E+00	-4.772E-06	-4.614E-06	1.079E+05
1	17	-5.56210E+00	-2.49355E+00	-4.898E-06	-5.125E-06	1.235E+05
1	18	-5.56210E+00	-2.41413E+00	-3.274E-07	-6.115E-07	8.688E+03
1	19	-5.56210E+00	-2.33944E+00	-2.223E-09	-4.905E-09	6.181E+01
1	20	-5.56210E+00	-1.68531E+00	-1.110E-02	-7.389E-03	4.466E+08
1	21	-5.56210E+00	-1.68346E+00	-1.821E-02	-1.320E-02	7.334E+08
1	22	-5.56210E+00	-1.67450E+00	-9.466E-05	-9.518E-05	3.830E+06
1	23	-5.56210E+00	-1.59625E+00	-5.222E-03	-3.143E-03	2.199E+08
1	24	-5.56210E+00	-1.59532E+00	-1.810E-03	-1.229E-03	7.624E+07
1	25	-5.56210E+00	-1.58926E+00	-1.444E-03	-1.553E-03	6.100E+07
1	26	-5.56210E+00	-1.58695E+00	-2.143E-01	-1.527E-01	9.066E+09
1	27	-5.56210E+00	-1.58282E+00	-1.247E-01	-8.966E-02	5.285E+09
1	28	-5.56210E+00	-1.56818E+00	-3.245E-03	-2.354E-03	1.386E+08
1	29	-5.56210E+00	-1.52505E+00	-1.908E-02	-1.419E-02	8.326E+08
1	30	-5.56210E+00	-1.51857E+00	-4.315E-03	-3.201E-03	1.889E+08
1	31	-5.56210E+00	-1.51106E+00	-9.942E-04	-7.265E-04	4.369E+07
1	32	-5.56210E+00	-1.48630E+00	-1.718E-05	-1.163E-05	7.641E+05
1	33	-5.56210E+00	-1.45506E+00	-1.579E-04	-1.075E-04	7.130E+06
1	34	-5.56210E+00	-1.45100E+00	-7.533E-06	-4.042E-06	3.409E+05
1	35	-5.56210E+00	-1.44432E+00	-5.868E-04	-3.975E-04	2.664E+07
1	36	-5.56210E+00	-1.44049E+00	-1.021E-01	-7.036E-02	4.642E+09
1	37	-5.56210E+00	-1.43765E+00	-3.304E-04	-2.278E-04	1.505E+07
1	38	-5.56210E+00	-1.43257E+00	-3.309E-05	-2.303E-05	1.511E+06
1	39	-5.56210E+00	-1.42555E+00	-2.467E-07	-1.329E-07	1.130E+04
1	40	-5.56210E+00	-1.41678E+00	-2.418E-05	-1.832E-05	1.112E+06
1	41	-5.56210E+00	-1.41009E+00	-1.689E-02	-1.254E-02	7.797E+08
1	42	-5.56210E+00	-1.40208E+00	-5.592E-05	-3.657E-05	2.591E+06
1	43	-5.56210E+00	-1.40135E+00	-1.642E-05	-1.154E-05	7.613E+05
1	44	-5.56210E+00	-1.39712E+00	-1.010E-04	-6.246E-05	4.691E+06
1	45	-5.56210E+00	-1.39057E+00	-1.312E-05	-9.621E-06	6.115E+05
1	46	-5.56210E+00	-1.37572E+00	-1.298E-05	-8.241E-06	6.089E+05
1	47	-5.56210E+00	-1.36381E+00	-1.730E-04	-1.098E-04	8.166E+06
1	48	-5.56210E+00	-1.34841E+00	-5.225E-07	-1.695E-06	2.484E+04
1	49	-5.56210E+00	-1.33149E+00	-2.354E-06	-1.675E-06	1.128E+05
1	50	-5.56210E+00	-1.32616E+00	-5.604E-05	-3.284E-05	2.692E+06

Semi-empirical atomic structure calculations have been carried out be other workers (Fawcett 1989; Quinet & Hansen 1995). Present oscillator strengths are compared with available calculations by Fawcett (1989), the LS coupling R-matrix calculations from the OP (Butler, TOPbase 1993) and from the IP (Bautista 1996), for some low lying transitions. Comparison in Table 5b shows various degrees of agreement. Present f-values agree very well (within 10%) with those by Fawcett for some fine-structure transitions while disagree considerably with the others within the same LS multiplet. For example, the agreement is good for most of the fine-structure transitions of 3d⁴(⁵D)  $\rightarrow 3$d³(⁴F)4p(⁵D$^\circ)$, 3d⁴(⁵D)  $\rightarrow$3d³(⁴P)4p(⁵P$^\circ)$, and 3d⁴2(³P)  $\rightarrow$ 3d³(⁴F)4p(³D$^\circ)$ while the disagreement is large with other as well as with those of 3d⁴(⁵D)  $\rightarrow$ 3d³(⁴F)4p(⁵F$^\circ)$. The agreement of the present LS multiplets with the others is good for strong transitions such as 3d⁴(⁵D)  $\rightarrow$3d³(⁴F)4p(⁵F$^\circ,^5$D$^\circ,^5$P$^\circ)$, and 3d⁴2(³P)  $\rightarrow$3d³(⁴F)4p(³D$^\circ)$, but is poor for the weak ones.

4.2.4 Estimate of uncertainties

The uncertainties of the BPRM transition probabilities for the allowed transitons are expected to be within 10% for the strong transitions, and 10-30% for the weak ones. A measure of the uncertainty can be obtained from the dispersion of the f-values in length and velocity forms, which generally indicate deviations from the "exact'' wavefunctions (albeit with some exceptions). Figure 1 presents a plot of ${\rm log}_{10}{gf}$ values, length vs. velocity, for the transitions $(J=2)^{\rm e}-(J=3)^3$of Fe V. Though most of the points lie close to the gf_L = gf_V line, significant dispersion is seen for gf values smaller than 0.01. We should note that the level of uncertainty may in fact be less than the dispersion shown in Fig. 1; in the close coupling R-matrix calculations the length formulation is likely to be more accurate than the velocity formulaton since the wavefunctions are better represented in the asymptotic region that dominates the contribution to the length form of the oscillator strength.

 

 

Table 4: Calculated energy level indices for various $J\pi$symmetries; allowed transitions among all these levels have been reprocessed using observed energies. n_j is the total number of $J\pi$levels observed

$J\pi$	nj	level indices
0 e	6	1,2,3,4,5,6
0 o	6	1,2,3,4,6,7
1 e	11	1,2,3,4,5,6,7,8,9,10,11
1 o	19	1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19
2 e	18	1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18
2 o	24	1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25
3 e	14	1,2,3,4,5,6,7,8,9,10,11,12,13,14
3 o	24	1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24
4 e	13	1,2,3,4,5,6,7,8,9,10,11,12,13
4 o	18	1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18
5 e	6	1,2,3,4,5,6
5 o	11	1,2,3,4,5,6,7,8,9,10,11
6 e	3	1,2,3
6 o	5	1,2,3,4,5
7 o	1	1

4.3 Forbidden transition probabilities

The transition probabilities, $A^{\rm q}$ and $A^{\rm m}$, for 362 forbidden E2 and M1 transitions are obtained using some semi-empirical corrections. The $A^{\rm q}$ in general are much smaller than the $A^{\rm m}$. Although $A^{\rm q}$ is smaller, there are many cases where one or the other is negligible. Owing to the widespread use of the only other previous calculation by Garstang (1957), it is important to establish the general level of differences with the previous work. Table 6 gives a detailed comparison. The agreement between the two sets of data is generally good with a few noticeable discrepancies.

A partial set of the transition probabilities are given in Table 7 along with the observed wavelengths in microns. The full Table of forbidden transition probabilities is available electronically.

 

 

Table 5: a) Sample set of reprocessed f- and A-values with observed transition energies. I_i and I_j are the level indices

Ci	Cj	$S_iL_i\pi_i$	$S_jL_j\pi_j$	2Ji+1	Ii	2Jj+1	Ij	$E_i({\rm Ry})$	$E_j({\rm Ry})$	f	$A({\rm s}^{-1})$
3d4	-3d3(4F)4p	5D$^{\rm e}$	5D$^\circ$	1	1	3	2	5.5132	3.1540	5.515E-03	8.22E+07
3d4	-3d3(4F)4p	5D$^{\rm e}$	3D$^\circ$	1	1	3	3	5.5132	3.1439	5.744E-02	8.63E+08
3d4	-3d3(4P)4p	5D$^{\rm e}$	5P$^\circ$	1	1	3	4	5.5132	3.0195	8.420E-02	1.40E+09
3d4	-3d3(4P)4p	5D$^{\rm e}$	5D$^\circ$	1	1	3	5	5.5132	3.0058	4.401E-03	7.41E+07
3d4	-3d3(4P)4p	5D$^{\rm e}$	3P$^\circ$	1	1	3	6	5.5132	2.9911	8.365E-05	1.42E+06
3d4	-3d3(2P)4p	5D$^{\rm e}$	3P$^\circ$	1	1	3	7	5.5132	2.9439	1.035E-03	1.83E+07
3d4	-3d3(2D2)4p	5D$^{\rm e}$	1P$^\circ$	1	1	3	8	5.5132	2.9073	1.306E-08	2.38E+02
3d4	-3d3(2D2)4p	5D$^{\rm e}$	3D$^\circ$	1	1	3	9	5.5132	2.8826	2.062E-06	3.82E+04
3d4	-3d3(2P)4p	5D$^{\rm e}$	3D$^\circ$	1	1	3	10	5.5132	2.9274	1.222E-03	2.19E+07
3d4	-3d3(2P)4p	5D$^{\rm e}$	3S$^\circ$	1	1	3	11	5.5132	2.9052	4.138E-06	7.54E+04
3d4	-3d3(4P)4p	5D$^{\rm e}$	3D$^\circ$	1	1	3	12	5.5132	2.8991	4.318E-06	7.90E+04
3d4	-3d3(2D2)4p	5D$^{\rm e}$	3P$^\circ$	1	1	3	13	5.5132	2.8652	3.020E-05	5.67E+05
3d4	-3d3(2P)4p	5D$^{\rm e}$	1P$^\circ$	1	1	3	14	5.5132	2.8161	2.397E-06	4.67E+04
3d4	-3d3(4P)4p	5D$^{\rm e}$	3S$^\circ$	1	1	3	15	5.5132	2.8282	6.009E-05	1.16E+06
3d4	-3d3(2F)4p	5D$^{\rm e}$	3D$^\circ$	1	1	3	16	5.5132	2.7003	4.619E-06	9.78E+04
3d4	-3d3(2D1)4p	5D$^{\rm e}$	3D$^\circ$	1	1	3	17	5.5132	2.5285	4.765E-06	1.14E+05
3d4	-3d3(2D1)4p	5D$^{\rm e}$	3P$^\circ$	1	1	3	18	5.5132	2.4580	3.177E-07	7.94E+03
3d4	-3d3(2D1)4p	5D$^{\rm e}$	1P$^\circ$	1	1	3	19	5.5132	2.3924	2.152E-09	5.61E+01
3d42	-3d3(4F)4p	3P$^{\rm e}$	5F$^\circ$	1	2	3	1	5.2940	3.1644	2.317E-02	2.81E+08
3d42	-3d3(4F)4p	3P$^{\rm e}$	5D$^\circ$	1	2	3	2	5.2940	3.1540	1.751E-02	2.15E+08
3d42	-3d3(4F)4p	3P$^{\rm e}$	3D$^\circ$	1	2	3	3	5.2940	3.1439	6.702E-02	8.29E+08
3d42	-3d3(4P)4p	3P$^{\rm e}$	5P$^\circ$	1	2	3	4	5.2940	3.0195	7.726E-05	1.07E+06
3d42	-3d3(4P)4p	3P$^{\rm e}$	5D$^\circ$	1	2	3	5	5.2940	3.0058	2.863E-03	4.01E+07
3d42	-3d3(4P)4p	3P$^{\rm e}$	3P$^\circ$	1	2	3	6	5.2940	2.9911	1.907E-02	2.71E+08
3d42	-3d3(2P)4p	3P$^{\rm e}$	3P$^\circ$	1	2	3	7	5.2940	2.9439	9.377E-02	1.39E+09
3d42	-3d3(2D2)4p	3P$^{\rm e}$	1P$^\circ$	1	2	3	8	5.2940	2.9073	6.430E-03	9.81E+07
3d42	-3d3(2D2)4p	3P$^{\rm e}$	3D$^\circ$	1	2	3	9	5.2940	2.8826	7.067E-03	1.10E+08
3d42	-3d3(2P)4p	3P$^{\rm e}$	3D$^\circ$	1	2	3	10	5.2940	2.9274	7.538E-02	1.13E+09
3d42	-3d3(2P)4p	3P$^{\rm e}$	3S$^\circ$	1	2	3	11	5.2940	2.9052	2.193E-03	3.35E+07
3d42	-3d3(4P)4p	3P$^{\rm e}$	3D$^\circ$	1	2	3	12	5.2940	2.8991	3.284E-02	5.04E+08
3d42	-3d3(2D2)4p	3P$^{\rm e}$	3P$^\circ$	1	2	3	13	5.2940	2.8652	6.023E-03	9.51E+07
3d42	-3d3(2P)4p	3P$^{\rm e}$	1P$^\circ$	1	2	3	14	5.2940	2.8161	1.578E-04	2.59E+06
3d42	-3d3(4P)4p	3P$^{\rm e}$	3S$^\circ$	1	2	3	15	5.2940	2.8282	2.772E-04	4.51E+06
3d42	-3d3(2F)4p	3P$^{\rm e}$	3D$^\circ$	1	2	3	16	5.2940	2.7003	1.347E-03	2.43E+07
3d42	-3d3(2D1)4p	3P$^{\rm e}$	3D$^\circ$	1	2	3	17	5.2940	2.5285	4.641E-03	9.50E+07
3d42	-3d3(2D1)4p	3P$^{\rm e}$	3P$^\circ$	1	2	3	18	5.2940	2.4580	3.200E-04	6.89E+06
3d42	-3d3(2D1)4p	3P$^{\rm e}$	1P$^\circ$	1	2	3	19	5.2940	2.3924	1.102E-05	2.48E+05
3d42	-3d3(4F)4p	1S$^{\rm e}$	5F$^\circ$	1	3	3	1	5.1520	3.1644	7.493E-06	7.93E+04
3d42	-3d3(4F)4p	1S$^{\rm e}$	5D$^\circ$	1	3	3	2	5.1520	3.1540	7.672E-06	8.20E+04
3d42	-3d3(4F)4p	1S$^{\rm e}$	3D$^\circ$	1	3	3	3	5.1520	3.1439	2.529E-05	2.73E+05
3d42	-3d3(4P)4p	1S$^{\rm e}$	5P$^\circ$	1	3	3	4	5.1520	3.0195	1.024E-05	1.25E+05
3d42	-3d3(4P)4p	1S$^{\rm e}$	5D$^\circ$	1	3	3	5	5.1520	3.0058	1.932E-04	2.38E+06
3d42	-3d3(4P)4p	1S$^{\rm e}$	3P$^\circ$	1	3	3	6	5.1520	2.9911	2.404E-05	3.01E+05
3d42	-3d3(2P)4p	1S$^{\rm e}$	3P$^\circ$	1	3	3	7	5.1520	2.9439	7.035E-03	9.18E+07
3d42	-3d3(2D2)4p	1S$^{\rm e}$	1P$^\circ$	1	3	3	8	5.1520	2.9073	8.021E-03	1.08E+08
3d42	-3d3(2D2)4p	1S$^{\rm e}$	3D$^\circ$	1	3	3	9	5.1520	2.8826	2.263E-01	3.12E+09
3d42	-3d3(2P)4p	1S$^{\rm e}$	3D$^\circ$	1	3	3	10	5.1520	2.9274	1.305E-03	1.73E+07
3d42	-3d3(2P)4p	1S$^{\rm e}$	3S$^\circ$	1	3	3	11	5.1520	2.9052	1.968E-04	2.66E+06
3d42	-3d3(4P)4p	1S$^{\rm e}$	3D$^\circ$	1	3	3	12	5.1520	2.8991	2.048E-03	2.78E+07
3d42	-3d3(2D2)4p	1S$^{\rm e}$	3P$^\circ$	1	3	3	13	5.1520	2.8652	1.148E-02	1.61E+08
3d42	-3d3(2P)4p	1S$^{\rm e}$	1P$^\circ$	1	3	3	14	5.1520	2.8161	7.864E-02	1.15E+09
3d42	-3d3(4P)4p	1S$^{\rm e}$	3S$^\circ$	1	3	3	15	5.1520	2.8282	2.714E-02	3.92E+08
3d42	-3d3(2F)4p	1S$^{\rm e}$	3D$^\circ$	1	3	3	16	5.1520	2.7003	5.453E-07	8.78E+03
3d42	-3d3(2D1)4p	1S$^{\rm e}$	3D$^\circ$	1	3	3	17	5.1520	2.5285	6.569E-05	1.21E+06
3d42	-3d3(2D1)4p	1S$^{\rm e}$	3P$^\circ$	1	3	3	18	5.1520	2.4580	2.050E-07	3.98E+03
3d42	-3d3(2D1)4p	1S$^{\rm e}$	1P$^\circ$	1	3	3	19	5.1520	2.3924	2.421E-04	4.94E+06
3d41	-3d3(4F)4p	3P$^{\rm e}$	5F$^\circ$	1	4	3	1	4.9352	3.1644	9.362E-05	7.86E+05
3d41	-3d3(4F)4p	3P$^{\rm e}$	5D$^\circ$	1	4	3	2	4.9352	3.1540	2.852E-05	2.42E+05
3d41	-3d3(4F)4p	3P$^{\rm e}$	3D$^\circ$	1	4	3	3	4.9352	3.1439	1.131E-04	9.72E+05
3d41	-3d3(4P)4p	3P$^{\rm e}$	5P$^\circ$	1	4	3	4	4.9352	3.0195	4.206E-04	4.13E+06
3d41	-3d3(4P)4p	3P$^{\rm e}$	5D$^\circ$	1	4	3	5	4.9352	3.0058	1.295E-02	1.29E+08
3d41	-3d3(4P)4p	3P$^{\rm e}$	3P$^\circ$	1	4	3	6	4.9352	2.9911	1.009E-02	1.02E+08
3d41	-3d3(2P)4p	3P$^{\rm e}$	3P$^\circ$	1	4	3	7	4.9352	2.9439	7.813E-03	8.29E+07
3d41	-3d3(2D2)4p	3P$^{\rm e}$	1P$^\circ$	1	4	3	8	4.9352	2.9073	3.255E-04	3.58E+06
3d41	-3d3(2D2)4p	3P$^{\rm e}$	3D$^\circ$	1	4	3	9	4.9352	2.8826	3.644E-04	4.11E+06
3d41	-3d3(2P)4p	3P$^{\rm e}$	3D$^\circ$	1	4	3	10	4.9352	2.9274	2.974E-03	3.21E+07
3d41	-3d3(2P)4p	3P$^{\rm e}$	3S$^\circ$	1	4	3	11	4.9352	2.9052	2.856E-04	3.15E+06
3d41	-3d3(4P)4p	3P$^{\rm e}$	3D$^\circ$	1	4	3	12	4.9352	2.8991	4.236E-04	4.70E+06
3d41	-3d3(2D2)4p	3P$^{\rm e}$	3P$^\circ$	1	4	3	13	4.9352	2.8652	5.201E-02	5.97E+08
3d41	-3d3(2P)4p	3P$^{\rm e}$	1P$^\circ$	1	4	3	14	4.9352	2.8161	1.028E-02	1.24E+08
3d41	-3d3(4P)4p	3P$^{\rm e}$	3S$^\circ$	1	4	3	15	4.9352	2.8282	4.824E-02	5.73E+08
3d41	-3d3(2F)4p	3P$^{\rm e}$	3D$^\circ$	1	4	3	16	4.9352	2.7003	1.648E-01	2.20E+09
3d41	-3d3(2D1)4p	3P$^{\rm e}$	3D$^\circ$	1	4	3	17	4.9352	2.5285	2.144E-08	3.33E+02
3d41	-3d3(2D1)4p	3P$^{\rm e}$	3P$^\circ$	1	4	3	18	4.9352	2.4580	4.867E-02	8.00E+08
3d41	-3d3(2D1)4p	3P$^{\rm e}$	1P$^\circ$	1	4	3	19	4.9352	2.3924	4.875E-05	8.44E+05
3d41	-3d3(4F)4p	1S$^{\rm e}$	5F$^\circ$	1	5	3	1	4.4093	3.1644	8.262E-08	3.43E+02
3d41	-3d3(4F)4p	1S$^{\rm e}$	5D$^\circ$	1	5	3	2	4.4093	3.1540	3.663E-08	1.55E+02
3d41	-3d3(4F)4p	1S$^{\rm e}$	3D$^\circ$	1	5	3	3	4.4093	3.1439	1.626E-07	6.97E+02
3d41	-3d3(4P)4p	1S$^{\rm e}$	5P$^\circ$	1	5	3	4	4.4093	3.0195	8.343E-08	4.31E+02
3d41	-3d3(4P)4p	1S$^{\rm e}$	5D$^\circ$	1	5	3	5	4.4093	3.0058	1.509E-09	7.96E+00
3d41	-3d3(4P)4p	1S$^{\rm e}$	3P$^\circ$	1	5	3	6	4.4093	2.9911	2.573E-07	1.39E+03
3d41	-3d3(2P)4p	1S$^{\rm e}$	3P$^\circ$	1	5	3	7	4.4093	2.9439	1.238E-05	7.12E+04
3d41	-3d3(2D2)4p	1S$^{\rm e}$	1P$^\circ$	1	5	3	8	4.4093	2.9073	2.067E-05	1.25E+05
3d41	-3d3(2D2)4p	1S$^{\rm e}$	3D$^\circ$	1	5	3	9	4.4093	2.8826	3.442E-04	2.15E+06
3d41	-3d3(2P)4p	1S$^{\rm e}$	3D$^\circ$	1	5	3	10	4.4093	2.9274	1.868E-05	1.10E+05

 

Table 5: b) Fine-structure transitions, ordered in LS multiplets, compared with previous values

Ci	Cj	$S_iL_i\pi_i$	$S_jL_j\pi_j$	2Ji+1	Ii	2Jj+1	Ij	$f_{ij}({\rm present})$	$f_{ij}({\rm others})$
3d4	-3d3(4F)4p	5D0	5F1	1	1	3	1	0.2154	0.163a
3d4	-3d3(4F)4p	5D0	5F1	3	1	3	1	3.790E-04
3d4	-3d3(4F)4p	5D0	5F1	3	1	5	3	0.00136
3d4	-3d3(4F)4p	5D0	5F1	5	1	3	1	0.04617	0.0126a
3d4	-3d3(4F)4p	5D0	5F1	5	1	5	3	0.05967	0.0596a
3d4	-3d3(4F)4p	5D0	5F1	5	1	7	3	0.01462	0.0138a
3d4	-3d3(4F)4p	5D0	5F1	7	1	5	3	0.006895	0.0274a
3d4	-3d3(4F)4p	5D0	5F1	7	1	7	3	0.05889	0.0544a
3d4	-3d3(4F)4p	5D0	5F1	9	1	7	3	0.001966	0.00756a
3d4	-3d3(4F)4p	5D0	5F1	7	1	9	3	0.03262	0.0414a
3d4	-3d3(4F)4p	5D0	5F1	9	1	9	3	0.05139	0.03a
3d4	-3d3(4F)4p	5D0	5F1	9	1	11	2	0.07548	0.0686a
3d4	-3d3(4F)4p	5D0	5F1	25		35		0.107	0.0804b,0.0915c
3d4	-3d3(4F)4p	5D0	5D1	1	1	3	2	0.00551	0.041a
3d4	-3d3(4F)4p	5D0	5D1	3	1	1	1	0.06255	0.0607a
3d4	-3d3(4F)4p	5D0	5D1	3	1	3	2	0.03888	0.0343a
3d4	-3d3(4F)4p	5D0	5D1	3	1	5	2	0.1360	0.1257a
3d4	-3d3(4F)4p	5D0	5D1	5	1	3	2	0.01704	0.0532a
3d4	-3d3(4F)4p	5D0	5D1	5	1	5	2	0.01372	0.0092a
3d4	-3d3(4F)4p	5D0	5D1	5	1	7	2	0.1087	0.1006a
3d4	-3d3(4F)4p	5D0	5D1	7	1	5	2	0.04155	0.0247a
3d4	-3d3(4F)4p	5D0	5D1	7	1	7	2	0.04936	0.0517a
3d4	-3d3(4F)4p	5D0	5D1	9	1	7	2	0.02644	0.0222a
3d4	-3d3(4F)4p	5D0	5D1	7	1	9	2	0.07311	0.0588a
3d4	-3d3(4F)4p	5D0	5D1	9	1	9	2	0.1168	0.130a
3d4	-3d3(4F)4p	5D0	5D1	25		25		0.1541	0.1708b,0.192c
3d4	-3d3(4P)4p	5D0	5P1	1	1	3	4	0.08420	0.076a
3d4	-3d3(4P)4p	5D0	5P1	3	1	3	4	0.06281	0.057a
3d4	-3d3(4P)4p	5D0	5P1	3	1	5	6	0.02114	0.019a
3d4	-3d3(4P)4p	5D0	5P1	5	1	3	4	0.02926	0.0266a
3d4	-3d3(4P)4p	5D0	5P1	5	1	5	6	0.04831	0.0442a
3d4	-3d3(4P)4p	5D0	5P1	5	1	7	7	0.00622	0.0054a
3d4	-3d3(4P)4p	5D0	5P1	7	1	5	6	0.05555	0.0499a
3d4	-3d3(4P)4p	5D0	5P1	7	1	7	7	0.03105	0.0264a
3d4	-3d3(4P)4p	5D0	5P1	9	1	7	7	0.08782	0.0758a
3d4	-3d3(4P)4p	5D0	5P1	25		15		0.0861	0.076b,0.0893c
3d4	-3d3(4P)4p	5D0	5D1	1	1	3	5	4.401E-03
3d4	-3d3(4P)4p	5D0	5D1	3	1	1	2	4.902E-04
3d4	-3d3(4P)4p	5D0	5D1	3	1	3	5	7.201E-04
3d4	-3d3(4P)4p	5D0	5D1	3	1	5	7	2.402E-03
3d4	-3d3(4P)4p	5D0	5D1	5	1	3	5	1.502E-03
3d4	-3d3(4P)4p	5D0	5D1	5	1	5	7	2.248E-03
3d4	-3d3(4P)4p	5D0	5D1	5	1	7	8	1.474E-03
3d4	-3d3(4P)4p	5D0	5D1	7	1	5	7	2.675E-03
3d4	-3d3(4P)4p	5D0	5D1	7	1	7	8	1.048E-03
3d4	-3d3(4P)4p	5D0	5D1	9	1	7	8	2.846E-06
3d4	-3d3(4P)4p	5D0	5D1	7	1	9	7	1.408E-03
3d4	-3d3(4P)4p	5D0	5D1	9	1	9	7	4.558E-03
3d4	-3d3(4P)4p	5D0	5D1	25		25		0.0047	0.00436b,0.00564c
3d4 2	-3d3(4F)4p	3P0	3D1	1	2	3	3	6.702E-02	0.061a
3d4 2	-3d3(4F)4p	3P0	3D1	3	2	3	3	1.585E-02	0.0147a
3d4 2	-3d3(4F)4p	3P0	3D1	3	2	5	4	6.279E-02	0.057a
3d4 2	-3d3(4F)4p	3P0	3D1	5	2	3	3	6.685E-04
3d4 2	-3d3(4F)4p	3P0	3D1	5	2	5	4	1.144E-02	0.011a
3d4 2	-3d3(4F)4p	3P0	3D1	5	2	7	4	7.753E-02	0.0756a
3d4 2	-3d3(4F)4p	3P0	3D1	9		15		0.0833	0.0973b,0.106c
3d4 2	-3d3(4P)4p	3P0	3P1	1	2	3	6	1.907E-02
3d4 2	-3d3(4P)4p	3P0	3P1	3	2	1	3	3.593E-03
3d4 2	-3d3(4P)4p	3P0	3P1	3	2	3	6	3.409E-03
3d4 2	-3d3(4P)4p	3P0	3P1	3	2	5	8	3.037E-03
3d4 2	-3d3(4P)4p	3P0	3P1	5	2	3	6	3.742E-03
3d4 2	-3d3(4P)4p	3P0	3P1	5	2	5	8	2.134E-03
3d4 2	-3d3(4P)4p	3P0	3P1	9		9		0.0087	0.00542b,0.0127c
3d4 2	-3d3(2P)4p	3P0	3S1	1	2	3	11	2.193E-03
3d4 2	-3d3(2P)4p	3P0	3S1	3	2	3	11	5.853E-03
3d4 2	-3d3(2P)4p	3P0	3S1	5	2	3	11	3.582E-04
3d4 2	-3d3(2P)4p	3P0	3S1	9		3		0.00239	0.00142b,0.056c
aFawcett (1989), bButler,  cBautista (1996).

 

 

Table 6: Comparison of A-values for forbidden transitions, $A_{fi}^{{\rm cal}}$, among 3d⁴ fine-structure levels with those, $A_{fi}^{\rm G}$, by Garstang (1957)

Transition		$\lambda_{{\rm vac}}$	$E_{i}({\rm cm}^{-1})$	$E_{f}({\rm cm}^{-1})$	$A_{fi}^{\rm G}({\rm s}^{-1})$	$A_{fi}^{{\rm cal}}({\rm s}^{-1})$
5D1	3P20	4181.8	142.1	24055.4	1.30E+00	1.39E+00
5D0	3P21	4004.3	0.0	24972.9	1.30E-01	1.23E-01
5D2	3P21	4072.4	417.3	24972.9	1.10E+00	1.07E+00
5D1	3P22	3798.5	142.1	26468.3	3.60E-02	3.54E-02
5D3	3P22	3896.3	803.1	26468.3	7.10E-01	7.08E-01
5D4	3H4	4228.4	1282.8	24932.5	1.10E-03	4.34E-03
5D1	3F22	3756.8	142.1	26760.7	1.00E-01	1.04E-01
5D2	3F22	3796.0	417.3	26760.7	2.00E-01	2.01E-01
5D3	3F22	3852.4	803.1	26760.7	4.70E-02	5.25E-02
5D2	3F23	3784.3	417.3	26842.3	1.60E-01	1.78E-01
5D3	3F23	3840.4	803.1	26842.3	4.00E-01	4.66E-01
5D4	3F23	3912.4	1282.8	26842.3	6.60E-02	6.43E-02
5D3	3F24	3821.0	803.1	26974.0	1.60E-01	1.66E-01
5D4	3F24	3892.4	1282.8	26974.0	7.40E-01	7.92E-01
5D2	3G3	3401.4	417.3	29817.1	7.00E-03	6.76E-03
5D3	3G3	3446.6	803.1	29817.1	1.70E-02	1.62E-02
5D4	3G3	3504.6	1282.8	29817.1	2.60E-03	2.32E-03
5D3	3G4	3407.9	803.1	30147.0	7.80E-03	7.20E-03
5D4	3G4	3464.5	1282.8	30147.0	3.20E-02	2.58E-02
5D2	3D3	2761.5	417.3	36630.1	9.70E-02	9.76E-02
5D3	3D3	2791.2	803.1	36630.1	8.90E-02	9.15E-02
5D4	3D3	2829.1	1282.8	36630.1	3.70E-01	3.80E-01
5D1	3D2	2731.0	142.1	36758.5	2.00E-01	1.96E-01
5D2	3D2	2751.7	417.3	36758.5	1.80E-01	1.60E-01
5D3	3D2	2781.2	803.1	36758.5	1.10E-01	1.05E-01
5D0	3D1	2708.2	0.0	36925.4	2.20E-01	2.37E-01
5D1	3D1	2718.6	142.1	36925.4	1.90E-01	2.11E-01
5D2	3D1	2739.1	417.3	36925.4	1.90E-03	2.73E-03
3H4	3G3	20472.5	24932.5	29817.1	3.60E-02	3.98E-02
3H4	3G4	19177.3	24932.5	30147.0	3.30E-02	3.33E-02
3H4	3G5	18189.8	24932.5	30430.1	1.20E-03	8.77E-04
3H5	3G5	19215.2	25225.9	30430.1	4.10E-02	4.40E-02
3H6	3G5	20401.5	25528.5	30430.1	4.10E-02	4.39E-02
3H5	1I6	8139.5	25225.9	37511.7	1.10E-01	1.16E-01
3H6	1I6	8345.0	25528.5	37511.7	1.40E-01	1.52E-01
3F22	3G3	32718.2	26760.7	29817.1	3.00E-02	3.03E-02
3F23	3G3	33615.7	26842.3	29817.1	3.70E-02	3.76E-02
3F24	3G4	31515.9	26974.0	30147.0	2.70E-02	2.80E-02
3F24	3G5	28934.3	26974.0	30430.1	3.70E-02	3.74E-02
3F23	3D3	10216.8	26842.3	36630.1	6.40E-03	5.97E-03
3F24	3D3	10356.1	26974.0	36630.1	6.90E-03	6.37E-03
3F22	3D2	10002.2	26760.7	36758.5	1.70E-02	1.44E-02
3F23	3D2	10084.5	26842.3	36758.5	1.60E-03	1.21E-03
3F22	3D1	9838.0	26760.7	36925.4	1.40E-02	1.36E-02
3F22	1D22	5120.2	26760.7	46291.2	2.10E-01	2.28E-01
3F23	1D22	5141.7	26842.3	46291.2	4.20E-01	4.48E-01
3G3	1F3	4363.8	29817.1	52732.7	1.20E-01	1.23E-01
3G4	1F3	4427.6	30147.0	52732.7	1.70E-01	1.70E-01
3D3	1D22	10350.8	36630.1	46291.2	9.00E-02	1.08E-01
3D2	1D22	10490.2	36758.5	46291.2	1.70E-02	2.00E-02
3D1	1D22	10677.1	36925.4	46291.2	8.00E-02	9.60E-02
3D3	1F3	6210.2	36630.1	52732.7	1.50E-01	1.65E-01
3D2	1F3	6260.1	36758.5	52732.7	7.00E-02	7.41E-02

 

 

Table 7: Forbidden transitions in Fe V

Ci	Cj	$S_{i}L_{i}\Pi_{i}$	$S_{j}L_{j}\Pi_{j}$	Ji	Jj	$\lambda_{{\rm vac}}$	$E_{i}({\rm cm}^{-1})$	$E_{j}({\rm cm}^{-1})$	$A_{ji}^{\rm M1}({\rm s}^{-1})$	$A_{ji}^{\rm E2}({\rm s}^{-1})$
3d4	3d4	5D	5D	0	1	703729.8	0.0	142.1	1.55E-04	0.00E+00
3d4	3d4	5D	5D	0	2	239635.8	0.0	417.3	0.00E+00	1.17E-10
3d4	3d4	5D	5D	1	2	363372.1	142.1	417.3	1.18E-03	1.10E-11
3d4	3d4	5D	5D	1	3	151285.9	142.1	803.1	0.00E+00	1.00E-09
3d4	3d4	5D	5D	2	3	259201.7	417.3	803.1	2.65E-03	1.29E-10
3d4	3d4	5D	5D	2	4	115540.2	417.3	1282.8	0.00E+00	1.84E-09
3d4	3d4	5D	5D	3	4	208463.6	803.1	1282.8	2.98E-03	4.19E-10
3d4	3d4	5D	3P2	2	0	4230.5	417.3	24055.4	0.00E+00	4.75E-04
3d4	3d4	5D	3P2	1	1	4027.3	142.1	24972.9	8.72E-05	2.01E-04
3d4	3d4	5D	3P2	3	1	4137.4	803.1	24972.9	0.00E+00	7.02E-05
3d4	3d4	5D	3P2	0	2	3778.1	0.0	26468.3	0.00E+00	6.83E-05
3d4	3d4	5D	3P2	2	2	3838.6	417.3	26468.3	3.52E-05	2.00E-05
3d4	3d4	5D	3P2	4	2	3970.5	1282.8	26468.3	0.00E+00	2.04E-05
3d4	3d4	5D	3H	2	4	4079.1	417.3	24932.5	0.00E+00	1.44E-07
3d4	3d4	5D	3H	3	4	4144.3	803.1	24932.5	8.32E-04	1.15E-09
3d4	3d4	5D	3H	3	5	4094.5	803.1	25225.9	0.00E+00	2.15E-06
3d4	3d4	5D	3H	4	5	4176.6	1282.8	25225.9	1.25E-05	1.09E-07
3d4	3d4	5D	3H	4	6	4124.4	1282.8	25528.5	0.00E+00	1.67E-05
3d4	3d4	5D	3F2	0	2	3736.8	0.0	26760.7	0.00E+00	3.67E-05
3d4	3d4	5D	3F2	4	2	3925.0	1282.8	26760.7	0.00E+00	2.54E-06
3d4	3d4	5D	3F2	1	3	3745.3	142.1	26842.3	0.00E+00	1.28E-05
3d4	3d4	5D	3F2	2	4	3765.5	417.3	26974.0	0.00E+00	1.14E-06
3d4	3d4	5D	3G	1	3	3369.8	142.1	29817.1	0.00E+00	5.37E-05
3d4	3d4	5D	3G	2	4	3363.6	417.3	30147.0	0.00E+00	8.67E-05
3d4	3d4	5D	3G	3	5	3375.3	803.1	30430.1	0.00E+00	8.86E-05
3d4	3d4	5D	3G	4	5	3430.8	1282.8	30430.1	5.93E-04	2.13E-04
3d4	3d3(4F)	5D	5F	0	1	536.4	0.0	186433.6	6.97E-05	0.00E+00
3d4	3d3(4F)	5D	5F	1	1	536.8	142.1	186433.6	1.59E-04	1.54E+04
3d4	3d3(4F)	5D	5F	2	1	537.6	417.3	186433.6	6.48E-05	1.09E+04
3d4	3d3(4F)	5D	5F	3	1	538.7	803.1	186433.6	0.00E+00	1.09E+03
3d4	3d3(4F)	5D	5F	0	2	535.5	0.0	186725.5	0.00E+00	7.79E+03
3d4	3d3(4F)	5D	5F	1	2	536.0	142.1	186725.5	1.77E-05	1.90E-04
3d4	3d3(4F)	5D	5F	2	2	536.7	417.3	186725.5	1.26E-04	1.26E+04
3d4	3d3(4F)	5D	5F	3	2	537.9	803.1	186725.5	5.30E-05	6.83E+03
3d4	3d3(4F)	5D	5F	4	2	539.3	1282.8	186725.5	0.00E+00	3.51E+02
3d4	3d3(4F)	5D	5F	1	3	534.7	142.1	187157.5	0.00E+00	1.01E+04
3d4	3d3(4F)	5D	5F	2	3	535.5	417.3	187157.5	4.29E-07	1.19E+03
3d4	3d3(4F)	5D	5F	3	3	536.6	803.1	187157.5	8.40E-05	1.35E+04
3d4	3d3(4F)	5D	5F	4	3	538.0	1282.8	187157.5	2.36E-05	2.94E+03
3d4	3d3(4F)	5D	5F	2	4	533.9	417.3	187719.0	0.00E+00	1.01E+04
3d4	3d3(4F)	5D	5F	3	4	535.0	803.1	187719.0	3.95E-05	6.97E+03
3d4	3d3(4F)	5D	5F	4	4	536.4	1282.8	187719.0	4.06E-05	1.09E+04
3d4	3d3(4F)	5D	5F	3	5	533.1	803.1	188395.3	0.00E+00	7.09E+03
3d4	3d3(4F)	5D	5F	4	5	534.4	1282.8	188395.3	1.56E-04	2.10E+04
3d4	3d4	3P2	3P2	0	1	108991.8	24055.4	24972.9	1.38E-02	0.00E+00
3d4	3d4	3P2	3P2	0	2	41443.9	24055.4	26468.3	0.00E+00	8.70E-09
3d4	3d4	3P2	3P2	1	2	66871.7	24972.9	26468.3	4.52E-02	1.97E-09
3d4	3d4	3P2	3F2	0	2	36964.5	24055.4	26760.7	0.00E+00	3.47E-07
3d4	3d4	3P2	3F2	1	2	55934.7	24972.9	26760.7	2.22E-05	4.87E-08
3d4	3d4	3P2	3F2	2	2	341997.3	26468.3	26760.7	7.92E-07	1.19E-12
3d4	3d4	3P2	3F2	1	3	53493.1	24972.9	26842.3	0.00E+00	6.78E-08
3d4	3d4	3P2	3F2	2	3	267379.7	26468.3	26842.3	3.55E-07	1.48E-11
3d4	3d4	3P2	3F2	2	4	197745.7	26468.3	26974.0	0.00E+00	1.38E-10
3d4	3d4	3P2	3G	1	3	20643.2	24972.9	29817.1	0.00E+00	7.16E-08
3d4	3d4	3P2	3G	2	3	29861.4	26468.3	29817.1	1.16E-05	1.36E-08
3d4	3d4	3P2	3G	2	4	27183.5	26468.3	30147.0	0.00E+00	1.00E-08
3d4	3d3(4F)	3P2	5F	0	1	615.8	24055.4	186433.6	6.41E-08	0.00E+00
3d4	3d3(4F)	3P2	5F	1	1	619.3	24972.9	186433.6	6.00E-07	1.12E+00
3d4	3d3(4F)	3P2	5F	2	1	625.1	26468.3	186433.6	9.64E-08	3.48E-01
3d4	3d3(4F)	3P2	5F	0	2	614.7	24055.4	186725.5	0.00E+00	2.06E-01

 

Table 7: continued

Ci	Cj	$S_{i}L_{i}\Pi_{i}$	$S_{j}L_{j}\Pi_{j}$	Ji	Jj	$\lambda_{{\rm vac}}$	$E_{i}({\rm cm}^{-1})$	$E_{j}({\rm cm}^{-1})$	$A_{ji}^{\rm M1}({\rm s}^{-1})$	$A_{ji}^{\rm E2}({\rm s}^{-1})$
3d4	3d3(4F)	3P2	5F	1	2	618.2	24972.9	186725.5	1.68E-07	1.63E-01
3d4	3d3(4F)	3P2	5F	2	2	624.0	26468.3	186725.5	3.12E-07	6.09E-01
3d4	3d3(4F)	3P2	5F	1	3	616.6	24972.9	187157.5	0.00E+00	4.94E-02
3d4	3d3(4F)	3P2	5F	2	3	622.3	26468.3	187157.5	6.44E-07	3.56E-01
3d4	3d3(4F)	3P2	5F	2	4	620.2	26468.3	187719.0	0.00E+00	5.32E-03
3d4	3d4	3H	3P2	4	2	65112.6	24932.5	26468.3	0.00E+00	6.81E-10
3d4	3d4	3H	3H	4	5	340831.6	24932.5	25225.9	6.60E-04	1.09E-13
3d4	3d4	3H	3H	4	6	167785.2	24932.5	25528.5	0.00E+00	2.54E-12
3d4	3d4	3H	3H	5	6	330469.3	25225.9	25528.5	6.12E-04	6.75E-15
3d4	3d4	3H	3F2	4	2	54698.6	24932.5	26760.7	0.00E+00	9.98E-08
3d4	3d4	3H	3F2	4	3	52361.5	24932.5	26842.3	1.55E-03	1.85E-08
3d4	3d4	3H	3F2	5	3	61865.9	25225.9	26842.3	0.00E+00	6.77E-08
3d4	3d4	3H	3F2	4	4	48983.6	24932.5	26974.0	6.05E-03	1.10E-10
3d4	3d4	3H	3F2	5	4	57205.0	25225.9	26974.0	9.40E-04	1.17E-08
3d4	3d4	3H	3F2	6	4	69180.2	25528.5	26974.0	0.00E+00	3.72E-08
3d4	3d4	3H	3G	5	3	21780.8	25225.9	29817.1	0.00E+00	4.24E-06
3d4	3d4	3H	3G	5	4	20320.7	25225.9	30147.0	4.59E-04	9.52E-05
3d4	3d4	3H	3G	6	4	21652.1	25528.5	30147.0	0.00E+00	3.21E-06
3d4	3d3(4F)	3H	5F	4	2	618.1	24932.5	186725.5	0.00E+00	1.66E+01
3d4	3d3(4F)	3H	5F	4	3	616.4	24932.5	187157.5	1.72E-06	3.91E+00
3d4	3d3(4F)	3H	5F	5	3	617.5	25225.9	187157.5	0.00E+00	2.08E+01
3d4	3d3(4F)	3H	5F	4	4	614.3	24932.5	187719.0	2.68E-06	2.75E-01
3d4	3d3(4F)	3H	5F	5	4	615.4	25225.9	187719.0	5.44E-07	6.70E+00
3d4	3d3(4F)	3H	5F	6	4	616.6	25528.5	187719.0	0.00E+00	1.47E+01
3d4	3d3(4F)	3H	5F	4	5	611.8	24932.5	188395.3	1.06E-07	3.46E-03
3d4	3d3(4F)	3H	5F	5	5	612.9	25225.9	188395.3	3.70E-06	2.25E-01
3d4	3d3(4F)	3H	5F	6	5	614.0	25528.5	188395.3	3.61E-07	8.33E+00
3d4	3d4	3F2	3F2	2	3	1225490.2	26760.7	26842.3	1.34E-05	4.26E-15
3d4	3d4	3F2	3F2	2	4	468823.3	26760.7	26974.0	0.00E+00	5.33E-15
3d4	3d4	3F2	3F2	3	4	759301.4	26842.3	26974.0	4.60E-05	2.91E-14
3d4	3d4	3F2	3G	4	3	35172.9	26974.0	29817.1	1.89E-04	1.37E-07
3d4	3d4	3F2	3G	2	4	29530.8	26760.7	30147.0	0.00E+00	1.13E-07
3d4	3d4	3F2	3G	3	4	30259.9	26842.3	30147.0	7.94E-04	1.22E-06
3d4	3d4	3F2	3G	3	5	27872.2	26842.3	30430.1	0.00E+00	8.99E-08
3d4	3d4	3G	3G	3	4	303122.2	29817.1	30147.0	9.18E-04	5.80E-13
3d4	3d4	3G	3G	3	5	163132.1	29817.1	30430.1	0.00E+00	3.11E-12
3d4	3d4	3G	3G	4	5	353232.1	30147.0	30430.1	4.69E-04	5.41E-13