4 Results and discussions

The fine structure energy levels and oscillator strengths for the dipole allowed and the intercombination transitions are discussed in separate subsections below.

4.1 Energy levels

A total of 1274 bound fine structure energy levels of Ar XIII and 1611 levels of Fe XXI are obtained. These correspond to total angular momenta of 0 $\leq J \leq$ 7 of both even and odd parities formed from spin multiplicities of 2S+1 = 5, 3, 1, and total orbital angular momenta of 0 $\leq L\leq$ 9 with $n\leq$ 10, 0 $\leq l \leq (n-1)$. The levels are presented in two formats: (i) in $J\pi$ order for practical applications and (ii) in LS term order for spectroscopy and completeness check up.

Tables 2a and 3a present a partial set of energy levels of Ar XIII and Fe XXI, respectively, in format (i), i.e., in $J\pi$ order (the complete tables are available electronically). At the top of each set. N_J is the total number of energy levels for symmetry of $J\pi$. For example, there are 56 fine structure levels of Ar XIII with $J\pi$ = $0^{\rm e}$. However, in the table, only part of the levels belonging to symmetry $J\pi$ is presented for illustration. The levels are identified with the configuration and LS term of the core and the outer electron quantum numbers. The effective quantum number, $\nu~=~z/\sqrt(E-E_{\rm t})$ where $E_{\rm t}$ is the immediate target threshold, is given next to the energies. However, $\nu$ is not given for the equivalent electron levels as it is not defined for these levels. Each level is assigned to one or more LS terms in the last column. If number of possible term is more than one, all are specified. However, the proper term from a multiple possibilities can be determined from Hund's rule; the term with higher angular momentum lies lower in energy. For example, the three levels 4, 5, and 6 of set $J\pi$ = 1$^{\rm e}$ in Table 2a are assigned with 3 possible terms, $^3(SPD)^{\rm e}$, whereupon the first level, i.e., level 4 can be designated as the $^3{\rm D^e}$, while level 5 is $^3{\rm P^e}$, and level 6 is $^3{\rm S^e}$. One reason for specifying all possible terms is that the order of calculated energy levels may not match exactly that of the measured ones. The other reason is that Hund's rule may not apply to all cases for complex ions; nonetheless it is useful to establish completeness. Similar sets of levels for Fe XXI are presented in Table 3a.

Tables 2b and 3b present the energy levels of Ar XIII and Fe XXI, respectively, in ascending order regardless of $J\pi$ values, and are grouped together according to the same configuration to show the correspondence between two sets of representations, in J-levels and in LS terms. (Listing of the lowest levels of equivalent electron states are omitted as they are given in energy comparison table). The grouping of levels provides the check for completeness of sets of energy levels that should belong to the corresponding LS term, and detects any missing level. The title line of each set of levels in the tables lists spin multiplicity (2S+1), parity, all possible L-values that can be formed from the core or target term, and outer or the valence electron angular momentum. The J-values for each possible LS term are specified within the parentheses next to the value of L. "Nlv'' is the total number of J-levels that are expected from this set of LS terms. This line is followed by the set of BPRM energy levels of same configurations. "Nlv(c)'', at the end of the set, specifies the total number of J-levels obtained. If Nlv = Nlv(c) for a set, the calculated energy set is complete. The correspondence of couplings and completeness of levels are carried out by the program PRCBPID which also detects and prints the missing levels. For example, in the set for $^3({\rm G,H,I)^e}$ for Ar XIII near the end of Table 2b, the set is found to be incomplete where four levels of J=5, 4, 6, 5 are missing. Sets with missing levels usually lie in the high energy region. Each level of a set is further identified by all possible LS terms (specified in the last column of the set). The multiple LS terms can be reduced to the most probable (but approximately) one using Hund's rule, as explained above. It may be noted that levels are grouped consistently in closely spaced energies and in effective quantum numbers confirming proper designation of the LS terms.

The BPRM energy levels for Ar XIII and Fe XXI are compared in Table 4 with the limited number of levels observed. The 55 observed levels of Ar XIII (Kelly, NIST) are not in the compiled list by the NIST. However, the calculated fine structure energies agree with these observed ones to about 1% for most of the levels. The difference is upto 9%. The agreement between the observed and calculated energies is much better for Fe XXI (Table 4).

 

Table 4: Comparison of absolute calculated BPRM energies ($E_{\rm c}$) with the observed ones ($E_{\rm o}$, Sugar & Corliss 1985) for Ar XIII and Fe XXI. I_J is the level index for the energy position in symmetry $J\pi$. The asterisk next to the J-value indicates that the term has incomplete set of observed fine structure levels

Level		J	IJ	$E_{\rm o}$(Ry)	$E_{\rm c}$(Ry)	Level		J	IJ	$E_{\rm o}$(Ry)	$E_{\rm c}$(Ry)
Ar XIII
${\rm 2s^22p^2}$	${\rm ^3P}$	2	1	-50.133	-50.209	${\rm 2s^22p3d}$	${\rm ^3P^o}$	2	9	-19.053	-19.149
${\rm 2s^22p^2}$	${\rm ^3P}$	1	1	-50.243	-50.326	${\rm 2s^22p3d}$	${\rm ^3P^o}$	1	8	-19.037	-19.112
${\rm 2s^22p^2}$	${\rm ^3P}$	0	1	-50.332	-50.416	${\rm 2s^22p3d}$	${\rm ^3P^o}$	0	3	-19.025	-19.079
${\rm 2s^22p^2}$	${\rm ^1D}$	2	2	-49.558	-49.621	${\rm 2s^22p3d}$	${\rm ^1P^o}$	1	9	-18.740	-18.772
${\rm 2s^22p^2}$	${\rm ^1S}$	0	2	-48.856	-48.905	${\rm 2s^22p3d}$	${\rm ^1F^o}$	3	4	-18.736	-18.787
${\rm 2s2p^3}$	${\rm ^5S^o}$	2	1	-48.274	-48.346	${\rm 2s2p^23p}$	${\rm ^3D^o}$	3	8	-17.126	-16.822
${\rm 2s2p^3}$	${\rm ^3D^o}$	3	1	-46.469	-46.508	${\rm 2s2p^23p}$	${\rm ^3D^o}$	2	16	-17.126	-16.805
${\rm 2s2p^3}$	${\rm ^3D^o}$	2	2	-46.480	-46.533	${\rm 2s2p^23p}$	${\rm ^3D^o}$	1	16	-17.126	-16.605
${\rm 2s2p^3}$	${\rm ^3D^o}$	1	1	-46.476	-46.527	${\rm 2s2p^2(^4P)3d}$	${\rm ^5P}$	3*	6	-17.117	-17.281
${\rm 2s2p^3}$	${\rm ^3P^o}$	2	3	-45.803	-45.826	${\rm 2s2p^2(^4P)3d}$	${\rm ^5P}$	2*	14	-17.074	-17.274
${\rm 2s2p^3}$	${\rm ^3P^o}$	1	2	-45.814	-45.844	${\rm 2s2p^23p}$	${\rm ^1D^o}$	2	15	-16.019	-16.867
${\rm 2s2p^3}$	${\rm ^3P^o}$	0	1	-45.817	-45.852	${\rm 2s2p^23p}$	${\rm ^3P^o}$	2	19	-15.784	-15.731
${\rm 2s2p^3}$	${\rm ^1D^o}$	2	4	-44.630	-44.627	${\rm 2s2p^23p}$	${\rm ^3P^o}$	1	18	-15.784	-15.798
${\rm 2s2p^3}$	${\rm ^3S^o}$	1	3	-44.604	-44.597	${\rm 2s2p^23p}$	${\rm ^3P^o}$	0	8	-15.784	-15.721
${\rm 2s2p^3}$	${\rm ^1P^o}$	1	4	-43.966	-43.949	${\rm 2s2p^23p}$	${\rm ^1P^o}$	1	20	-15.581	-15.589
${\rm 2s^22p3s}$	${\rm ^3P^o}$	2	5	-21.535	-21.845	${\rm 2s2p^23p}$	${\rm ^3S^o}$	1	21	-15.563	-15.475
${\rm 2s^22p3s}$	${\rm ^3P^o}$	1	5	-21.659	-22.001	${\rm 2s^22p4s}$	${\rm ^1P^o}$	1	31	-11.826	-12.379
${\rm 2s^22p3s}$	${\rm ^3P^o}$	0	2	-21.722	-22.058	${\rm 2s^22p4s}$	${\rm ^3P^o}$	2	29	-11.580	-12.395
${\rm 2s^22p3s}$	${\rm ^1P^o}$	1	6	-21.381	-21.725	${\rm 2s^22p4s}$	${\rm ^3P^o}$	1	30	-11.580	-12.588
${\rm 2s^22p3d}$	${\rm ^3F^o}$	4	1	-19.286	-19.358	${\rm 2s^22p4s}$	${\rm ^3P^o}$	0	12	-11.580	-12.602
${\rm 2s^22p3d}$	${\rm ^3F^o}$	3	2	-19.419	-19.463	${\rm 2s^22p4d}$	${\rm ^1P^o}$	1	45	-10.774	-10.520
${\rm 2s^22p3d}$	${\rm ^3F^o}$	2	7	-19.520	-19.428	${\rm 2s^22p4d}$	${\rm ^1D^o}$	2	46	-10.599	-10.641
${\rm 2s^22p3d}$	${\rm ^1D^o}$	2	6	-19.398	-19.575	${\rm 2s^22p4d}$	${\rm ^3P^o}$	2	44	-10.565	-10.835
${\rm 2s^22p3d}$	${\rm ^3D^o}$	3	3	-19.106	-19.177	${\rm 2s^22p4d}$	${\rm ^3P^o}$	1	43	-10.565	-10.785
${\rm 2s^22p3d}$	${\rm ^3D^o}$	2	8	-19.194	-19.208	${\rm 2s^22p4d}$	${\rm ^3P^o}$	0	18	-10.565	-10.625
${\rm 2s^22p3d}$	${\rm ^3D^o}$	1	7	-19.253	-19.258
Fe XXI
${\rm 2s^22p^2}$	${\rm ^3P}$	2	1	-123.050	-123.185	${\rm 2s^22p3d}$	${\rm ^1D^o}$	2	6	-50.320	-50.589
${\rm 2s^22p^2}$	${\rm ^3P}$	1	1	-123.440	-123.615	${\rm 2s^22p3d}$	${\rm ^3F^o}$	3*	2	-50.289	-50.012
${\rm 2s^22p^2}$	${\rm ^3P}$	0	1	-124.110	-124.292	${\rm 2s^22p3d}$	${\rm ^3D^o}$	3*	3	-49.436	-49.402
${\rm 2s^22p^2}$	${\rm ^1D}$	2	2	-121.890	-122.009	${\rm 2s^22p3d}$	${\rm ^3D^o}$	2*	8	-49.506	-49.463
${\rm 2s^22p^2}$	${\rm ^1S}$	0	2	-120.730	-120.849	${\rm 2s^22p3d}$	${\rm ^3P^o}$	2*	9	-49.109	-49.237
${\rm 2s2p^3}$	${\rm ^5S^o}$	2	1	-119.680	-119.850	${\rm 2s^22p3d}$	${\rm ^1P^o}$	1	11	-48.535	-48.480
${\rm 2s2p^3}$	${\rm ^3D^o}$	3	1	-116.790	-116.897	${\rm 2s^22p3d}$	${\rm ^1F^o}$	3	4	-48.355	-48.578
${\rm 2s2p^3}$	${\rm ^3D^o}$	2	2	-117.030	-117.155	${\rm 2s^22p4d}$	${\rm ^3F^o}$	3*	22	-27.939	-27.934
${\rm 2s2p^3}$	${\rm ^3D^o}$	1	1	-117.040	-117.168	${\rm 2s^22p4d}$	${\rm ^3P^o}$	2*	39	-27.703	-27.949
${\rm 2s2p^3}$	${\rm ^3P^o}$	2	3	-115.530	-115.651	${\rm 2s^22p4d}$	${\rm ^3P^o}$	1*	40	-26.718	-26.990
${\rm 2s2p^3}$	${\rm ^3P^o}$	1	2	-115.690	-115.815	${\rm 2s^22p4d}$	${\rm ^3D^o}$	3	23	-26.718	-27.064
${\rm 2s2p^3}$	${\rm ^3P^o}$	0	1	-115.760	-115.895	${\rm 2s^22p4d}$	${\rm ^3D^o}$	2	41	-27.019	-27.005
${\rm 2s2p^3}$	${\rm ^3S^o}$	1	3	-114.130	-114.241	${\rm 2s^22p4d}$	${\rm ^3D^o}$	1	39	-27.693	-27.887
${\rm 2s2p^3}$	${\rm ^1D^o}$	2	4	-113.850	-113.922	${\rm 2s^22p4d}$	${\rm ^1D^o}$	2	40	-26.837	-27.069
${\rm 2s2p^3}$	${\rm ^1P^o}$	1	4	-112.620	-112.695	${\rm 2s^22p4d}$	${\rm ^1F^o}$	3	24	-26.782	-26.785
${\rm 2p^4}$	${\rm ^3P}$	2	3	-109.110	-109.226	${\rm 2s^22p5d}$	${\rm ^3D^o}$	3*	50	-16.567	-16.849
${\rm 2p^4}$	${\rm ^3P}$	1	2	-108.250	-108.362	${\rm 2s^22p5d}$	${\rm ^3P^o}$	1*	67	-16.494	-16.813
${\rm 2p^4}$	${\rm ^3P}$	0	3	-108.300	-108.406	${\rm 2s^22p5d}$	${\rm ^1D^o}$	2	72	-16.494	-16.854
${\rm 2p^4}$	${\rm ^1D}$	2	4	-107.550	-107.626	${\rm 2s^22p5d}$	${\rm ^1F^o}$	3	51	-16.457	-16.724
${\rm 2p^4}$	${\rm ^1S}$	0	4	-105.450	-105.511

There are 39 observed energy levels of Fe XXI (Sugar & Corliss 1985). Present energies agree with the observed ones to less than or about 1% for all except two levels that agree within 2%. In Table 4 the column next to the J-column is for the energy level index, I_J. The energy level index specifies the position, in ascending order, of the level in the calculated set of energies of $J\pi$ symmetry. It is necessary to use the level indices to make correspondence between the calculated and observed levels for later use.

4.2 Oscillators strengths

The total number of oscillator strengths (f-values) for bound-bound fine structure transitions is 198259 for Ar XIII and is 300079 for Fe XXI. These include both the dipole allowed ( $\Delta S=0$) and the intercombination ( $\Delta S \neq$ 0) transitions. Complete sets of f-values for both Ar XIII and Fe XXI are available electronically.

Partial sets of the oscillator strengths for Ar XIII and Fe XXI are presented in Tables 5 and 6 respectively.

 

Table 5: Oscillator strengths and transition probabilities for Ar XIII (see text for explanation)

18    6
0    0         2    1
56	136	$E_i({\rm Ry})$	$E_j({\rm Ry})$	$gf_{\rm L}$	S	$A_{ji}({\rm s}^{-1})$
1	1	-5.04159E+01	-4.65272E+01	-7.432E-02	5.734E-02	3.009E+09
1	2	-5.04159E+01	-4.58436E+01	-3.719E-02	2.440E-02	2.082E+09
1	3	-5.04159E+01	-4.45972E+01	-7.896E-02	4.071E-02	7.158E+09
1	4	-5.04159E+01	-4.39490E+01	-8.538E-03	3.961E-03	9.561E+08
1	5	-5.04159E+01	-2.20006E+01	-5.614E-02	5.927E-03	1.214E+11
1	6	-5.04159E+01	-2.17248E+01	-3.410E-04	3.566E-05	7.517E+08
1	7	-5.04159E+01	-1.92584E+01	-8.122E-01	7.820E-02	2.111E+12
1	8	-5.04159E+01	-1.91117E+01	-3.833E-01	3.673E-02	1.006E+12
1	9	-5.04159E+01	-1.87724E+01	-8.515E-03	8.073E-04	2.283E+10
1	10	-5.04159E+01	-1.86813E+01	-2.095E-02	1.980E-03	5.649E+10
1	11	-5.04159E+01	-1.86458E+01	-5.138E-03	4.852E-03	1.389E+10
1	12	-5.04159E+01	-1.84751E+01	-1.566E-04	1.471E-05	4.278E+08
1	13	-5.04159E+01	-1.82444E+01	-2.107E-01	1.965E-02	5.839E+11
1	14	-5.04159E+01	-1.79813E+01	-9.334E-02	8.633E-03	2.629E+11
1	15	-5.04159E+01	-1.66700E+01	-1.963E-02	1.745E-03	5.986E+10
1	16	-5.04159E+01	-1.66046E+01	-2.252E-04	1.998E-05	6.894E+08
1	17	-5.04159E+01	-1.64673E+01	-2.083E-03	1.841E-04	6.427E+09
1	18	-5.04159E+01	-1.57979E+01	-7.669E-03	6.646E-04	2.461E+10
1	19	-5.04159E+01	-1.57593E+01	-4.275E-02	3.701E-03	1.375E+11
1	20	-5.04159E+01	-1.55895E+01	-1.030E-02	8.873E-04	3.346E+10
1	21	-5.04159E+01	-1.54751E+01	-1.992E-02	1.710E-03	6.512E+10
1	22	-5.04159E+01	-1.54647E+01	-8.200E-03	7.038E-04	2.682E+10
1	23	-5.04159E+01	-1.48961E+01	-2.989E-04	2.525E-05	1.010E+09
1	24	-5.04159E+01	-1.46203E+01	-5.201E-03	4.359E-04	1.784E+10
1	25	-5.04159E+01	-1.42630E+01	-1.841E-03	1.528E-04	6.443E+09
1	26	-5.04159E+01	-1.33759E+01	-4.990E-04	4.042E-05	1.833E+09
1	27	-5.04159E+01	-1.31269E+01	-3.161E-05	2.543E-06	1.177E+08
1	28	-5.04159E+01	-1.30556E+01	-1.439E-06	1.156E-07	5.377E+06
1	29	-5.04159E+01	-1.26698E+01	-4.509E-03	3.584E-04	1.720E+10
1	30	-5.04159E+01	-1.25883E+01	-2.180E-03	1.729E-04	8.353E+09
1	31	-5.04159E+01	-1.23791E+01	-1.555E-03	1.226E-04	6.024E+09
1	32	-5.04159E+01	-1.19016E+01	-4.197E-03	3.269E-04	1.667E+10
1	33	-5.04159E+01	-1.18386E+01	-1.906E-03	1.482E-04	7.595E+09
1	34	-5.04159E+01	-1.17009E+01	-4.479E-03	3.471E-04	1.797E+10
1	35	-5.04159E+01	-1.15532E+01	-6.841E-04	5.281E-05	2.766E+09
1	36	-5.04159E+01	-1.14449E+01	-2.326E-03	1.791E-04	9.457E+09
1	37	-5.04159E+01	-1.13763E+01	-3.650E-03	2.805E-04	1.489E+10
1	38	-5.04159E+01	-1.13214E+01	-5.940E-03	4.558E-04	2.431E+10
1	39	-5.04159E+01	-1.12634E+01	-4.570E-02	3.502E-03	1.876E+11
1	40	-5.04159E+01	-1.11175E+01	-2.745E-02	2.096E-03	1.135E+11
1	41	-5.04159E+01	-1.10946E+01	-4.751E-03	3.625E-04	1.967E+10
1	42	-5.04159E+01	-1.09356E+01	-1.423E-02	1.081E-03	5.940E+10
1	43	-5.04159E+01	-1.07848E+01	-8.384E-02	6.347E-03	3.526E+11
1	44	-5.04159E+01	-1.06338E+01	-1.724E-01	1.300E-02	7.306E+11
1	45	-5.04159E+01	-1.05204E+01	-7.928E-03	5.962E-04	3.379E+10
1	46	-5.04159E+01	-1.03856E+01	-7.162E-05	5.367E-06	3.073E+08
1	47	-5.04159E+01	-9.45149E+00	-1.226E-03	8.979E-05	5.508E+09
1	48	-5.04159E+01	-9.40487E+00	-5.841E-05	4.273E-06	2.630E+08
1	49	-5.04159E+01	-9.36936E+00	-1.525E-06	1.115E-07	6.878E+06
1	50	-5.04159E+01	-8.69880E+00	-7.136E-06	5.132E-07	3.325E+07

 

Table 6: Oscillator strengths and transition probabilities for Fe XXI (see text for explanation)

26    6
0    0         2    1
64	157	$E_i({\rm Ry})$	$E_j({\rm Ry})$	$gf_{\rm L}$	S	$A_{ji}({\rm s}^{-1})$
1	1	-1.24292E+02	-1.17168E+02	-8.556E-02	3.603E-02	1.163E+10
1	2	-1.24292E+02	-1.15815E+02	-2.267E-02	8.023E-03	4.362E+09
1	3	-1.24292E+02	-1.14241E+02	-3.606E-02	1.076E-02	9.752E+09
1	4	-1.24292E+02	-1.12695E+02	-1.038E-04	2.685E-05	3.738E+07
1	5	-1.24292E+02	-5.45579E+01	-5.459E-02	2.348E-03	7.108E+11
1	6	-1.24292E+02	-5.36838E+01	-2.443E-06	1.038E-07	3.261E+07
1	7	-1.24292E+02	-4.98528E+01	-1.097E+00	4.421E-02	1.628E+13
1	8	-1.24292E+02	-4.92676E+01	-2.376E-01	9.501E-03	3.581E+12
1	9	-1.24292E+02	-4.89841E+01	-6.728E-02	2.680E-03	1.022E+12
1	10	-1.24292E+02	-4.87720E+01	-2.967E-02	1.179E-03	4.530E+11
1	11	-1.24292E+02	-4.84796E+01	-2.779E-02	1.100E-03	4.277E+11
1	12	-1.24292E+02	-4.79949E+01	-4.288E-02	1.686E-03	6.684E+11
1	13	-1.24292E+02	-4.78167E+01	-1.718E-01	6.739E-03	2.690E+12
1	14	-1.24292E+02	-4.69872E+01	-2.536E-02	9.842E-04	4.058E+11
1	15	-1.24292E+02	-4.57908E+01	-3.615E-02	1.382E-03	5.965E+11
1	16	-1.24292E+02	-4.51108E+01	-4.164E-03	1.578E-04	6.990E+10
1	17	-1.24292E+02	-4.48241E+01	-1.864E-03	7.037E-05	3.151E+10
1	18	-1.24292E+02	-4.43456E+01	-1.420E-03	5.329E-05	2.431E+10
1	19	-1.24292E+02	-4.40629E+01	-1.372E-02	5.130E-04	2.364E+11
1	20	-1.24292E+02	-4.38519E+01	-1.681E-02	6.269E-04	2.912E+11
1	21	-1.24292E+02	-4.33769E+01	-4.298E-02	1.594E-03	7.534E+11
1	22	-1.24292E+02	-4.26163E+01	-1.653E-03	6.072E-05	2.953E+10
1	23	-1.24292E+02	-4.22948E+01	-7.745E-03	2.834E-04	1.394E+11
1	24	-1.24292E+02	-4.18241E+01	-1.151E-02	4.187E-04	2.096E+11
1	25	-1.24292E+02	-4.13257E+01	-9.296E-04	3.361E-05	1.713E+10
1	26	-1.24292E+02	-3.98368E+01	-8.523E-04	3.028E-05	1.628E+10
1	27	-1.24292E+02	-3.91261E+01	-5.482E-07	1.931E-08	1.065E+07
1	28	-1.24292E+02	-3.89117E+01	-2.576E-06	9.051E-08	5.028E+07
1	29	-1.24292E+02	-3.81248E+01	-3.895E-03	1.356E-04	7.743E+10
1	30	-1.24292E+02	-3.72353E+01	-3.496E-03	1.205E-04	7.093E+10
1	31	-1.24292E+02	-3.68057E+01	-3.001E-05	1.029E-06	6.150E+08
1	32	-1.24292E+02	-3.66023E+01	-2.169E-03	7.420E-05	4.465E+10
1	33	-1.24292E+02	-3.62569E+01	-1.857E-03	6.328E-05	3.853E+10
1	34	-1.24292E+02	-3.56225E+01	-6.271E-04	2.122E-05	1.320E+10
1	35	-1.24292E+02	-3.52504E+01	-4.418E-04	1.489E-05	9.379E+09
1	36	-1.24292E+02	-3.41344E+01	-2.004E-04	6.668E-06	4.361E+09
1	37	-1.24292E+02	-2.96152E+01	-3.262E-03	1.034E-04	7.829E+10
1	38	-1.24292E+02	-2.86486E+01	-5.945E-03	1.865E-04	1.456E+11
1	39	-1.24292E+02	-2.78866E+01	-1.027E-01	3.196E-03	2.556E+12
1	40	-1.24292E+02	-2.69896E+01	-1.375E-01	4.239E-03	3.485E+12
1	41	-1.24292E+02	-2.67722E+01	-5.394E-03	1.659E-04	1.373E+11
1	42	-1.24292E+02	-2.51918E+01	-1.245E-03	3.769E-05	3.273E+10
1	43	-1.24292E+02	-2.48551E+01	-3.036E-02	9.160E-02	8.038E+11
1	44	-1.24292E+02	-2.47189E+01	-6.847E-04	2.063E-05	1.818E+10
1	45	-1.24292E+02	-2.44906E+01	-1.546E-02	4.647E-04	4.124E+11
1	46	-1.24292E+02	-2.40150E+01	-5.308E-02	1.588E-03	1.429E+12
1	47	-1.24292E+02	-2.33917E+01	-9.461E-06	2.813E-07	2.579E+08
1	48	-1.24292E+02	-2.29626E+01	-1.697E-06	5.024E-08	4.664E+07
1	49	-1.24292E+02	-2.29205E+01	-3.144E-05	9.304E-07	8.651E+08
1	50	-1.24292E+02	-2.20492E+01	-4.263E-03	1.251E-04	1.193E+11

The format of the tables is the same as that of the electronic files for the f-values. At the top of each table, the two numbers are the nuclear charge (Z = 18 for Ar XIII and = 26 for Fe XXI) and number of electrons in the ion, $N_{\rm elc}$ (= 6 for carbon like ions). Below this line are the sets of oscillator strengths belonging to a pair of symmetries, $J_i\pi_i~-~J_k\pi_k$, specified at the top. The symmetries are expressed in the form of 2J_i and $\pi_i$ ($\pi=0$ for even and =1 for odd parity), 2J_k and $\pi_k$. For example, Tables 5 and 6 present partial transitions among the levels of symmetries $J=0^{\rm e}$ and $J=1^{\circ}$ for Ar XIII and Fe XXI respectively. The line following the transition symmetries are the number of bound levels, N_Ji and N_Jk. This line is followed by $N_{Ji}\times N_{Jk}$ number of transitions. The first two columns are the energy level indices, I_i and I_k (as mentioned above), and the third and the fourth columns are their energies, E_i and E_k, in Rydberg unit. The fifth column is the $gf_{\rm L}$ for the allowed transitions ($\Delta J$ = 0, $\pm 1$). $f_{\rm L}$ is the oscillator strength in length form, and g = 2J+1 is the statistical weight factor of the initial or the lower level. A negative value for gf means that i is the lower level, while a positive one means that k is the lower level. Column six is the line strength (S). The last column in the table gives the transition probability, $A_{ki}({\rm s}^{-1})$. Complete spectroscopic identification of the transition can be obtained from Tables 2a and 3a by referring to the values of $J_i\pi_i$, I_i, $J_k\pi_k$, and I_k. For example, the first transition for Fe XXI in Table 6 corresponds to, as identified in Table 3a, dipole allowed transition $2{\rm s}^22{\rm p}^2(^3{\rm P^e}_0)(I_i=1) \rightarrow 2{\rm s}2{\rm p}^3(^3 {\rm D^o}_1)(I_k=1)$.

A set of transition probabilities for both Ar XIII and Fe XXI has been reprocessed such that observed energy differences, rather than the calculated ones, are used to obtain the f- and A-values from BPRM line strengths (S). The S-values are energy independent quantities. As the observed energies have lower uncertainties than the calculated ones, use of them, instead of the calculated energies, with the S-values (Eqs. 7 and 8) improves the accuracy of the f- and A-values for the relevant transitions. (This is a commonly used procedure adopted first in the NIST compilation.) The astrophysical models also in general use the observed transition energies for the relevant f-, S and A-values. For any comparison or spectral diagnostics, therefore, values from these sets should be used.

The reprocessing of f- and A-values has been carried out for all the allowed transitions ( $\Delta J=0,\, \pm 1$) among the observed levels. The set consists of 333 transitions of Ar XII and 184 of Fe XXI (these sets are also available electronically). Sample sets of the reprocessed oscillator strengths are presented in Tables 7a and 8a for Ar XIII and Fe XXI.

 

Table 7: a. Sample set of reprocessed f- and A-values for Ar XIII using observed transition energies. The negative sign for the energies is omitted for convenience. I_i and I_j are the level indices

Ci	Cj	$S_iL_i\pi_i$	$S_jL_j\pi_j$	gi(Ii)	gj(Ij)	$E_i({\rm Ry})$	$E_j({\rm Ry})$	f	$A_{ji}({\rm s}^{-1})$
${\rm 2s^22p^2}$	${\rm -~2s2p^3}$	${\rm ^3P^e}$	${\rm ^3D^o}$	1 (1)	3 (1)	50.3320	46.4760	7.370E-02	2.93E+09
${\rm 2s^22p^2}$	${\rm -~2s2p^3}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (1)	3 (2)	50.3320	45.8140	3.675E-02	2.01E+09
${\rm 2s^22p^2}$	${\rm -~2s2p^3}$	${\rm ^3P^e}$	${\rm ^3S^o}$	1 (1)	3 (3)	50.3320	44.6040	7.773E-02	6.83E+09
${\rm 2s^22p^2}$	${\rm -~2s2p^3}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (1)	3 (4)	50.3320	43.9660	8.405E-03	9.12E+08
${\rm 2s^22p^2}$	${\rm -~2s^22p3s}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (1)	3 (5)	50.3320	21.6590	5.665E-02	1.25E+11
${\rm 2s^22p^2}$	${\rm -~2s^22p3s}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (1)	3 (6)	50.3320	21.3810	3.441E-04	7.72E+08
${\rm 2s^22p^2}$	${\rm -~2s^22p3d}$	${\rm ^3P^e}$	${\rm ^3D^o}$	1 (1)	3 (7)	50.3320	19.2530	8.101E-01	2.10E+12
${\rm 2s^22p^2}$	${\rm -~2s^22p3d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (1)	3 (8)	50.3320	19.0370	3.832E-01	1.00E+12
${\rm 2s^22p^2}$	${\rm -~2s^22p3d}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (1)	3 (9)	50.3320	18.7400	8.501E-03	2.27E+10
${\rm 2s^22p^2}$	${\rm -~2s2p^23p}$	${\rm ^3P^e}$	${\rm ^3D^o}$	1 (1)	3 (16)	50.3320	17.1260	2.212E-04	6.53E+08
${\rm 2s^22p^2}$	${\rm -~2s2p^23p}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (1)	3 (18)	50.3320	15.7840	7.654E-03	2.45E+10
${\rm 2s^22p^2}$	${\rm -~2s2p^23p}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (1)	3 (20)	50.3320	15.5810	1.028E-02	3.32E+10
${\rm 2s^22p^2}$	${\rm -~2s2p^23p}$	${\rm ^3P^e}$	${\rm ^3S^o}$	1 (1)	3 (21)	50.3320	15.5630	1.982E-02	6.41E+10
${\rm 2s^22p^2}$	${\rm -~2s^22p4s}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (1)	3 (30)	50.3320	11.5800	2.233E-03	8.98E+09
${\rm 2s^22p^2}$	${\rm -~2s^22p4s}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (1)	3 (31)	50.3320	11.8260	1.574E-03	6.25E+09
${\rm 2s^22p^2}$	${\rm -~2s^22p4d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (1)	3 (43)	50.3320	10.5650	8.413E-02	3.56E+11
${\rm 2s^22p^2}$	${\rm -~2s^22p4d}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (1)	3 (45)	50.3320	10.7740	7.861E-03	3.29E+10
${\rm 2s^22p^2}$	${\rm -~2s2p^3}$	${\rm ^1S^e}$	${\rm ^3D^o}$	1 (2)	3 (1)	48.8560	46.4760	2.257E-04	3.42E+06
${\rm 2s^22p^2}$	${\rm -~2s2p^3}$	${\rm ^1S^e}$	${\rm ^3P^o}$	1 (2)	3 (2)	48.8560	45.8140	4.438E-04	1.10E+07
${\rm 2s^22p^2}$	${\rm -~2s2p^3}$	${\rm ^1S^e}$	${\rm ^3S^o}$	1 (2)	3 (3)	48.8560	44.6040	8.290E-03	4.01E+08
${\rm 2s^22p^2}$	${\rm -~2s2p^3}$	${\rm ^1S^e}$	${\rm ^1P^o}$	1 (2)	3 (4)	48.8560	43.9660	1.314E-01	8.41E+09
${\rm 2s^22p^2}$	${\rm -~2s^22p3s}$	${\rm ^1S^e}$	${\rm ^3P^o}$	1 (2)	3 (5)	48.8560	21.6590	8.977E-04	1.78E+09
${\rm 2s^22p^2}$	${\rm -~2s^22p3s}$	${\rm ^1S^e}$	${\rm ^1P^o}$	1 (2)	3 (6)	48.8560	21.3810	7.492E-02	1.51E+11
${\rm 2s^22p^2}$	${\rm -~2s^22p3d}$	${\rm ^1S^e}$	${\rm ^3D^o}$	1 (2)	3 (7)	48.8560	19.2530	8.055E-03	1.89E+10
${\rm 2s^22p^2}$	${\rm -~2s^22p3d}$	${\rm ^1S^e}$	${\rm ^3P^o}$	1 (2)	3 (8)	48.8560	19.0370	1.741E-03	4.15E+09
${\rm 2s^22p^2}$	${\rm -~2s^22p3d}$	${\rm ^1S^e}$	${\rm ^1P^o}$	1 (2)	3 (9)	48.8560	18.7400	1.227E+00	2.98E+12
${\rm 2s^22p^2}$	${\rm -~2s2p^23p}$	${\rm ^1S^e}$	${\rm ^3D^o}$	1 (2)	3 (16)	48.8560	17.1260	8.095E-03	2.18E+10
${\rm 2s^22p^2}$	${\rm -~2s2p^23p}$	${\rm ^1S^e}$	${\rm ^3P^o}$	1 (2)	3 (18)	48.8560	15.7840	4.672E-02	1.37E+11
${\rm 2s^22p^2}$	${\rm -~2s2p^23p}$	${\rm ^1S^e}$	${\rm ^1P^o}$	1 (2)	3 (20)	48.8560	15.5810	2.188E-01	6.49E+11
${\rm 2s^22p^2}$	${\rm -~2s2p^23p}$	${\rm ^1S^e}$	${\rm ^3S^o}$	1 (2)	3 (21)	48.8560	15.5630	6.007E-04	1.78E+09
${\rm 2s^22p^2}$	${\rm -~2s^22p4s}$	${\rm ^1S^e}$	${\rm ^3P^o}$	1 (2)	3 (30)	48.8560	11.5800	2.184E-03	8.13E+09
${\rm 2s^22p^2}$	${\rm -~2s^22p4s}$	${\rm ^1S^e}$	${\rm ^1P^o}$	1 (2)	3 (31)	48.8560	11.8260	3.867E-03	1.42E+10
${\rm 2s^22p^2}$	${\rm -~2s^22p4d}$	${\rm ^1S^e}$	${\rm ^3P^o}$	1 (2)	3 (43)	48.8560	10.5650	2.516E-02	9.88E+10
${\rm 2s^22p^2}$	${\rm -~2s^22p4d}$	${\rm ^1S^e}$	${\rm ^1P^o}$	1 (2)	3 (45)	48.8560	10.7740	2.355E-01	9.14E+11
${\rm 2S2p^3}$	${\rm -~2p^4}$	${\rm ^3D^o}$	${\rm ^3P^e}$	3 (1)	1 (3)	46.4760	41.2420	3.321E-02	2.19E+10
${\rm 2s2p^3}$	${\rm -~2p^4}$	${\rm ^3P^o}$	${\rm ^3P^e}$	3 (2)	1 (3)	45.8140	41.2420	2.436E-02	1.23E+10
${\rm 2s2p^3}$	${\rm -~2p^4}$	${\rm ^3S^o}$	${\rm ^3P^e}$	3 (3)	1 (3)	44.6040	41.2420	1.657E-02	4.51E+09
${\rm 2s2p^3}$	${\rm -~2p^4}$	${\rm ^1P^o}$	${\rm ^3P^e}$	3 (4)	1 (3)	43.9660	41.2420	1.568E-03	2.80E+08
${\rm 2p^4}$	${\rm -~2s^22p3s}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (3)	3 (5)	41.2420	21.6590	2.841E-06	2.92E+06
${\rm 2p^4}$	${\rm -~2s^22p3s}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (3)	3 (6)	41.2420	21.3810	9.904E-07	1.05E+06
${\rm 2p^4}$	${\rm -~2s^22p3d}$	${\rm ^3P^e}$	${\rm ^3D^o}$	1 (3)	3 (7)	41.2420	19.2530	7.887E-06	1.02E+07
${\rm 2p^4}$	${\rm -~2s^22p3d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (3)	3 (8)	41.2420	19.0370	2.720E-05	3.59E+07
${\rm 2p^4}$	${\rm -~2s^22p3d}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (3)	3 (9)	41.2420	18.7400	6.594E-06	8.94E+06
${\rm 2p^4}$	${\rm -~2s2p^23p}$	${\rm ^3P^e}$	${\rm ^3D^o}$	1 (3)	3 (16)	41.2420	17.1260	9.606E-09	1.50E+04
${\rm 2p^4}$	${\rm -~2s2p^23p}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (3)	3 (18)	41.2420	15.7840	4.387E-04	7.61E+08
${\rm 2p^4}$	${\rm -~2s2p^23p}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (3)	3 (20)	41.2420	15.5810	5.815E-04	1.03E+09
${\rm 2p^4}$	${\rm -~2s2p^23p}$	${\rm ^3P^e}$	${\rm ^3S^o}$	1 (3)	3 (21)	41.2420	15.5630	1.354E-02	2.39E+10
${\rm 2p^4}$	${\rm -~2s^22p4s}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (3)	3 (30)	41.2420	11.5800	3.678E-07	8.66E+05
${\rm 2p^4}$	${\rm -~2s^22p4s}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (3)	3 (31)	41.2420	11.8260	1.251E-05	2.90E+07
${\rm 2p^4}$	${\rm -~2s^22p4d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (3)	3 (43)	41.2420	10.5650	1.511E-02	3.81E+10
${\rm 2p^4}$	${\rm -~2s^22p4d}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (3)	3 (45)	41.2420	10.7740	4.366E-04	1.09E+09
${\rm 2s^22p^2}$	${\rm -~2s2p^3}$	${\rm ^3P^e}$	${\rm ^3P^o}$	3 (1)	1 (1)	50.2430	45.8170	2.071E-02	9.78E+09
${\rm 2s2p^3}$	${\rm -~2p^4}$	${\rm ^3P^o}$	${\rm ^3P^e}$	1 (1)	3 (2)	45.8170	41.2860	4.223E-02	2.32E+09
${\rm 2s^22p^2}$	${\rm -~2s^22p3s}$	${\rm ^3P^e}$	${\rm ^3P^o}$	3 (1)	1 (2)	50.2430	21.7220	1.874E-02	3.67E+11
${\rm 2p^4}$	${\rm -~2s^22p3s}$	${\rm ^3P^e}$	${\rm ^3P^o}$	3 (2)	1 (2)	41.2860	21.7220	7.065E-07	6.52E+06

 

Table 7: b. Fine structure transitions of Ar XIII are ordered in LS multiplets and are compared with previous values. Notation $a\pm b$ means $a\times 10^b$, "O'' means for others and "P'' for present. The last line of a set of dipole allowed transitions corresponds to the LS multiplet

Ci	Cj	$S_iL_i\pi_i$	$S_jL_j\pi_j$	gi(Ii)	gj(Ij)	fij(O)	fij(P)	$A_{ji}({\rm s}^{-1},O)$	$A_{ji}({\rm s}^{-1},P)$
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3D1}$	1(1)	3(1)	8.267-21	7.370-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3D1}$	3(1)	3(1)	1.163-21	1.078-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3D1}$	3(1)	5(2)	5.865-21	5.352-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3D1}$	5(1)	3(2)	1.487-41	9.623-6
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3D1}$	5(1)	5(2)	3.399-31	2.623-3
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3D1}$	5(1)	7(1)	5.037-21	4.507-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3D1}$	9	15	5.33-22	5.209-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3P1}$	1(1)	3(2)	5.750-21
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3P1}$	3(1)	1(1)	2.347-21	2.071-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3P1}$	3(1)	3(2)	2.642-21	1.574-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3P1}$	3(1)	5(3)	1.622-21	1.318-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3P1}$	5(1)	3(2)	1.421-21	1.947-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3P1}$	5(1)	5(3)	5.865-21	5.271-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3P1}$	9	9	5.96-22	6.096-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3S1}$	1(1)	3(3)	7.053-21	7.773-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3S1}$	3(1)	3(3)	7.163-21	7.544-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3S1}$	5(1)	3(3)	8.013-21	6.635-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^3S1}$	9	3	7.0-22	7.060-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^1P1}$	1(1)	3(4)	7.251-61	8.405-3
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^1P1}$	3(1)	3(4)	1.690-31	3.256-3
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^1P1}$	5(1)	3(4)	6.231-61	5.59E-6
${\rm 2s22p2}$	${\rm -2S2p3}$	${\rm ^1S0}$	${\rm ^3D1}$	1(2)	3(1)	3.263-41	2.257-4
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1S0}$	${\rm ^3P1}$	1(2)	3(2)	7.137-41	4.438-4
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1S0}$	${\rm ^3S1}$	1(2)	3(3)	9.600-41	8.290-3
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1S0}$	${\rm ^1P1}$	1(2)	3(4)	1.514-11,1.35-12	1.314-1
${\rm 2s22p2}$	${\rm -2s22p3s}$	${\rm ^3P0}$	${\rm ^3P1}$	1(1)	3(5)	4.966-21	5.665-2
${\rm 2s22p2}$	${\rm -2s22p3s}$	${\rm ^3P0}$	${\rm ^3P1}$	3(1)	1(2)	1.734-21	1.874-2
${\rm 2s22p2}$	${\rm -2s22p3s}$	${\rm ^3P0}$	${\rm ^3P1}$	3(1)	3(5)	1.157-21	1.431-2
${\rm 2s22p2}$	${\rm -2s22p3s}$	${\rm ^3P0}$	${\rm ^3P1}$	3(1)	5(5)	2.194-21	2.357-2
${\rm 2s22p2}$	${\rm -2s22p3s}$	${\rm ^3P0}$	${\rm ^3P1}$	5(1)	3(5)	1.388-21	1.110-2
${\rm 2s22p2}$	${\rm -2s22p3s}$	${\rm ^3P0}$	${\rm ^3P1}$	5(1)	5(5)	3.843-21	4.274-2
${\rm 2s22p2}$	${\rm -2s22p3s}$	${\rm ^3P0}$	${\rm ^3P1}$	9	9	6.07-22	5.507-2
${\rm 2S2p3}$	${\rm -2p4}$	${\rm ^3D1}$	${\rm ^3P0}$	3(1)	1(3)	3.817-21	3.321-2
${\rm 2S2p3}$	${\rm -2p4}$	${\rm ^3D1}$	${\rm ^3P0}$	3(1)	3(2)	3.765-21	3.720-2
${\rm 2S2p3}$	${\rm -2p4}$	${\rm ^3D1}$	${\rm ^3P0}$	3(1)	5(3)	4.857-31	3.430-3
${\rm 2S2p3}$	${\rm -2p4}$	${\rm ^3D1}$	${\rm ^3P0}$	15	9	6.867-22	1.452-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3S1}$	${\rm ^3P0}$	3(3)	1(3)	7.175-21	1.657-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3S1}$	${\rm ^3P0}$	3(3)	3(2)	6.660-21	5.504-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3S1}$	${\rm ^3P0}$	3(3)	5(3)	5.916-21	9.966-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3S1}$	${\rm ^3P0}$	3	9	1.58-12	1.716-1
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^1P1}$	${\rm ^3P0}$	3(4)	1(3)	8.069-51	1.568-3
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^1P1}$	${\rm ^3P0}$	3(4)	3(2)	1.103-31	1.809-3
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^1P1}$	${\rm ^3P0}$	3(4)	5(3)	-3.784-41	4.007-4
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^5S1}$	3(1)	5(1)		3.752-5	7.28+53	7.01+5
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^3P0}$	${\rm ^5S1}$	5(1)	5(1)		4.810-5	1.35+63	1.34+6
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1D0}$	${\rm ^5S1}$	5(2)	5(1)		4.730-7	7.15+33	6.26+3

1  Zhang & Sampson (1997), 2 Luo & Pradhan (1989), 3 Mendoza et al. (1999).

 

Table 8: a. Sample set of reprocessed f- and A-values for Fe XXI using observed transition energies. The negative sign for the energies is omitted for convenience. I_i and I_j are the level indices

Ci	Cj	$S_iL_i\pi_i$	$S_jL_j\pi_j$	gi(Ii)	gj(Ij)	$E_i({\rm Ry})$	$E_j({\rm Ry})$	f	$A_{ji}({\rm s}^{-1})$
${\rm 2s^22p2}$	${\rm -2s2p^3}$	${\rm ^3P^e}$	${\rm ^3D^o}$	1 (1)	3 (1)	124.1100	117.0400	8.491E-02	1.14E+10
${\rm 2s^22p^2}$	${\rm -2s2p^3}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (1)	3 (2)	124.1100	115.6900	2.252E-02	4.27E+09
${\rm 2s^22p^2}$	${\rm -2s2p^3}$	${\rm ^3P^e}$	${\rm ^3S^o}$	1 (1)	3 (3)	124.1100	114.1300	3.579E-02	9.55E+09
${\rm 2s^22p^2}$	${\rm -2s2p^3}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (1)	3 (4)	124.1100	112.6200	1.028E-04	3.63E+07
${\rm 2s^22p^2}$	${\rm - 2s^22p3d}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (1)	3 (11)	124.1100	48.5350	2.771E-02	4.24E+11
${\rm 2s^22p^2}$	${\rm - 2s^22p4d}$	${\rm ^3P^e}$	${\rm ^3D^o}$	1 (1)	3 (39)	124.1100	27.6930	1.027E-01	2.56E+12
${\rm 2s^22p^2}$	${\rm - 2s^22p4d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (1)	3 (40)	124.1100	26.7180	1.376E-01	3.49E+12
${\rm 2s^22p^2}$	${\rm - 2s^22p5d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (1)	3 (67)	124.1100	16.4940	5.546E-02	1.72E+12
${\rm 2s^22p^2}$	${\rm -2s2p^3}$	${\rm ^1S^e}$	${\rm ^3D^o}$	1 (2)	3 (1)	120.7300	117.0400	1.066E-03	3.88E+07
${\rm 2s^22p^2}$	${\rm -2s2p^3}$	${\rm ^1S^e}$	${\rm ^3P^o}$	1 (2)	3 (2)	120.7300	115.6900	2.208E-03	1.50E+08
${\rm 2s^22p^2}$	${\rm -2s2p^3}$	${\rm ^1S^e}$	${\rm ^3S^o}$	1 (2)	3 (3)	120.7300	114.1300	5.568E-03	6.49E+08
${\rm 2s^22p^2}$	${\rm -2s2p^3}$	${\rm ^1S^e}$	${\rm ^1P^o}$	1 (2)	3 (4)	120.7300	112.6200	9.789E-02	1.72E+10
${\rm 2s^22p^2}$	${\rm - 2s^22p3d}$	${\rm ^1S^e}$	${\rm ^1P^o}$	1 (2)	3 (11)	120.7300	48.5350	1.276E+00	1.78E+13
${\rm 2s^22p^2}$	${\rm - 2s^22p4d}$	${\rm ^1S^e}$	${\rm ^3D^o}$	1 (2)	3 (39)	120.7300	27.6930	2.722E-02	6.31E+11
${\rm 2s^22p^2}$	${\rm - 2s^22p4d}$	${\rm ^1S^e}$	${\rm ^3P^o}$	1 (2)	3 (40)	120.7300	26.7180	1.458E-03	3.45E+10
${\rm 2s^22p^2}$	${\rm - 2s^22p5d}$	${\rm ^1S^e}$	${\rm ^3P^o}$	1 (2)	3 (67)	120.7300	16.4940	1.678E-03	4.88E+10
${\rm 2s2p^3}$	${\rm - 2p^4}$	${\rm ^3D^o}$	${\rm ^3P^e}$	3 (1)	1 (3)	117.0400	108.3000	1.911E-02	3.52E+10
${\rm 2s2p^3}$	${\rm - 2p^4}$	${\rm ^3P^o}$	${\rm ^3P^e}$	3 (2)	1 (3)	115.6900	108.3000	1.379E-02	1.81E+10
${\rm 2s2p^3}$	${\rm - 2p^4}$	${\rm ^3S^o}$	${\rm ^3P^e}$	3 (3)	1 (3)	114.1300	108.3000	2.095E-02	1.72E+10
${\rm 2s2p^3}$	${\rm - 2p^4}$	${\rm ^1P^o}$	${\rm ^3P^e}$	3 (4)	1 (3)	112.6200	108.3000	3.176E-05	1.43E+07
${\rm 2p^4}$	${\rm - 2s^22p3d}$	${\rm ^3P^e}$	${\rm ^1P^o}$	1 (3)	3 (11)	108.3000	48.5350	1.067E-06	1.02E+07
${\rm 2p^4}$	${\rm -~2s^22p4d}$	${\rm ^3P^e}$	${\rm ^3D^o}$	1 (3)	3 (39)	108.3000	27.6930	2.334E-05	4.06E+08
${\rm 2p^4}$	${\rm -~2s^22p4d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (3)	3 (40)	108.3000	26.7180	1.608E-04	2.87E+09
${\rm 2p^4}$	${\rm - 2s^22p5d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	1 (3)	3 (67)	108.3000	16.4940	5.095E-04	1.15E+10
${\rm 2s2p^3}$	${\rm -~2p^4}$	${\rm ^3D^o}$	${\rm ^1S^e}$	3 (1)	1 (4)	117.0400	105.4500	8.736E-05	2.83E+08
${\rm 2s2p^3}$	${\rm - 2p^4}$	${\rm ^3P^o}$	${\rm ^1S^e}$	3 (2)	1 (4)	115.6900	105.4500	1.739E-03	4.39E+09
${\rm 2s2p^3}$	${\rm - 2p^4}$	${\rm ^3S^o}$	${\rm ^1S^e}$	3 (3)	1 (4)	114.1300	105.4500	2.770E-03	5.03E+09
${\rm 2s2p^3}$	${\rm - 2p^4}$	${\rm ^1P^o}$	${\rm ^1S^e}$	3 (4)	1 (4)	112.6200	105.4500	6.055E-02	7.50E+10
${\rm 2p^4}$	${\rm - 2s^22p3d}$	${\rm ^1S^e}$	${\rm ^1P^o}$	1 (4)	3 (11)	105.4500	48.5350	8.194E-05	7.11E+08
${\rm 2p^4}$	${\rm - 2s^22p4d}$	${\rm ^1S^e}$	${\rm ^3D^o}$	1 (4)	3 (39)	105.4500	27.6930	7.892E-06	1.28E+08
${\rm 2p^4}$	${\rm -~2s^22p4d}$	${\rm ^1S^e}$	${\rm ^3P^o}$	1 (4)	3 (40)	105.4500	26.7180	1.302E-05	2.16E+08
${\rm 2p^4}$	${\rm - 2s^22p5d}$	${\rm ^1S^e}$	${\rm ^3P^o}$	1 (4)	3 (67)	105.4500	16.4940	3.718E-08	7.88E+05
${\rm 2s^22p^2}$	${\rm -2s2p^3}$	${\rm ^3P^e}$	${\rm ^3P^o}$	3 (1)	1 (1)	123.4400	115.7600	1.537E-02	2.18E+10
${\rm 2s2p^3}$	${\rm - 2p^4}$	${\rm ^3P^o}$	${\rm ^3P^e}$	1 (1)	3 (2)	115.7600	108.2500	3.117E-02	4.71E+09
${\rm 2s^22p^2}$	${\rm -2s2p^3}$	${\rm ^3P^e}$	${\rm ^3D^o}$	3 (1)	3 (1)	123.4400	117.0400	2.453E-03	8.07E+08
${\rm 2s^22p^2}$	${\rm -2s2p^3}$	${\rm ^3P^e}$	${\rm ^3P^o}$	3 (1)	3 (2)	123.4400	115.6900	3.234E-02	1.56E+10
${\rm 2s^22p^2}$	${\rm -2s2p^3}$	${\rm ^3P^e}$	${\rm ^3S^o}$	3 (1)	3 (3)	123.4400	114.1300	3.671E-02	2.56E+10
${\rm 2s^22p^2}$	${\rm -2s2p^3}$	${\rm ^3P^e}$	${\rm ^1P^o}$	3 (1)	3 (4)	123.4400	112.6200	5.291E-03	4.98E+09
${\rm 2s^22p^2}$	${\rm - 2s^22p3d}$	${\rm ^3P^e}$	${\rm ^1P^o}$	3 (1)	3 (11)	123.4400	48.5350	6.550E-03	2.95E+11
${\rm 2s^22p^2}$	${\rm - 2s^22p4d}$	${\rm ^3P^e}$	${\rm ^3D^o}$	3 (1)	3 (39)	123.4400	27.6930	4.825E-02	3.55E+12
${\rm 2s^22p^2}$	${\rm - 2s^22p4d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	3 (1)	3 (40)	123.4400	26.7180	2.762E-03	2.08E+11
${\rm 2s^22p^2}$	${\rm - 2s^22p5d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	3 (1)	3 (67)	123.4400	16.4940	4.713E-04	4.33E+10
${\rm 2s2p^3}$	${\rm - 2p^4}$	${\rm ^3D^o}$	${\rm ^3P^e}$	3 (1)	3 (2)	117.0400	108.2500	2.322E-02	1.44E+10
${\rm 2s2p^3}$	${\rm - 2p^4}$	${\rm ^3P^o}$	${\rm ^3P^e}$	3 (2)	3 (2)	115.6900	108.2500	1.921E-04	8.54E+07
${\rm 2s2p^3}$	${\rm - 2p^4}$	${\rm ^3S^o}$	${\rm ^3P^e}$	3 (3)	3 (2)	114.1300	108.2500	4.638E-02	1.29E+10
${\rm 2s2p^3}$	${\rm -~2p^4}$	${\rm ^1P^o}$	${\rm ^3P^e}$	3 (4)	3 (2)	112.6200	108.2500	4.176E-03	6.41E+08
${\rm 2p^4}$	${\rm - 2s^22p3d}$	${\rm ^3P^e}$	${\rm ^1P^o}$	3 (2)	3 (11)	108.2500	48.5350	5.993E-06	1.72E+08
${\rm 2p^4}$	${\rm -2s^2.2p.4d}$	${\rm ^3P^e}$	${\rm ^3D^o}$	3 (2)	3 (39)	108.2500	27.6930	5.489E-06	2.86E+08
${\rm 2p^4}$	${\rm -2s^2.2p.4d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	3 (2)	3 (40)	108.2500	26.7180	2.160E-06	1.15E+08
${\rm 2p^4}$	${\rm -2s^2.2p.5d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	3 (2)	3 (67)	108.2500	16.4940	1.847E-04	1.25E+10
${\rm 2s^2.2p2}$	${\rm -2s^.2p3}$	${\rm ^3P^e}$	${\rm ^5S^o}$	3 (1)	5 (1)	123.4400	119.6800	5.155E-04	3.51E+07
${\rm 2s^2.2p2}$	${\rm -2s^.2p3}$	${\rm ^3P^e}$	${\rm ^3D^o}$	3 (1)	5 (2)	123.4400	117.0300	4.621E-02	9.15E+09
${\rm 2s^2.2p2}$	${\rm -2s^.2p3}$	${\rm ^3P^e}$	${\rm ^3P^o}$	3 (1)	5 (3)	123.4400	115.5300	1.379E-03	4.16E+08
${\rm 2s^2.2p2}$	${\rm -2s^.2p3}$	${\rm ^3P^e}$	${\rm ^1D^o}$	3 (1)	5 (4)	123.4400	113.8500	9.379E-04	4.16E+08
${\rm 2s^2.2p2}$	${\rm -2s^2.2p.3d}$	${\rm ^3P^e}$	${\rm ^1D^o}$	3 (1)	5 (6)	123.4400	50.3200	4.192E-05	1.08E+09
${\rm 2s^2.2p2}$	${\rm -2s^2.2p.3d}$	${\rm ^3P^e}$	${\rm ^3D^o}$	3 (1)	5 (8)	123.4400	49.5060	8.502E-01	2.24E+13
${\rm 2s^2.2p2}$	${\rm -2s^2.2p.3d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	3 (1)	5 (9)	123.4400	49.1090	6.579E-03	1.75E+11
${\rm 2s^2.2p2}$	${\rm -2s^2.2p.4d}$	${\rm ^3P^e}$	${\rm ^3P^o}$	3 (1)	5 (39)	123.4400	27.7030	1.682E-02	7.43E+11
${\rm 2s^2.2p2}$	${\rm -2s^2.2p.4d}$	${\rm ^3P^e}$	${\rm ^1D^o}$	3 (1)	5 (40)	123.4400	26.8370	6.750E-02	3.04E+12
${\rm 2s^2.2p2}$	${\rm -2s^2.2p.4d}$	${\rm ^3P^e}$	${\rm ^3D^o}$	3 (1)	5 (41)	123.4400	27.0190	7.369E-02	3.30E+12
${\rm 2s^2.2p2}$	${\rm -2s^2.2p.5d}$	${\rm ^3P^e}$	${\rm ^1D^o}$	3 (1)	5 (72)	123.4400	16.4940	1.839E-02	1.01E+12
${\rm 2s^.2p3}$	${\rm - 2p^4}$	${\rm ^5S^o}$	${\rm ^3P^e}$	5 (1)	3 (2)	119.6800	108.2500	1.586E-04	2.77E+08
${\rm 2s^.2p3}$	${\rm - 2p^4}$	${\rm ^3D^o}$	${\rm ^3P^e}$	5 (2)	3 (2)	117.0300	108.2500	2.093E-02	2.16E+10
${\rm 2s^.2p3}$	${\rm -~2p^4}$	${\rm ^3P^o}$	${\rm ^3P^e}$	5 (3)	3 (2)	115.5300	108.2500	2.219E-02	1.57E+10

 

Table 8: b. Fine structure transitions of Ar XIII are ordered in LS multiplets and are compared with previous values. Notation $a\pm b$ means $a\times 10^b$, "O'' means for others and "P'' for present. The last line of a set of dipole allowed transitions corresponds to the LS multiplet

Ci	Cj	$S_iL_i\pi_i$	$S_jL_j\pi_j$	gi(Ii)	gj(Ij)	fij(O)	fij(P)	$A_{ji}({\rm s}^{-1},O)$	$A_{ji}({\rm s}^{-1},P)$
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3D1}$	1 (1)	3 (1)	9.3-21	8.49-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3D1}$	3 (1)	3 (1)	2.4-31	2.45-3
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3D1}$	3 (1)	5 (2)	5.1-21	4.62-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3D1}$	5 (1)	3 (1)	1.5-41	5.02-3
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3D1}$	5 (1)	5 (2)	4.4-51	7.64-6
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3D1}$	5 (1)	7 (1)	2.95-21	2.70-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3D1}$	9	15	4.5-21,3.71-22	4.20-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3P1}$	1 (1)	3 (2)	2.25-21	2.25-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3P1}$	3 (1)	1 (1)	1.70-21	1.54-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3P1}$	3 (1)	3 (2)	3.54-21	3.23-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3P1}$	3 (1)	5 (3)	1.2-31	1.38-3
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3P1}$	5 (1)	3 (2)	4.4-31	1.13-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3P1}$	5 (1)	5 (3)	4.79-21	4.46-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3P1}$	9	9	4.98-21,4.09-22	5.03-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3S1}$	1 (1)	3 (3)	3.70-21	3.58-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3S1}$	3 (1)	3 (3)	3.79-21	3.67-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3S1}$	5 (1)	3 (3)	6.0-21	4.01-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^3S1}$	9	3	5.1-21,4.68-22	3.86-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^1D1}$	3 (1)	5(4)	9.5-41	9.38-4
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^1D1}$	5 (1)	5(4)	1.3-21	1.20-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^1P1}$	1 (1)	3 (4)		1.03-4
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^1P1}$	3 (1)	3 (4)	5.6-31	5.29-3
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^1P1}$	5 (1)	3 (4)	1.6-41	8.45-4
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1D0}$	${\rm ^3D1}$	5 (2)	3 (1)	6.4-41	2.96-5
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1D0}$	${\rm ^3D1}$	5 (2)	5 (2)	2.0-41	2.27-4
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1D0}$	${\rm ^3D1}$	5 (2)	7 (1)	7.0-31	6.59-3
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1D0}$	${\rm ^1P1}$	5(2)	3(4)	6.2-21,5.36-22	5.30-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1D0}$	${\rm ^1D1}$	5	5	9.2-21,9.14-22	8.56-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1S0}$	${\rm ^1P1}$	1 (2)	3 (4)	1.04-12	9.79-2
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1S0}$	${\rm ^3D1}$	1 (2)	3 (1)	1.5-31	1.07-3
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1S0}$	${\rm ^3P1}$	1 (2)	3 (2)	2.4-31	2.21-3
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1S0}$	${\rm ^3S1}$	1 (2)	3 (3)	5.9-31	5.57-3
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3P1}$	${\rm ^1D0}$	3 (2)	5(4)	4.1-31	7.81-5
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3P1}$	${\rm ^1D0}$	5 (3)	5(4)	4.9-31	4.79-3
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3D1}$	${\rm ^1D0}$	5 (2)	5 (4)	1.0-31	1.08-3
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3D1}$	${\rm ^1D0}$	7 (1)	5 (4)	6.2-31	5.96-3
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3S1}$	${\rm ^3P0}$	3(3)	1(3)	2.35-21	2.10-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3S1}$	${\rm ^3P0}$	3(3)	3(2)	5.2-21	4.64-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3S1}$	${\rm ^3P0}$	3(3)	5(3)	5.6-21	6.60-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3S1}$	${\rm ^3P0}$	3	9	0.131,0.1122	0.133
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3P1}$	${\rm ^3P0}$	3(2)	1(3)	1.55-21	1.38-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3P1}$	${\rm ^3P0}$	1(1)	3(2)	3.41-21	3.12-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3P1}$	${\rm ^3P0}$	3(2)	3(2)	3.4-41	1.92-4
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3P1}$	${\rm ^3P0}$	5(3)	3(2)	2.50-21	2.22-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3P1}$	${\rm ^3P0}$	3(2)	5(3)	1.84-21	2.68-3
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3P1}$	${\rm ^3P0}$	5(3)	5(3)	1.11-21	1.12-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^3P1}$	${\rm ^3P0}$	9	9	3.6-21,2.62-22	2.70-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm 3D1}$	${\rm ^3P0}$	3 (1)	1(3)	2.03-21	1.91-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm 3D1}$	${\rm ^3P0}$	3 (1)	3 (2)	2.52-21	2.32-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm 3D1}$	${\rm ^3P0}$	5 (2)	3 (2)	2.20-21	2.09-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm 3D1}$	${\rm ^3P0}$	3 (1)	5 (3)	1.25-21	8.03-4
${\rm 2s2p3}$	${\rm -2p4}$	${\rm 3D1}$	${\rm ^3P0}$	5 (2)	5 (3)	2.92-21	2.62-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm 3D1}$	${\rm ^3P0}$	7 (1)	5 (3)	4.67-21	4.23-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm 3D1}$	${\rm ^3P0}$	15	9	5.1-21,4.69-22	4.43-2
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^1P1}$	${\rm ^3P0}$	3(4)	1(3)		3.18-5
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^1P1}$	${\rm ^3P0}$	3(4)	3(2)	4.8-31	4.18-3
${\rm 2s2p3}$	${\rm -2p4}$	${\rm ^1P1}$	${\rm ^3P0}$	3(4)	5(3)	1.9-31	2.31-3
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^5S1}$	3 (1)	5 (1)	5.3-41	5.155-4	3.61+73	3.51+7
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm 3P0}$	${\rm ^5S1}$	5 (1)	5 (1)	3.8-41	3.72-4	3.27+73	3.39+7
${\rm 2s22p2}$	${\rm -2s2p3}$	${\rm ^1D0}$	${\rm ^5S1}$	5	2		3.53-5	1.46+63	1.38+6

1  Cheng et al. (1979), 2 Luo & Pradhan (1989), 3 Mendoza et al. (1999).

Transitions are listed in $J\pi$ order, and in contrast to the large complete files (Tables 5 and 6) they are given with complete identification. The level index, I_i, for each energy level in the tables is given next to the J-value for an easy access to the complete f-file. For example, the transition $J=0^{\rm e}(I_i=1)\rightarrow J=1^{\circ}(I_j=1)$ in Table 7a corresponds to the first transition in Table 5, and hence, the f- and A-values of Table 7a should replace those in Table 5. The overall replacement in Tables 5 or 6 (as may be needed in a model calculation requring large number of transitions) can be carried out by sorting out the reprocessed transitions through their energy level indices. The set of level indices of each symmetry $J\pi$ for both Ar XIII and Fe XXI that correspond to these transitions are given in Table 9.

 

Table 9: Level indices of the calculated fine structure energy levels for various $J\pi$ symmetries that have been observed and among which the allowed transitions have been reprocessed using the observed energies. n_j is the number of observed levels in each symmetry

$J\pi$	nj	level indices
Ar XIII
$0^{\rm e}$	3	1,2,3
$0^{\rm o}$	6	1,2,3,8,12,18
$1^{\rm e}$	2	1,2
$1^{\rm o}$	17	1,2,3,4,5,6,7,8,9,16,18,20,21,30,31,43,45
$2^{\rm e}$	5	1,2,3,4,14
$2^{\rm o}$	15	1,2,3,4,5,6,7,8,9,15,16,19,29,44,46
$3^{\rm e}$	1	6
$3^{\rm o}$	5	1,2,3,4,8
$4^{\rm o}$	1	1
Fe XXI
$0^{\rm e}$	4	1,2,3,4
$0^{\rm o}$	1	1
$1^{\rm e}$	2	1,2
$1^{\rm o}$	8	1,2,3,4,11,39,40,67
$2^{\rm e}$	4	1,2,3,4
$2^{\rm o}$	11	1,2,3,4,6,8,9,39,40,41,72
$3^{\rm o}$	9	1,2,3,4,22,23,24,50,51

The reprocessed transitions are further ordered in terms of their configurations and LS terms. This enables one to obtain the f-values for the LS multiplets and check the completeness of the set of fine structure components belonging to the multiplet. However, the completeness depends also on the observed set of fine structure levels since the transitions correspond only to the observed levels. The LS multiplets are useful for various comparisons with other calculations and experiment where fine structure transitions can not be resolved. A partial set of these transitions is presented in Table 7b for Ar XIII and Table 8b for Fe XXI (the complete table is available electronically).

The oscillator strengths are compared with other calculations in Tables 7b for Ar XIII and 8b for Fe XXI. The oscillator strengths for a large number of fine structure transitions in Ar XIII and other carbon like ions have been obtained by Zhang & Sampson (1997) in the relativistic distorted wave calculations. They consider the transitions among the n = 2 and n = 3 levels. The other source of transition probabilities for Ar XIII is TOPbase (the database for the Opacity Project data) where transition probabilties for LS multiplets are given for states with $n \leq 10$. These values were calculated by Luo & Pradhan (1989) in the close coupling approximation using non-relativistic R-matrix method. Comparison of the present BPRM oscillator strengths with the previous calculations in Table 7b shows that present LS multiplets obtained from the fine structure components agree quite well with those of Luo and Pradhan except for the transition, ${\rm 2s2p^3(^3D^o)~-~2p^4(^3P)}$. However, comparison with Zhang and Sampson shows various degrees of agreement. There is good agreement for some fine structure components compared to others in the same LS multiplet, e.g. for ${\rm 2s^22p^2(^3P)~-~2s2p^3(^3D^o)}$. The largest difference is found in the weak transitions.

The f-values of Fe XXI have been compiled by Fuhr et al. (1988) and Shirai et al. (1990) (both references present the same values). They report mainly the multiconfiguration Dirac-Fock calculations by Cheng et al. (1979). The other source of large amount of data in LS coupling is from TOPbase (Cunto et al. 1993) calculated by Luo & Pradhan (1989) under the Opacity Project. Similar to the above case of Ar XIII, the Fe XXI oscillator strengths compare well for some but poorly for other fine structure components within a multiplet of previous calculations (Table 8b). For example, most of the fine structure components of the dipole allowed multiplets, ${\rm 2s^22p^2(^3P)~-~2s2p^3(^3D^o,^3P^o,^3S^o)}$, have comparable values from the two calculations, BPRM and Dirac-Fock, except for the weak transitions. While BPRM f-values agree well with those by Cheng et al. for the intercombination transitions, 5-5 and 5-7 of ${\rm 2s^22p^2(^1D)~-~2s2p^3(^3D^o)}$, they differ considerably for the transition 5-3. The LS multiplets are compared with those of Luo & Pradhan (1989) and in general agree very well with the present BPRM A-values.

Recently Mendoza et al. (1999) have calculated the transition probabilties for the intercombination transitions ${\rm 2s2p^3(^5S^o_2)~-~2s^22p^2(^3P_{1,2},^1D_2)}$ for the carbon isoelectronic sequence ions. Through extensive relativistic atomic structure calculations they study the effects of Breit interaction in the transition probabilties for these weak transitions. They estimate an accuracy better than 10% for A-values belonging to the ground levels $^3{\rm P_{1,2}}$ and 20% for the $^1{\rm D_2}$. Their values for Ar XIII agree very well with the present BPRM A-values (Table 7b), especially those to the ground levels; it is 4% for the ⁵S^o₂ - ³P₁and 0.01% for the ${\rm ^5S^o_2~-~^3P_2}$ transitions. The agreement is 14% for the ${\rm ^5S^o_2~-~^1D_2}$ for which they assign a larger uncertainty. For Fe XXI, present f-values for transitions to the ground configuration levels ${\rm 2s2p^3(^5S^o)~-~2s^22p^2(^3P_{1,2}, ^1D_2})$ agree very well with those by Cheng et al. The agreement is also quite good with the A-values obtained in elaborate calculations by Mendoza et al. (1999); about 4% for both the transitions to the ground term, ${\rm ^5S^o_2~-~^3P_{1,2}}$, and 5% for the ${\rm ^5S^o_2~-~^1D_2}$ transition.

Comparison of the present transition probabilities for the intercombination transitions with those of Mendoza et al. (1999) provides a measure of uncertainty of the present BPRM results. They studied the effect of Breit spin-spin and spin-other orbit interactions which are not included in the present work. The good agreement with them for these very weak transtions indicate the uncertainty of the present results to a maximum of 14% for most of the transitions. The discrepancy between the oscillator strengths in length and velocity forms ($f_{\rm L}$ and $f_{\rm V}$) is an indicator of accuracy consistent with the method of calculations. In the present results, it is found that the dispersion of the $f_{\rm L}$ and $f_{\rm V}$ values for Fe XXI is mainly in the very weak transitons. However, the dispersion is larger for Ar XIII; it is expected that the dispersion is caused mainly by the values of $f_{\rm V}$. Inclusion of more configurations in the Ar XIII wavefunction expansion could have improved the agreement; n = 3 configurations are still important and should be included in the target as spectroscopic configurations. However, that is computationally intractable in the BPRM calculations. It may be noted that the length form in a close coupling approximation is more accurate than the velocity form as it depends more on the asymptotic form of the wavefunction which is better represented in the R-matrix calculations.