J/A+AS/147/253 IRON Project. XLV. Ar XIII and Fe XXI (Nahar, 2000)
Atomic data from the Iron Project XLV.
Relativistic transition probabilities for carbon-like Ar XIII and Fe XXI
using Breit-Paili R-matrix method
Nahar S.N.
<Astron. Astrophys. Suppl. Ser. 147, 253 (2000)>
=2000A&AS..147..253N 2000A&AS..147..253N
ADC_Keywords: Atomic physics
Keywords: atomic data
Abstract:
The Breit-Pauli R-matrix method developed under the Iron Project has
been used to obtain extensive sets of oscillator strengths and
transition probabilities for dipole allowed and intercombination fine
structure transitions in carbon like ions, Ar XIII and Fe XXI. The
complete set consists of 1274 fine structure bound energy levels and
198259 oscillator strengths for Ar XIII, and 1611 bound levels and
300079 oscillator strengths for Fe XXI. These correspond to levels of
total angular momenta of 0≤J≤7 of even and odd parities formed from
total spin of 2S+1=5, 3, 1, and orbital angular momenta 0≤L≤9 with
n≤10, 0≤l≤9 for each ion. The relativistic effects are included in
the Breit-Pauli approximation. The close coupling wavefunction
expansion for each ion is represented by the lowest 15 fine structure
levels of target configurations, 2s22p, 2s2p2 and 2p3. The
energy levels are identified spectroscopically using a newly developed
identification procedure. The procedure also makes a correspondence
between the fine structure energy levels and LS terms. This provides
the check for completeness of the calculated levels. Comparison is
made of the present energies and the f-values with the available
observed and theoretical values. Present transition probabilities
agree very well with the relativistic atomic structure calculations of
Mendoza et al. for the intercombination transitions,
2s2p3(5S°2) - 2s22p2(3P1,2,1D2). This further
indicates that the importance of the neglected Breit interaction
decreases with ion charge and constrains the uncertainty in the
present calculations to within 15% even for the weak transitions.
Description:
Corrected atomic datafiles of A&A article:
--------------------------------------------
The transition probabilities for Ar XIII and Fe XXI (Nahar 2000) have
been recomputed. The new files are:
i) ar13.en.fs.user -> fine structure energy levels of Ar XIII
ii) ar13.f.fs.user -> complete table of fine structure transitions in
Ar XIII
iii) ar13.f.exp.user -> table of fine structure transitions in Ar XIII
using observed energies
iv) fe21.en.fs.user -> fine structure energy levels of Fe XXI
v) fe21.f.fs.user -> complete table of fine structure transitions in
Fe XXI
vi) fe21.f.exp.user -> table of fine structure transitions in Fe XXI
using observed energies
A bug was detected in 2007 (Storey & Berrington, 2007, private Iron
Project communications) in calculation of the phase factor of dipole
matrix elements in stage RECUPD of Breit-Pauli R-matrix (BPRM) suite
of codes of the Iron Project (Berrington et al., 1995, Comput. Phys.
Commun. 92, 290). The bug affected certain transition probabilities.
The new results on energies and transition probabilities for Ar XIII
and Fe XXI using the corrected code are replacing the earlier results
at CDS.
It should be noted that stage RECUPD in BPRM codes does not exist in
the LS coupling R-matrix code from the Opacity Project (Berrington et
al., 1987, J.Phys.B 20, 6379) and hence does not affect the
non-relativistic results.
Transition probabilities of two ions, Fe XX (Nahar, 2003, Cat.
J/A+A/413/779) and Fe XVIII (Nahar, S.N., 2006, Cat.
J/A+A/457/721) from BPRM approximation are also being recomputed and
will replace the earlier files at CDS.
Results for other ions, obtained using BPRM codes, did not indicate
the bug effect when compared with existing results. However, the plan
is to repeat the calculations for these ions and replace the earlier
results.
File Summary:
--------------------------------------------------------------------------------
FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
table2a.dat 68 1283 Ar XIII identified fine structure energy levels,
ordered in Jπ
table2b.dat 96 1827 Ar XIII identified fine structure energy levels,
ordered in energy and grouped as LS terms
table3a.dat 68 1628 Fe XXI identified fine structure energy levels,
ordered in Jπ
table3b.dat 93 2266 Fe XXI identified fine structure energy levels,
ordered in energy and grouped as LS terms
table5a.dat 79 1283 Ar XIII table of fine structure levels
table5b.dat 76 191912 Ar XIII complete table of transition probabilities
table6a.dat 79 1628 Fe XXI table of fine structure levels XXI
table6b.dat 76 301964 Fe XXI complete table of transition probabilities
table7b.dat 80 211 Ar XIII oscillator strengths ordered in energy and
grouped according to components of same
LS multiplets
table8b.dat 80 199 Fe XXI oscillator strengths ordered in energy and
grouped according to components of same
LS multiplets
ar13.dat 86 191889 *Transitions for Ar XIII
fe21.dat 86 301941 *Transitions for FeXXI
ar13/* . 3 Original files for Ar XIII
fe21/* . 3 Original files for Fe XXI
--------------------------------------------------------------------------------
Note on ar13.dat, fe21.dat, table5b.dat, table6b.dat:
ar13.dat is the tabular equivalent of table5b.dat, and
fe21.dat is the tabular equivalent of table6b.dat.
--------------------------------------------------------------------------------
Description of file: table2b.dat, table3b.dat
Total number of levels processed= 1274 for table2b.dat,
1611 for table3b.dat
Nlv=Number of levels expected
Nlv(c)=Number of levels obtained
Nlv=Nlv(c) -> set complete
For Equivalent electron levels:
(i) no EQN (effective qn)
(ii) no check of set completeness
First lines (table2b.dat):
Configuration J E(Ry) EQN LS terms
Eqv electron/unidentified levels, parity: e
2s22p2 0 -5.04465E+01 3 P e
2s22p2 1 -5.03578E+01 3 P e
2s22p2 2 -5.02417E+01 3 P e
Nlv(c)= 3 : set complete
Eqv electron/unidentified levels, parity: e
2s22p2 2 -4.96510E+01 1 D e
Nlv(c)= 1 : set complete
Eqv electron/unidentified levels, parity: e
Description of file: table5b.dat, table6b.dat
First line - The two numbers in the table are the nuclear charge
(Z = 18 for Ar XIII and Z = 26 for Fe XXI)
and the number of electrons (N_{elc} = 6) in the ion, Ar XIII or Fe XXI.
Below the above line, sets of transitions of a pair of symmetries
Jπ - J'π' are given.
For each set, the first line contains the 7 values:
2Ji, parity π (=0 for even and =1 for odd),
2Jk and πk, the symmetries of transitions, followed by
N{Ji} and N{Jk}, the number of bound levels for the two symmetries,
followed by N{Ji} x N{Jk} number of transitions.
For each transition the first two columns are the level indices, Ii
and Ik for the energies.
The third and the fourth columns are the energies, Ei and Ek.
The fifth column is gfL where g=2J+1 (J is the total angular momentum
of the lower level).
The sixth column is S (line strength).
The last column is the transition probability, A_{ki}(sec-1).
If a gf-value is negative the lower level is i (absorption) and if it is
positive, the lower level is k (emission). The identification of the
transition can be determined from the levels of indices Ii and Ik
in Table 5a and Table 6a respectively.
First lines (table5b.dat):
18 6 : Z, Number of electrons
i j wl(A) Ei(Ry) Ej(Ry) fL S Aji(s-1)
1 0 3 1 55 131 7205 : gi Pi gf Pf Ni Nf NN
1 1 236.32 -5.0332E+01 -4.6476E+01 -7.293E-02 5.674E-02 2.904E+09
1 2 201.70 -5.0332E+01 -4.5814E+01 -5.219E-02 3.465E-02 2.852E+09
1 3 159.09 -5.0332E+01 -4.4604E+01 -6.538E-02 3.424E-02 5.743E+09
1 4 143.15 -5.0332E+01 -4.3966E+01 -2.069E-05 9.751E-06 2.246E+06
1 5 31.93 -5.0332E+01 -2.1796E+01 -5.839E-02 6.138E-03 1.273E+11
1 6 31.48 -5.0332E+01 -2.1381E+01 -2.101E-03 2.177E-04 4.713E+09
-------------------------------------------------------------------------------
See also:
J/A+AS/103/273 : IRON Project II IR collision strengths of C-like ions
J/A+A/283/319 : IRON Project III B-like ions
J/A+AS/108/1 : IRON Project V Collision strengths of O-like ions
J/A+A/293/953 : IRON Project VI Fe II collision strengths
J/A+A/293/967 : IRON Project VII Fe II radiative transitions
J/A+AS/109/193 : IRON Project VIII Electron excitation of Ti-like ions
J/A+AS/119/509 : IRON Project XVII Radiative transition in Fe III
J/A+AS/119/523 : IRON Project XVIII Electron impact for Fe III
J/A+AS/120/361 : IRON Project XIX Fe II radiative transitions
J/A+AS/123/159 : IRON Project XXII C and O radiative rates
J/A+AS/123/575 : IRON Project XXIII Fe XXII excitation rate coefficients
J/A+AS/126/373 : IRON Project XXVII Fe IV collision strengths
J/A+AS/131/499 : IRON Project XXIX Boron isoelectronic sequence
J/A+AS/131/153 : IRON Project XXXI Fe XII electron excitation
J/A+AS/135/347 : IRON Project XXXV Fe XXIV & Fe XXV oscillator strengths
J/A+AS/136/395 : IRON Project XXXVII Fe VI collision strengths
J/A+AS/137/165 : IRON Project XXXVIII Fe XV fine-structure transitions
J/A+AS/143/483 : IRON Project XLII Fe XXI electron impact excitation
J/A+AS/144/141 : IRON Project XLIII Fe V transition probabilities
J/A+AS/147/111 : IRON Project XLIV Fe VI trans. prob. & line ratio
J/A+A/365/268 : IRON Project XLVII Ni III electron impact excitation
J/A+A/372/1078 : IRON Project XLIX Fe XX electron impact excitation
J/A+A/372/1083 : IRON Project L Fe XIX electron impact excitation
J/A+A/394/753 : IRON Project LI Fe IX electron impact excitation
J/A+A/408/789 : IRON Project LIII Fe XVII transition probabilities
J/A+A/413/779 : IRON Project LIV Fe XX transition probabilities
J/A+A/420/763 : IRON Project LV Ni II electron impact excitation
J/A+A/437/345 : IRON Project LIX Fe IV transition probabilities
J/A+A/448/779 : IRON Project LXI Fe IV radiative transitions
J/A+A/457/721 : IRON Project LXII Fe XVIII allowed and forbidden trans.
J/A+A/466/763 : IRON Project LXIII Fe19+ electron impact excitation
Table 1: Target levels of Ar XIV (Fe XXII) in the
eigenfunction expansion of Ar XIII (Fe XXI)
-----------------------------------------------------------------
Config SLp J Ar XIV E(Ry) Fe XXII E(Ry)
-----------------------------------------------------------------
1 2s22p 2Po 1/2 0.00000E+00 0.00000E+00
2 2s22p 2Po 3/2 2.06470E-01 1.07776E+00
3 2s2p2 4Pe 1/2 1.79250E+00 3.68653E+00
4 2s2p2 4Pe 3/2 1.87090E+00 4.19365E+00
5 2s2p2 4Pe 5/2 1.97560E+00 4.67717E+00
6 2s2p2 2De 3/2 3.73870E+00 6.71166E+00
7 2s2p2 2De 5/2 3.74710E+00 6.92217E+00
8 2s2p2 2Se 1/2 4.68780E+00 7.77748E+00
9 2s2p2 2Pe 1/2 4.96850E+00 8.91420E+00
10 2s2p2 2Pe 3/2 5.05440E+00 9.04241E+00
11 2p3 4So 3/2 6.24550E+00 1.14428E+01
12 2p3 2Do 3/2 7.11150E+00 1.27251E+01
13 2p3 2Do 5/2 7.13610E+00 1.30027E+01
14 2p3 2Po 1/2 8.03010E+00 1.43035E+01
15 2p3 2Po 3/2 8.07110E+00 1.48329E+01
-----------------------------------------------------------------
Notes: Ar XIV: Z = 18, No. of core electrons = 5
Fe XXII: Z = 26, No. of core electrons = 5
-----------------------------------------------------------------
Byte-by-byte Description of file: table2a.dat table3a.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 3 I3 --- Nlv Number of levels (1)
5- 6 I2 --- J Total angular momentum of the lower level
8 A1 --- pi [eo] Spin symmetry (even/odd)
13- 15 I3 --- Level Level
17- 32 A16 --- T Target (config SLpi Jt) of the level
34- 36 A3 --- nl Principal and orbital quantum numbers of
the outer electron
39 I1 --- --- Total angular momentum of the lower level
42- 53 E12.5 Ry E Energy
55- 59 F5.2 --- EQN ? Effective Quantum Number (2)
62- 68 A7 --- Terms Possible LS terms of the energy level
--------------------------------------------------------------------------------
Note (1): Number of fine structure levels:
-------------------------------
Ar XIII Fe XXI
J pi Nlv(c) Nlv(c)
-------------------------------
0 0 55 64
0 1 51 60
2 0 128 153
2 1 131 155
4 0 153 187
4 1 150 185
6 0 126 159
6 1 124 159
8 0 89 115
8 1 85 116
10 0 56 75
10 1 50 73
12 0 29 42
12 1 24 41
14 0 15 21
14 1 17 23
-------------------------------
Total 1283 1628
Note (2): No EQN is assigned for Equivalent electron levels
--------------------------------------------------------------------------------
Table 9: Calculated energy level indices for various Jπ
that have been observed
----------------------------------------------------------------------------
Allowed transitions among the following levels have been reprocessed with
observed energies to improve the accuracy:
----------------------------------------------------------------------------
FINE STRUCTURE TRANSITIONS IN Ar XIII
----------------------------------------------------------------------------
J pi nlv levels
----------------------------------------------------------------------------
0 e 3 1,2,3
0 o 6 1,2,3,8,12,18
1 e 2 1,2
1 o 17 1,2,3,4,5,6,7,8,9,16,18,20,21,30,31,43,45
2 e 5 1,2,3,4,14
2 o 15 1,2,3,4,5,6,7,8,9,15,16,19,29,44,46
3 e 1 6
3 o 5 1,2,3,4,8
4 o 1 1
----------------------------------------------------------------------------
FINE STRUCTURE TRANSITIONS IN Fe XXI
----------------------------------------------------------------------------
J pi nlv levels
----------------------------------------------------------------------------
0 e 4 1,2,3,4
0 o 1 1
1 e 2 1,2
1 o 8 1,2,3,4,11,39,40,67
2 e 4 1,2,3,4
2 o 11 1,2,3,4,6,8,9,39,40,41,72
3 o 9 1,2,3,4,22,23,24,50,51
----------------------------------------------------------------------------
Byte-by-byte Description of file: table5a.dat table6a.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
2- 5 I4 --- i i level index
8- 10 F3.1 --- J Total angular momentum
12 A1 --- p [eo] Parity
15- 17 I3 --- iiii Level position for (Jp)
22- 33 E12.7 Ry E(Ry) Energy of level
36- 52 A17 --- Conf Configuration
55- 61 A7 --- LS LS term of energy level (1)
73- 79 I7 --- jjpiiii Energy level id: jjpiiii
--------------------------------------------------------------------------------
Note (1): There may be more than one possible LS term for some j-levels.
Simple assumption: higher L -> lower energy
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table7b.dat table8b.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 12 A12 --- Ci Configurations of the level i (1)
13- 24 A12 --- Cf Configurations of the level j
25- 27 A3 ---- slpi Initial core level
29- 31 A3 --- slpf Final core level
33- 34 I2 --- Ji Lower J-value
36- 37 I2 --- Ni ? Energy level index of lower J-value
39- 40 I2 --- Jf Upper J-value
42- 43 I2 --- Nf ? Energy level index of upper J-value
45- 53 F9.2 Ry Ei ? Initial energy
55- 62 E8.3 Ry Ef Final energy
64- 71 E8.3 --- f f value
73- 80 E8.3 s-1 A A value
--------------------------------------------------------------------------------
Note (1): For table7a.dat and table7b.dat (Ar XIII):
nz = 18, No. of core electrons = 5, No of transitions = 333
For table8a.dat and table8b.dat (Fe XXI):
nz = 26, No. of core electrons = 5, No of transitions = 184
--------------------------------------------------------------------------------
Byte-by-byte Description of file: ar13.dat fe21.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 2 I2 --- gi (2J+1) quantum number of lower state
4 I1 --- pi [0,1] Parity of lower state (0=even, 1=odd)
6- 7 I2 --- gk (2J+1) quantum number of upper state
9 I1 --- pk [0,1] Parity of upper state (0=even, 1=odd)
12- 14 I3 --- Ii Index number of upper state (1)
16- 18 I3 --- Ik Index number of lower state (1)
20- 29 F10.2 0.1nm lambda Transition wavelength
31- 41 E11.5 Ry Ei Energy of lower state (1)
43- 53 E11.5 Ry Ek Energy of upper state (1)
55- 64 E10.4 --- fL Oscillator strength of the transition
66- 75 E10.4 --- S Line strength
77- 86 E10.4 s-1 Aki Transition probability
--------------------------------------------------------------------------------
Note (1): energies from tables 5a and 6a respectively, for the
specified values of J, parity and index iiii.
--------------------------------------------------------------------------------
Acknowledgements:
Sultana Nahar
References:
1993A&A...279..298H 1993A&A...279..298H : IRON Project I Goal and methods
1994A&AS..107...29S 1994A&AS..107...29S : IRON Project IV Electron excitation of F-like ions
1995A&AS..110..209P 1995A&AS..110..209P : IRON Project IX Electron excitation of Cl-like ion
1995A&AS..111..347G 1995A&AS..111..347G : IRON Project X Si- & S-like ions IR coll. strengths
1996A&AS..115..151S 1996A&AS..115..151S : IRON Project XI Ar VI, K VII & CaVIII fine-structure
1995A&AS..114..367B 1995A&AS..114..367B : IRON Project XII V-like ions electron excitation
1996A&AS..115..551B 1996A&AS..115..551B : IRON Project XIII Ni II & Fe II electron excitation
1996A&A...309..677S 1996A&A...309..677S : IRON Project XIV Fe XIV fine-structure transition
1996A&AS..118..157K 1996A&AS..118..157K : IRON Project XV He II & Fe XXVI Electron excitation
1996A&AS..119..105B 1996A&AS..119..105B : IRON Project XVI Fe V oscillator strengths
1997A&AS..122..167B 1997A&AS..122..167B : IRON Project XX Fe I oscillator strengths
1997A&AS..122..177P 1997A&AS..122..177P : IRON Project XXI Fe I fine-structure transition
1997A&AS..126..105B 1997A&AS..126..105B : IRON Project XXIV Fe XXIV electron excitation
1998A&AS..127..545B 1998A&AS..127..545B : IRON Project XXV Fe XII electron excitation
1997A&AS..126..365B 1997A&AS..126..365B : IRON Project XXVI Fe IV oscillator strengths
1998A&AS..129..161B 1998A&AS..129..161B : IRON Project XXVIII F-like ions fine-structure trans.
1999A&AS..134..369S 1999A&AS..134..369S : IRON Project XXX P III, S IV & Cl V collision data
1998A&AS..133..245G 1998A&AS..133..245G : IRON Project XXXII Ar III effective collision strength
1999A&AS..135..159M 1999A&AS..135..159M : IRON Project XXXIII Carbon radiative rates
1999A&AS..136..385E 1999A&AS..136..385E : IRON Project XXXIV Fe XVI electron impact excitation
1999A&AS..137..175C 1999A&AS..137..175C : IRON Project XXXVI Fe XXIII electron excitation
1999A&AS..137..529B 1999A&AS..137..529B : IRON Project XXXIX Ni II oscillator strengths
2000A&AS..141..285S 2000A&AS..141..285S : IRON Project XL Fe XIV electron excitation
2000A&AS..142..313B 2000A&AS..142..313B : IRON Project XLI Fe VII electron excitation
2001A&A...365..258P 2001A&A...365..258P : IRON Project XLVI Fe X electron excitation
2003A&A...401.1177C 2003A&A...401.1177C : IRON Project LII Ni24 electron excitation
2005A&A...436.1123M 2005A&A...436.1123M : IRON Project LVII Ni IV radiative transition rates
2005A&A...433..717S 2005A&A...433..717S : IRON Project LVIII Fe XII electron impact excitation
2006A&A...446..361W 2006A&A...446..361W : IRON Project LX Fe17+ electron impact excitation
History:
* 23-Nov-2000: Original files
* 22-Jan-2008: Corrected files
* 19-Mar-2008: Addition of ar13.dat and fe21.dat, created from
table5b and table6b.
(End) Patricia Bauer [CDS] 21-Sep-2000