J/A+A/413/779 Iron Project. LIV. Fe XX (Nahar+, 2004)
Atomic data from the Iron Project.
LIV. Relativistic calculations for allowed and forbidden fine structure
transitions in Fe XX.
Nahar S.N.
<Astron. Astrophys., 413, 779-787 (2004)>
=2004A&A...413..779N 2004A&A...413..779N
ADC_Keywords: Atomic physics
Keywords: Atomic data
Abstract:
An extensive set of oscillator strengths (f), line strengths (S) and
radiative decay rates (A) for dipole allowed, intercombination and
forbidden transitions in Fe XX is presented. Results include 1792
bound fine structure levels of total angular momenta J=1/2-19/2 of
even and odd parities, with 2≤n≤10, 0≤l≤14, orbital angular
momenta, 0≤L≤14, and total spin multiplicities 2S+1=2,4,6, yielding
to about 3.8x105 allowed and 13,874 forbidden transitions in Fe XX.
These results far exceed the available data in literature. The
existing data compiled by the National Institute for Standards and
Technology (NIST) are available for little over one hundred
transitions, and the previously calculated data under the Opacity
Project includes 75 590 LS multiplets. The present ab initio
calculations are carried out in the close coupling approximation using
the relativistic Breit-Pauli R-matrix method for allowed and
intercombination E1 transitions. The wavefunction expansion includes
20 fine structure levels of configurations 2s 22p2, 2s2p3, and
2p4 of the core ion Fe XXI. Computed energy levels are identified
spectroscopically using a newly developed procedure based on quantum
defects and channel contributions. All 55 observed levels have been
identified and are in agreement to much less than 1% with most of the
calculated values. Coefficients for radiative decays for the forbidden
E2, E3, M1 transitions are obtained through atomic structure
calculations including relativistic terms in the Breit-Pauli
approximation using the code SUPERSTRUCTURE. The theoretical
transition probabilities are compared with available values, with
varying degree of agreement.
Erratum:
A bug was detected and corrected in early 2007 in one of the stages
called RECUPD (Storey, Berrington, Werner, 2007, private Iron Project
communications) of the Breit-Pauli R-matrix (BPRM) codes of the Iron
Project. It was related to the the phase factor of dipole matrix
elements of the Iron Project (Berrington et al., 1995, Comput. Phys.
Commun. 92, 290) and affected certain transition probabilities. The
new results on energies and transition probabilities for Fe XX (Nahar,
2004, J/A+A/413/779, this paper) and Fe XVIII (Nahar, 2006,
J/A+A/457/721) 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.
Results for other ions, obtained using BPRM codes, did not indicate
the bug effect when compared with existing results. However, I am
repeating the calculations for these ions and will replace the earlier
results.
The E1 transition probabilities for Fe XX have been recomputed. The
new files are:
table3a, table3b -> fine structure energy levels of Fe XVIII
table4a, table4b -> complete table of E1 fine structure transitions in
Fe XVIII
table5 -> table of fine structure transitions in Fe XVIII using
observed energies
In paper LXII (Fe XVIII), J/A+A/457/721, files were also corrected.
File Summary:
--------------------------------------------------------------------------------
FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
table3.txt 94 4561 Original file of table3
table3a.txt 94 2516 *Energy table in LS-multiplets for spectroscopic
identifications
table3b.dat 75 1832 Energy table in Jπ order for easy use in
modeling code
table4.txt 79 387862 Original file of table4
table4a.dat 79 1832 Fine structure levels provided for direct
information on possible spectroscopic transitions
set.dat 26 28 Set of initial and final g, P and N values
for table4b.dat
table4b.dat 79 385915 Fine structure transitions
table5.txt 80 527 Original file of table5
table5.dat 80 353 Oscillator strengths corrected by observed
energies
table78.txt 75 14168 Original file of tables 7 and 8
table7.dat 56 215 Fine Structure energies (calculated):
relativistic (BP)
table8a.dat 55 3655 Forbidden E3 transitions in Breit-Pauli
approximation (Nb of M2/E3 transitions = 3655)
table8b.dat 74 10219 *Forbidden E2 and M1 transitions in Breit-Pauli
approximation.
Number of E2,M1 transitions = 10219
--------------------------------------------------------------------------------
Note on table3a.txt : Total number of levels processed= 1792
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:
Configuration J E(Ry) EQN LS terms
Eqv electron/unidentified levels, parity: o
2s22p3 3/2 -1.15778E+02 4 S o
Nlv(c)= 1 : set complete
Eqv electron/unidentified levels, parity: o
2s22p3 3/2 -1.14494E+02 2 D o
2s22p3 5/2 -1.14121E+02 2 D o
Nlv(c)= 2 : set complete
Eqv electron/unidentified levels, parity: o
2s22p3 1/2 -1.08889E+02 2 P o
2s22p3 3/2 -1.12741E+02 2 P o
Nlv(c)= 2 : set complete
Eqv electron/unidentified levels, parity: e
2s2p4 5/2 -1.08889E+02 4 P e
2s2p4 3/2 -1.08276E+02 4 P e
2s2p4 1/2 -1.08076E+02 4 P e
Nlv(c)= 3 : set complete
Note on table8a.dat and table8b.dat:
NT=10219 + 3655 = 13874 = total number of forbidden E2,M1,E3,M2 transitions
--------------------------------------------------------------------------------
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+AS/147/253 : IRON Project XLV Ar XIII, Fe XXI trans. probabilities
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/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
Byte-by-byte Description of file: table3b.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 3 I3 --- Nlv Total number of symmetry Jπ (1)
5- 8 A4 --- J J value
10 A1 --- P [oe] Parity (o: odd, e: even)
13- 15 I3 --- iii level (1≤i≤Nlv)
17- 22 A6 --- Ct t configuration (2)
28- 30 A3 --- SLpit t core level
33- 35 A3 --- Jt J value at t (2)
37- 39 A3 --- nl Principal and orbital quantum numbers of
the outer electron
42- 45 A4 --- Jv J value of the outer electron
48- 59 E12.5 Ry E Energy
61- 65 F5.2 --- EQN ? Effective Quantum Number (3)
68- 75 A8 --- Terms Possible LS terms of the energy level
--------------------------------------------------------------------------------
Note (1): Z = 26, No. of core electrons = 6, Target levels: 20
Target levels:
---------------------------------------
Config SLp J E(Ry)
---------------------------------------
1 2s22p2 3Pe 0 0.00000E+00
2 2s22p2 3Pe 1 6.72970E-01
3 2s22p2 3Pe 2 1.06940E+00
4 2s22p2 1De 2 2.22860E+00
5 2s22p2 1Se 0 3.38900E+00
6 2s2p3 5So 1 4.43740E+00
7 2s2p3 3Do 3 7.32600E+00
8 2s2p3 3Do 2 7.08370E+00
9 2s2p3 3Do 1 7.07850E+00
10 2s2p3 3Po 2 8.58710E+00
11 2s2p3 3Po 1 8.42810E+00
12 2s2p3 3Po 0 8.35070E+00
13 2s2p3 3So 1 9.98380E+00
14 2s2p3 1Do 2 1.02680E+01
15 2s2p3 1Po 1 1.14910E+01
16 2p4 3Pe 2 1.50020E+01
17 2p4 3Pe 1 1.58610E+01
18 2p4 3Pe 0 1.58170E+01
19 2p4 1De 1 1.65600E+01
20 2p4 1Se 0 1.86650E+01
---------------------------------------
Number of fine structure levels
---------------------------------------
J pi Nlv(c)
---------------------------------------
1 0 128
1 1 127
3 0 200
3 1 201
5 0 204
5 1 203
7 0 151
7 1 161
9 0 100
9 1 106
11 0 60
11 1 68
13 0 35
13 1 35
15 0 17
15 1 18
17 0 7
17 1 7
19 0 1
19 1 3
21 0 0
21 1 0
---------------------------------------
Total number of levels = 1832
Note (2): T(config SLpi Jt): T -> target (core) of the level
Note (3): No EQN is assigned for Equivalent electron levels
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table4a.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
2- 5 I4 --- i [1,1832] Level index
8- 10 F3.1 --- J J value
12 A1 --- p [eo] Parity (o: odd, e: even)
15- 17 I3 --- iii Level position index within J+p
22- 33 E12.6 Ry Eobs Energy (1)
36- 53 A18 --- conf Configuration
55- 61 A7 --- LS LS term (2)
73- 79 I7 --- jjpiiii Energy level ids (3)
--------------------------------------------------------------------------------
Note (1): nz = 26 , No. of core electrons= 8
1174 = number of energies (Ecalc are replaced by available' Eobs)
Note (2): Note that there may be more than one possible LS term for some
j-levels. Simple assumption: higher L -> lower energy
Note (3): Energy levels with ids: jjpiiii
jj=2 x total angular momentum j, p=parity, iii=level position.
--------------------------------------------------------------------------------
Byte-by-byte Description of file: set.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 2 I2 --- Set Set number
4- 5 I2 --- gi Initial statistical weight factor (2J+1)
7 I1 --- Pi [0/1] Initial parity value
9- 10 I2 --- gf Final statistical weight factor (2J+1)
12 I1 --- Pf [0/1] Final parity value
14- 16 I3 --- Ni Initial Nlv value
18- 20 I3 --- Nf Final Nlv value
22- 26 I5 --- NN Total number of transitions in the set
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table4b.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 2 I2 --- Set Set, as defined in set.dat file
5- 7 I3 --- i Initial level (index in set)
9- 11 I3 --- j Final level (index in set)
13- 22 F10.2 0.1nm wl Wavelength of the transition
24- 34 E11.5 Ry Ei Initial energy
36- 46 E11.5 Ry Ej Final energy
48- 57 E10.4 --- fL fL value
60- 68 E9.4 --- S Line strength
71- 79 E9.4 s-1 Aji Einstein Aji coefficient
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table5.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
2- 9 A8 --- Ci Initial configuration
14- 25 A12 --- Cj Final configuration
26- 28 A3 --- slpi Initial core level
30- 32 A3 --- slpj Final core level
34- 35 I2 --- gi Initial statistical weight factor
37- 38 I2 --- Ii ? Energy level index of 2Ji+1
(no value when Ci = LS)
40- 41 I2 --- gj Final statistical weight factor
43- 44 I2 ---- Ij ? Energy level index of 2Jj+1
(no value when Ci = LS)
48- 53 F6.2 0.1nm Eij ? Transition energy
55- 62 E8.3 --- f Oscillator strength (f value)
64- 71 E8.3 --- S Line strength
73- 80 E8.3 s-1 A Radiative decay rate (A-value)
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table7.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
2- 4 I3 --- ie [1,215] Fine structure level number
7- 13 A7 --- SLp(cf) Core level (1)
16- 17 I2 --- g Statistical weight factor, g=(2J+1),
with I=0 for J even, and I=1 for J odd
21- 29 F9.1 cm k k value
33- 43 E11.6 Ry E Energy
45- 56 A12 --- Conf Configuration set (1)
--------------------------------------------------------------------------------
Note (1): Configuration (cf) set (9 configurations):
1 2s2 2p3
2 2s 2p4
3 2p5
4 2s2 2p2 3s
5 2s2 2p2 3p
6 2s2 2p2 3d
7 2s 2p3 3s
8 2s 2p3 3p
9 2s 2p3 3d
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table8a.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 3 I3 --- Ni [1,215] Initial number
5- 7 I3 -- Nj [1,215] Final number
9- 13 A5 --- SLpCi Initial core level
15- 19 A5 --- SLpCj Final core level
22- 23 I2 --- gi Initial statistical weight factor
25- 26 I2 --- gj Final statistical weight factor
28- 36 F9.2 0.1nm wl Wavelength in vacuum
38- 46 E9.3 --- SE3 E3 line strength (1)
48- 55 E8.3 s-1 AE3 Forbidden E3 transition probability
--------------------------------------------------------------------------------
Note (1): Ignore the negative signs in line strengths S
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table8b.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 3 I3 --- Ni [1,215] Initial number
5- 7 I3 --- Nj [1,215] Final number
9- 13 A5 --- SLpCi Initial core level
15- 19 A5 --- SLpCj Final core level
22- 23 I2 --- gi Initial statistical weight factor
25- 26 I2 --- gj Final statistical weight factor
28- 36 F9.2 0.1nm wl Wavelength in vacuum
38- 46 E9.3 --- SE2 E2 line strength (1)
48- 55 E8.3 s-1 AE2 Forbidden E2 transition probability
57- 65 E9.3 --- SM1 M1 line strength (1)
67- 74 E8.3 s-1 AM1 Forbidden M1 transition probability
--------------------------------------------------------------------------------
Note (1): Ignore the negative signs in line strengths S
--------------------------------------------------------------------------------
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:
* 11-May-2004: Original version
* 06-Nov-2008: corrected version for table3, table4, table5
(End) Francois Ochsenbein [CDS] 29-Dec-2003