A&A 424, 363-369 (2004)

DOI: 10.1051/0004-6361:20040496

**V. Jonauskas ^{1,}^{} - F. P. Keenan ^{1} - M. E. Foord ^{2} - R. F. Heeter ^{2} - S. J. Rose ^{3} - G. J. Ferland ^{4} - R. Kisielius^{1,}^{}
- P. A. M. van Hoof ^{1} - P. H. Norrington ^{5} **

1 - Department of Pure and Applied Physics,
The Queen's University of Belfast,
Belfast BT7 1NN, Northern Ireland, UK

2 - University of California, Lawrence Livermore National Laboratory,
Livermore, CA 94551, USA

3 - Department of Physics, Clarendon Laboratory, Parks Road,
Oxford OX1 3PU, UK

4 - Department of Physics, University of Kentucky, Lexington,
KY 40506, USA

5 - Department of Applied Mathematics and Theoretical Physics,
The Queen's University of Belfast,
Belfast BT7 1NN, Northern Ireland, UK

Received 22 March 2004 / Accepted 26 May 2004

**Abstract**

Multiconfigurational Dirac-Fock calculations
are reported for
656 energy levels and the 214 840
electric dipole (E1), electric quadrupole (E2) and magnetic dipole (M1)
transition probabilities in oxygen-like Fe XIX.
The spectroscopic notations as well as the total transition probabilities
from each energy level are provided.
Good agreement is found with data compiled by NIST.

**Key words: **atomic data

Atomic data for O-like Fe XIX have been
extensively studied under the framework of the
IRON Project (Hummer et al. 1993).
Galavis et al. (1997) present radiative rates for
forbidden transitions in O-like ions with ,
for the *n*=2 complex.
Butler & Zeippen (2001)
provide energy levels, electron impact
collision strengths and rates for transitions
among the 92 lowest levels of the *n*=2 and *n*=3 complexes
of Fe XIX.
The atomic structure code
SUPERSTRUCTURE (SS) (Eissner et al. 1974) was employed
by both sets of authors.
On the other hand, McLaughlin et al. (2001) present the
25 lowest energy levels and effective collision
strengths, calculated with the atomic structure code CIV3
(Hibbert 1975), and the
Breit-Pauli version of the R-matrix codes (Berrington et al. 1995),
respectively. Zhang & Sampson (2002) obtain relativistic
distorted-wave collision strengths and oscillator strenghts
for transitions among 10 lowest levels of the *n*=2 complex.

High resolution spectra of astrophysical sources require
accurate atomic data for reliable plasma modelling. In
particular, the
*Chandra* and *XMM-Newton* satellites provide spectra with particularly
large effective areas
in the 6 to 18
wavelength range, covering Fe XIX
lines arising from the
complex
(McKernan et al. 2003; Behar et al. 2001; Heyden et al. 2003).
To allow the reliable interpretation of
these lines, we have studied Fe XIX
transitions among the levels of the
25 lowest configurations originating from the
*n*=3,4 and 5 complexes.
Previous calculations cover a smaller range of transitions.

In the present paper we report calculations for energy levels, transition probabilities and oscillator strengths for electric dipole (E1), electric quadrupole (E2), and magnetic dipole (M1) transitions among 656 levels of oxygen-like Fe XIX. A comparison between NIST data and our calculations, as well as the energy levels of McLaughlin et al. (2001) and Butler & Zeippen (2001), is made. The five strongest and the sum of all the radiative transition probabilities (useful to obtain decay branching ratios) from the levels are also presented.

The GRASP code of Parpia et al. (1996); Dyall et al. (1989); Norrington (2003) is used for
the calculation of wave functions as well as the matrix elements of
the
Dirac-Coulomb-Breit Hamiltonian and transition operators. As a result,
direct and indirect
relativistic effects are included in the calculations.
One-electron wave functions, obtained by solving multiconfigurational
Dirac-Fock (MCDF) equations, were used to build configuration state
wave functions. The intermediate coupling wave functions:

are generated in the basis of configuration state functions (CSF) by diagonalizing the Dirac-Coulomb-Breit Hamiltonian matrix. The frequency-dependent transverse Breit interaction operator is used for the calculation of Breit matrix elements. QED corrections are considered in the first order of perturbation theory, and the correlation corrections taken into account by the configuration interaction (CI) method. The relativistic line strengths are obtained from matrix elements of frequency-dependent transition operators. Coulomb and Babushkin gauges of the electric transition operators allow us to estimate the accuracy of wave function expansion in the intermediate coupling.

Results are presented for total number of 656 lowest energy levels
in Fe XIX.
We consider 565 energy levels arising from
the 1s^{2}2s^{2}2p^{4},
1s^{2}2s^{1}2p^{5},
1s^{2}2p^{6},
1s^{2}2s^{2}2p^{3}*nl*,
1s^{2}2s^{1}2p^{4}3*l*',
1s^{2}2s^{1}2p^{4}4s^{1},
1s^{2}2s^{1}2p^{4}4p^{1}, and
1s^{2}2p^{5}3*l*' (*n*=3,4,5,
*l*=0,..,*n*-1, *l*'=0,1,2) configurations.
Due to the high density of levels between highly excited configurations,
and strong
configuration interaction between these, there are also
included some
energy levels of other configurations (38 levels of 1s^{2}2s^{1}2p^{4}4d^{1} and
41 levels of 1s^{2}2s^{1}2p^{4}4f^{1})
with calculated binding energies larger
than our chosen
cut-off value, which corresponds to the highest level of the
1s^{2}2s^{2}2p^{3}5g^{1} configuration.

A large CI basis is used to generate one-electron wave functions
solving MCDF equations
as well to obtain accurate intermediate coupling wave functions
diagonalizing the Dirac-Coulomb-Breit Hamiltonian matrix.
We include one-electron excitations from 2s and
2p orbitals of the 1s^{2}2s^{2}2p^{4} configuration up to the 7*l*
orbital, and two-electron
excitations from 2s or/and 2p orbitals to all possible combinations of
two electrons in the shells with *n*=3.
The level energies and intermediate coupling wave functions
obtained after the
diagonalization of the Dirac-Coulomb-Breit Hamiltonian matrix are then
used to evaluate the
transition probabilities, oscillator and line strengths
for electric dipole, electric quadrupole and magnetic dipole
transitions
among the 656 lowest levels in our calculations.

The 656 fine-structure levels which give rise from
the above mentioned configurations are
listed in Table 1.
The indexes for levels presented in the first column of
Table 1 are used in all tables.
Energy levels are given in
cm^{-1} relative to the ground state 1s^{2}2s^{2}2p^{4} ^{3}P_{2}.
Configuration as well as term notations presented in the
second and third columns have the primary contribution
to the wavefunction of Eq. (1)
obtained after Dirac-Coulomb-Breit matrix diagonalization.
For brevity, filled 1s^{2}
shells are omitted in the notations of configurations,
and
intermediate many-electron quantum numbers are shown in the parentheses.
Leading percentage compositions are equal to squared expansion
coefficients
for the intermediate coupling function
of Eq. (1), and
are limited to values larger than 10%. As was mentioned above,
diagonalization of the Dirac-Coulomb-Breit matrix,
which is obtained in the *jj*-coupling scheme,
provides expansion coefficients
for the intermediate coupling functions in the basis of CSF.
We present the CSF in the *LS*-coupling scheme.
Therefore, the
corresponding percentage compositions are obtained from coefficients
calculated in the *jj*-coupling scheme using term-coupling coefficients.
The expansion of the
intermediate coupling function in the CSF basis depends on
the model used in calculations.
Leading percentage compositions obtained after Dirac-Coulomb matrix
diagonalization differ from our presented values. The discrepancies
between
the two sets of coefficients are not large, but in some cases the order of levels
identified by the largest contribution of CSF can be different.
Calculated energies of levels can also change after inclusion of Breit and QED
corrections.

**Table 2:**
Suggested change of spectroscopic identifications
of levels to ensure the completeness of spectroscopic dataset.
The indexes of levels for which spectroscopic identifications are
changed are presented in the first column. The second column contains index
of level with the same highest contribution of configuration state function
(Table 1)
as level from the first column before change.
Identification of level with index 492
was changed due to use for identification its * LS*-configuration state function
for level with index 482.
Indexes of levels in the first two columns are
taken from Table 1.

Some levels identified by the CSF obtained in *LS*-coupling scheme
with the largest contribution to an
intermediate coupling function have the same spectroscopic notations.
To ensure the completeness of the spectroscopic dataset, we suggest
new spectroscopic notations for levels with the same spectroscopic
identities. In some cases, the mixing of CSF
defined in *LS*-coupling scheme is so strong
that it is difficult to make definite identifications of levels.
The mixing of CSF especially increases for
highly excited levels where the separation
between level energies decreases.
Leading percentages of levels show that the
*LS*-coupling scheme is not
satisfactory for highly excited states.
Proposed spectroscopic notations for levels with the same
largest contribution of *LS*-coupling CSF are presented in Table 2.
If two levels have the same many-electron
quantum numbers for a given configuration in
the second and third columns of Table 1, the
identification of the level with the smaller contribution to the
intermediate coupling wave function
is changed to that of the secondary CSF.
If this secondary function is employed
for the identification of some other level, then the third CSF
is checked.
The spectroscopic notation of level 492
has had its *LS*-configuration state function
re-assigned to level 482. However, no other level
in the second and third columns of Table 1 has the
new spectroscopic notation proposed for level 492.
Therefore, no spectroscopic notation has been
assigned to level 492 in the second column of Table 2.

In Table 3 we compare our calculated energy levels as well as
the data obtained by McLaughlin et al. (2001) and
Butler & Zeippen (2001) with
values compiled by
NIST (National Institute for Standards and Technology:
www.physics.nist.gov). Fairly good agreement is obtained for the
MCDF calculations, with the
energy levels agreeing to better than 2% with the NIST
values.
Levels 10 (2p^{6} ^{1}S_{0})
and 9 (2s^{1}2p^{5} ^{1}P_{1}) show the largest differences
of 1.9% and 1.6%, respectively.
All highly excited levels agree to better than 1%.
Only level 493 has a large
deviation from
the NIST energy, but even this is only 1.3%.
The percentage composition of the *LS*-coupling CSF for the level shows
that there is strong mixing
between CSF and no single CSF has a contribution exceeding 50%.
Our energy of ground state
-230 793 799 cm^{-1} is slightly higher than
NIST value of
cm^{-1}.
Due to this some calculated energies of levels
relative to the calculated ground energy are lower than NIST values presented
in Table 3.

The average deviation
between our energy levels and the NIST values is only 0.35%.
On the other hand, the average deviation for energies obtained by
McLaughlin et al. (2001) is 0.8%. For the energies
in common, the
average deviation of the Butler & Zeippen (2001) values is 0.8%,
while for our data this is only 0.6%.
The largest deviation for energies obtained by
McLaughlin et al. (2001) is 3.2% for the
first excited level
(2s^{2}2p^{4} ^{3}P_{0}) and
2.7% for the second (2s^{2}2p^{4} ^{3}P_{1}).
Butler & Zeippen (2001) energies show an
average deviation of 0.6% with NIST data, while the
average for our values is 0.45% for the same range of levels.
The largest deviations for energies obtained by
Butler & Zeippen (2001)
is 3.3% for level 4 (2s^{2}2p^{4} ^{1}D_{2}) and 1.6%
for levels 10 (2p^{6} ^{1}S_{0})
and 9 (2s^{1}2p^{5} ^{1}P_{1}).
Therefore, our energy levels agree better with the
NIST values
than those calculated by previous
authors. The main reason for this is that we use
a larger base of CSF, and a fully relativistic approach.
Level ordering
differs from NIST in both large-scale calculations.

The total number of dipole allowed and intercombination E1-type transitions is
58 390, while the complete set of forbidden transitions totals 136 866.
Table 6 includes only E1-type transitions for which oscillator strengths exceed
0.001.
All forbidden E2-type transitions with
are reported in Table 7.
Table 8 provides data for
M1-type transitions with *f*-values exceeding 10^{-7}.
Differences between Babushkin and Coulomb gauges
(velocity and
length forms of the electric transition operators in the
nonrelativistic limit), which are an additional indicator of accuracy for the
wavefunctions, do not exceed 20% for most strong E1-type transitions
().
The average deviation between the two forms
is 5.3% for 812 lines with
and 9.6% for
4524 lines with
.
The electric quadrupole transition has the largest contribution
to the lifetime of
the first excited level, the
difference between the two forms is large, and the
oscillator strength is very small.
E2-type transition from level 5 (79% 2s^{2}2p^{4} ^{1}S_{0} + 19%
2s^{2}2p^{4} ^{3}P_{0}) also shows
a large deviation of 80% between the two forms, and a
small *f*-value (
).
On the other hand, our obtained leading compositions of
wavefunctions reports
similar values for these three levels as NIST ones;
1: 90% (2s^{2} 2p^{4} ^{3}P_{2}) + 10% (2s^{2} 2p^{4} ^{1}D_{2});
2: 80% (2s^{2} 2p^{4} ^{3}P_{0}) + 20% (2s^{2} 2p^{4} ^{1}S_{0});
5: 78% (2s^{2} 2p^{4} ^{1}S_{0}) + 20% (2s^{2} 2p^{4} ^{3}P_{0}).
The deviation between calculated (Babushkin gauge) and NIST
characteristics of the transition from the first excited level does not
exceed 4%.

**Table 3:**
Comparison of some calculated energies of Fe XIX levels with
data presented by NIST (
).
- values obtained by McLaughlin et al. (2001),
- energies calculated by Butler & Zeippen (2001),
- our values.
Indexes of levels in the first column are
taken from Table 1. Energies are in cm^{-1}.

**Table 4:**
Comparison of some calculated (GRASP) Fe XIX
wavelengths ,
radiative
transition probabilities *A*^{r}_{ki}, oscillator *f*_{ik} and line *S* strengths with values presented by NIST.
Indexes of levels in the first two columns are
taken from Table 1.

Our calculated wavelengths, transition probabilities, oscillator
and line strengths
as well as the NIST values are presented in Table 4.
The accuracy of the transition wavelengths is well above 1%
for short wavelengths (
Å).
The largest deviations of wavelengths (up to 4%)
are obtained for transitions
which involve levels 4, 9 and 10, as these show
the largest differences
in energies from NIST data.
Our
probabilities for most transitions are slightly smaller than the corresponding
NIST values, with
intercombination E1-type transitions showing the
largest
deviations. The difference for their radiative
probabilities varies from 4% to 20%.
Transitions 2s^{1}2p^{5} ^{3}P_{1}
2s^{2}2p^{4} ^{1}S_{0}
and 2s^{1}2p^{5} ^{1}P_{1}
2s^{2}2p^{4} ^{3}P_{0}
have the largest deviation of 20% and 16%, respectively.
On the other hand, their contributions to the radiative lifetimes of the
levels
do not exceed 1%.
The deviation for other intercombination E1-type
transitions does not exceed 12%,
while transition probabilities for other lines agree to better than 10%.
This is highly satisfactory for such a large-scale calculation.
The average deviation between our radiative transition probabilities and
NIST values presented in Table 4 is 5.8%.

The five largest spontaneous radiative transition probabilities
from each level are given in Table 5, and the
sum of all E1, E2, and M1 radiative transition probabilities
from the corresponding level are provided in the last column.
Forbidden E2 and M1 transitions have the largest weight for transitions
between fine-structure levels of the
ground configuration, where E1-type transitions
are forbidden. Levels 3, 4, and 5 (2s^{2}2p^{4} ^{3}P_{1}, ^{1}D_{2},
and ^{1}S_{0}) decay mainly due to magnetic dipole transitions.
The contribution of
electric quadrupole transitions from these levels is negligible.
For highly excited levels, the
contribution of magnetic dipole transitions is small.
On the other hand, the
first excited level decays only through E2-type transition.
Contribution of E2-type forbidden transitions to the lifetimes
of highly excited levels
is noticeable for levels of the
2s^{2}2p^{3}3p^{1} and 2s^{1}2p^{4}3d^{1} configurations.
For example, E2-type transitions amount to 40% of the
lifetime for
level 24 (2s^{2}2p^{3} (^{4}S) 3p^{1} ^{3}P_{0}), 28% for level 138
(2s^{1}2p^{4} (^{4}P) 3d^{1} ^{3}F_{4}), and 27% for
level 33 (2s^{2}2p^{3} (^{2}D) 3p^{1} ^{1}F_{3}).
Finally, electric quadrupole
transitions have contributions exceeding 10% of the
total transition
probability for 12 levels (24, 138, 33, 30, 34, 23, 28, 22, 176, 126, 18 and
172).

In the present paper we have reported large-scale calculations in the multiconfigurational Dirac-Fock approach of 656 lowest energy levels as well as corresponding transition wavelengths, absorption oscillator strengths and radiative transition probabilities for electric dipole, electric quadrupole as well as magnetic dipole type transitions in oxygen-like Fe XIX. To our knowledge, our work represents the largest calculation to date for Fe XIX. Fairly good agreement is obtained between our calculated and NIST data.

Spectroscopic notations of levels in the *LS*-coupling scheme
have been
presented, and checked for their completeness.
Contributions of CSF to intermediate coupling wave functions
indicate that *LS*-coupling scheme is not
satisfactory for highly excited states.

The five major radiative probabilities from each level and the total transition probability have been provided, taking into account forbidden transitions. The largest contributions of forbidden E2 and M1 transitions have been obtained for the lifetimes of fine-structure levels of the ground configuration.

Agreement between our presented theoretical values and available
NIST data as well as large basis of configuration state functions
and relativistic Dirac-Fock approach, allows us to conclude that our
calculations of energy levels and radiative transition data for Fe XIX
are reliable. They may successfully be used in various plasma codes for the
interpretation of astronomical and other spectral observations, especially
for high resolution spectra provided by the *Chandra* and
*XMM-Newton* satellites.

F.P.K. and S.J.R. are grateful to A. W. E. Aldermaston for the award of William Penney Fellowships. This work was supported by PPARC and EPSRC, and also by NATO Collaborative Linkage Grant CLG.979443. We are also grateful to the Defence Science and Technology Laboratory (dstl) for support under the Joint Grants Scheme.

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Online Material

**Table 1:**
Calculated energy levels of Fe XIX with spectroscopic identification
(in cm^{-1}) relative to the ground energy.
The leading percentage compositions
of levels which contributions exceed 10% are presented in the last column.

**Table 5:**
Calculated energy levels of Fe XIX (in cm^{-1}) relative to the ground
energy with spectroscopic notations. The five major spontaneous radiative transition probabilities
*A*^{r} (in s^{-1}) from each level are given. Arrow marks the final level to
which radiative transition happens from the level.
The sum of all radiative probabilities from the corresponding level is given in the
last column.

Copyright ESO 2004