A&A 410, 359-364 (2003)
DOI: 10.1051/0004-6361:20031262
P. Palmeri1,
-
C. Mendoza1,
-
T. R. Kallman 1 -
M. A. Bautista 2 -
M. Meléndez 2
1 - NASA Goddard Space Flight Center, Code 662, Greenbelt, MD 20771, USA
2 -
Centro de Física, Instituto Venezolano de Investigaciones
Científicas (IVIC), PO Box 21827, Caracas 1020A, Venezuela
Received 19 June 2003 / Accepted 8 August 2003
Abstract
A detailed analysis of the radiative and Auger de-excitation
channels of K-shell vacancy states in Fe II-Fe IX
has been carried out. Level energies, wavelengths, A-values,
Auger rates and fluorescence yields have been calculated for the
lowest fine-structure levels populated by photoionization of the
ground state of the parent ion. Different branching ratios,
namely K/K
,
K
/K
,
KLM/KLL, KMM/KLL,
and the total K-shell fluorescence yields,
,
obtained in the present
work have been compared with other theoretical data and
solid-state measurements, finding good general agreement with the
latter. The K
/K
ratio is found to be
sensitive to the excitation mechanism. From these comparisons it
has been possible to estimate an accuracy of
10% for the
present transition probabilities.
Key words: atomic data - atomic processes - techniques: spectroscopic
The iron K lines appear in a relatively unconfused spectral region and have a high diagnostic potential. The study of these lines has been encouraged by the quality spectra emerging from Chandra and by the higher resolution expected from Astro-E and Constellation-X. In addition there is a shortage of accurate and complete level-to-level atomic data sets for the K-vacancy states of the Fe isonuclear sequence, in particular for the lowly ionized species. This undermines line identification and realistic spectral modeling. We are currently remedying this situation by systematic calculations using suites of codes developed in the field of computational atomic physics. Publicly available packages have been chosen rather than in-house developments. In this context, complete data sets for the n=2K-vacancy states of the first row, namely Fe XVIII-Fe XXV, have been reported earlier by Bautista et al. (2003) and Palmeri et al. (2003), to be referred to hereafter as Papers I and II, and for the second row (Fe X-Fe XVII) by Mendoza et al. (2003), to be referred to as Paper III.
The K lines from Fe species with
electron occupancies N>17 have been studied very little.
Jacobs & Rozsnyai (1986) have computed fluorescence probabilities in a
frozen-core approximation for vacancies among the
subshells of
the Fe isonuclear sequence. Kaastra & Mewe (1993) have calculated
the inner-shell decay processes for all the ions from Be to Zn by
scaling published Auger and radiative rates in neutrals.
Both of these studies ignore multiplets and fine-structure. Otherwise,
the bulk of the data in the literature is devoted to solid-state
iron. Regarding wavelengths and line intensity ratios, numerous references
are listed in Hölzer et al. (1997) who measure the K
and
K
emission lines of the 3d transition metals using a
high-precision single-crystal spectrometer.
Fewer publications are available on the experimental K Auger
spectra: Kovalík et al. (1987) have derived the KLM/KLL and KMM/KLL ratios from
the Auger electron spectrum of iron produced by 57Co decay, and
Némethy et al. (1996) have measured the KLL and KLM spectra of the 3d
transition metals but have not determined the KLM/KLL ratio.
Concerning K-shell fluorescence yields, measurements
covering the period 1978-93 have been reviewed by Hubbell et al. (1994)
following major compilations by Bambynek et al. (1972) and Krause (1979).
The present work is a detailed analysis of the radiative and Auger de-excitation channels of the K-shell vacancy states in the third-row species Fe II-Fe IX. Energy levels, wavelengths, A-values, Auger rates and fluorescence yields have been computed for the lowest fine-structure levels in configurations obtained by removing a 1s electron from the ground configuration of the parent ion. In Sect. 2 the numerical method is briefly described. Section 3 outlines the decay trees and selection rules. Results and discussions are given in Sect. 4 followed by a summary and conclusions (Sect. 5). All the atomic data calculated in this work are available in the electronic Tables 3, 4.
In Paper III we conclude that the importance of core-relaxation
effects increases with electron occupancy, so calculations of third-row iron ions
require a computational platform which is well suited to treating these effects.
For this reason the calculations reported here are carried out using the
HFR package by Cowan (1981) although AUTOSTRUCTURE
(Badnell 1986,1997) is also heavily used for comparison purposes. In HFR
an orbital basis is obtained for each electronic configuration
by solving the Hartree-Fock equations for the spherically
averaged atom. The equations are derived from the application
of the variational principle to the configuration average
energy and include relativistic corrections, namely the
Blume-Watson spin-orbit, mass-velocity and the one-body Darwin terms.
The eigenvalues and eigenstates thus obtained
are used to compute the wavelength and A-value for each possible transition.
Autoionization rates are calculated in a perturbation theory scheme
where the radial functions of the initial and
final states are optimized separately, and configuration interaction is
accounted for only in the autoionizing state. Configuration interaction
is taken into account among the following configurations:
,
,
and
where
stands for a hole in
the
subshell and
represents all possible
distributions of M electrons among the
and
shells,
M ranging from M=0 in Fe IX to M=7 in Fe II.
Configurations
have been neglected
because their contribution do not affect the final results.
Given the complexity of
double-vacancy
channels in ions with an open 3d shell, the level-to-level computation of the Auger rates
with HFR and AUTOSTRUCTURE proved to
be intractable. However, average values can be
used for all the levels taking advantage of the near constancy of
the total Auger widths in ions for which the KLL channels reduce
the outer configuration to a spectator (see Paper III).
Therefore, we employ the formula given in Palmeri et al. (2001) for the
single-configuration average (SCA) Auger decay rate
We have focused our calculations on the Fe K-vacancy states populated by
photoionization of the ground state of the parent ion
The radiative and Auger decay manifolds of a K-vacancy configuration
can be outlined as follows:
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(3) |
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(4) |
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(5) |
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(6) | |
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(7) | |
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(8) | |
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(9) |
It has also been numerically verified that the participator Auger
channels (KMM(p) and KLM(p)) contribute less than one percent to
the total Auger widths, and hence, they have not been taken into
account. Of primary interest in the present work is the branching
ratios of the K,
K
,
KMM, KLM and KLL channels and
their variations with electron occupancy N.
![]() |
Figure 1:
Comparison of centroid wavelengths for a)
K![]() ![]() ![]() |
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Table 1:
Comparison of centroid wavelengths (Å) for the K
and
K
unresolved transition arrays in Fe ions with
.
The HFR wavelengths have been
weighted with the fluorescence yields. Experimental wavelengths for
Fe X (N=17) are from Decaux et al. (1995) and for solid-state iron
from Hölzer et al. (1997).
Centroid wavelengths for the K
and K
unresolved
transition arrays (UTAs) computed with HFR are presented in
Table 1, including also a comparison with experiment.
Since the calculated
fine
structure splittings range from
0.9 eV
in Fe II to
1.2 eV in Fe IX, they are not
resolved due to a natural line width of
1.2 eV; consequently,
the K
UTA wavelength splittings for these ions are not listed.
For the K
and K
lines, it can be seen that
the agreement with the solid-state measurements by Hölzer et al. (1997)
(
0.5 mÅ) is somewhat better than that with the EBIT
results for Fe X (Decaux et al. 1995) of within 2 mÅ, and the
slight blueshift with increasing N predicted by HFR is
consistent with experiment. A small redshift with N is also
found for the K
array. On the other hand, as shown in
Fig. 1, the present findings contrast with the steeper
redshift for both UTAs obtained from the data by Kaastra & Mewe (1993).
It is worth noting that Kaastra & Mewe (1993) never intended to provide accurate
wavelengths.
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Figure 2:
Comparison of K![]() ![]() ![]() |
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Figure 3:
Comparison of Auger rates for Fe ions with
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In Table 2, K/K
intensity ratios are
tabulated for different ionization stages. Two cases have been considered:
HFR1, only the decay lines from the K-vacancy levels populated by the
photoionization of the respective ground state are included; and HFR2, all the
transitions from the levels belonging to the
complex are taken into account. Noticeable differences in the ratios from
these two cases may be appreciated indicating sensitivity to the excitation
mechanism. The HFR2 ratio for Fe II is closer to the Dirac-Fock
value of Scofield (1974), who also considered all the K-vacancy states, and
to the solid-state experiments (Williams 1933; Salem & Wimmer 1970; Hölzer et al. 1997; McCrary et al. 1971).
In Fig. 2, theoretical and experimental K/K
intensity
ratios are plotted as a function of electron number. Most experimental ratios
(Hansen et al. 1970; Salem et al. 1972; Rao et al. 1986; Berényi et al. 1978; Slivinsky & Ebert 1972) have been scaled down by 8.8%
in order to extract the radiative-Auger (5%) and K
(3.8%) satellite
contributions from the K
UTA which theory does not include
(Verma 2000). The value quoted in Perujo et al. (1987) does not take into
account the blend with the K
satellite and has been corrected
accordingly. With the exception of the values by Kaastra & Mewe (1993), theory
predicts a decrease of the ratio with N, and the theoretical scatter
is comparable with that among the solid-state experiments of just under 20%.
The computed results by HFR, AUTOSTRUCTURE and Jacobs & Rozsnyai (1986)
for N=25 are in good agreement with the bulk of the experimental values
(Hansen et al. 1970; Salem et al. 1972; Rao et al. 1986; Perujo et al. 1987; Berényi et al. 1978; Slivinsky & Ebert 1972). Hölzer et al. (1997) mention a
possible systematic deviation in one of their corrections
to explain the discrepancy of their data with other measurements.
On the other hand, the Dirac-Fock ratios by Scofield (1974) and Jankowski & Polasik (1989)
at N=25 appear significantly higher. We have therefore proceeded to
verify these values by using the same code ( MCDF-SAL) as in Jankowski & Polasik (1989),
and as shown in Fig. 2, they are accurately reproduced; moreover,
a similar decrease in the ratio with N is also obtained with this method.
The spread of the different data sets in this comparison indicates a probable
accuracy of our HFR transition probabilities of
10%.
Table 2:
Comparison of HFR K
/K
ratios
for Fe ions (
)
with experiment and previous theoretical
estimates.
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Figure 4:
Comparison of K-shell fluorescence yields, ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 5:
Simulations carried out near 6.4 keV with the XSTAR modeling
code for several values of the ionization parameter ![]() |
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A decrease with N is also predicted by HFR for the Auger KLM/KLL and
KMM/KLL ratios (see Fig. 3). For Fe II, present results
are in excellent accord with the measurements of Kovalík et al. (1987) and other
theory (Chen et al. 1979; Bhalla & Ramsdale 1970) but somewhat higher than the older experimental
estimate of Mehlhorm & Albridge (1963). The total K-shell fluorescence yields, ,
for Fe ions with
are presented in Fig. 4.
In both HFR and AUTOSTRUCTURE data sets, the fluorescence yields have
been computed for fine-structure K-vacancy levels:
In order to evaluate the impact of the new atomic data on Fe K-line
modeling, the data sets generated in the present work and those in
Papers I-III have been included in the XSTAR modeling code
(Kallman & Bautista 2001). Runs for different ionization parameters, ,
are shown in
Fig. 5. The other parameters have been assigned the following values:
cosmic abundances; a gas column density of 1016 cm-2;
a gas density of 1012 cm-3; an X-ray source luminosity of 1038 erg/s;
a power-law index of 1; and energy bins (or channel widths) of 1 eV.
In Fig. 5, one clearly sees that the UTA centroid
is redshifted when
goes from 0.001 to 1 and then blueshifted for
.
The shape of the UTA changes also considerably for
where the ionization
balance favors the first and second row ions.
Electronic Tables 3, 4 list radiative and Auger widths for 295 energy levels; and wavelengths, A-values and fluorescence yields for 396 transitions.
Following the findings of our previous study on the second-row iron ions (Paper III), the HFR package (Cowan 1981) has been selected to compute level energies, wavelengths, decay rates and fluorescence yields for the K-vacancy states in Fe II-Fe IX. The calculations have focused states populated by ground-state photoionization. Due to the complexity of the level-to-level Auger calculations, we have employed a compact formula (Palmeri et al. 2001) to compute Auger widths from the HFR radial integrals.
The HFR centroid wavelengths for the K
and K
UTAs
in Fe II reproduce the solid-state measurements (Hölzer et al. 1997) to
better than 1 mÅ. Moreover, the redshift predicted by HFR for
the K
lines in species with higher ionization stage is in
accord with the EBIT wavelengths in Fe X (Decaux et al. 1995) thus
contradicting the previous trend specified by Kaastra & Mewe (1993).
We have also carried out extensive comparisons of different HFR
branching ratios, namely K
/K
,
K
/K
,
KLM/KLL, KMM/KLL and
,
with other theoretical and experimental
data. The present ratios for Fe II are in good agreement with the
solid-state measurements, and the K
/K
ratio has been
found to be sensitive to the excitation mechanism. It has been possible
from these comparisons to estimate an accuracy of
10% for the
HFR transition probabilities.
The new atomic data sets for the whole Fe isonuclear sequence
that have emerged from the present project are bound to provide a more
reliable platform for the modeling of Fe K lines. Preliminary
simulations of the emissivity of a photoionized gas with
XSTAR (Kallman & Bautista 2001) have shown K line profiles and
wavelength shifts that are sensitive to the ionization level of
the gas. Further work will therefore be concerned with improving
diagnostic capabilities by means of accurate K-shell
photoionization and electron impact excitation cross sections.
Acknowledgements
PP acknowledges a Research Associateship from University of Maryland and CM a Senior Research Associateship from the National Research Council. This work is partially funded by FONACIT, Venezuela, under contract No. S1-20011000912.