A&A 446, 1185-1190 (2006)
DOI: 10.1051/0004-6361:20053813
B. M. McLaughlin^{1} - A. Hibbert^{1} - M. P. Scott^{1} - C. J. Noble^{2} - V. M. Burke^{2} - P. G. Burke^{1}
1 - School of Mathematics and Physics, Queen's University of Belfast,
Belfast BT7 1NN, UK
2 -
Computational Science and Engineering Department,
CCLRC Daresbury Laboratory, Keckwick Lane,
Daresbury, Warrington WA4 4AD, UK
Received 11 July 2005 / Accepted 26 September 2005
Abstract
Electron-impact excitation collision strengths of
the Fe-peak element Fe IV are calculated in the close-coupling
approximation using the parallel R-matrix program PRMAT.
One hundred and eight LS - coupled states arising from the ,
and
configurations of Fe IV,
are retained in the present calculations. Accurate multi-configuration
target wavefunctions are employed with the aid of
electron promotions and a
correlation orbital.
The effective collision strengths required
in the analysis of astrophysically important
lines in the Fe IV spectra, are obtained by averaging the electron collision
strengths for a wide range of incident electron energies,
over a Maxwellian distribution of velocities.
Results are tabulated for forbidden transitions between the
,
and the
manifolds
for electron temperatures (
in degrees Kelvin) in the range
that are applicable to many
laboratory and astrophysical plasmas.
The present results provide new results for
forbidden lines in the Fe IV spectrum studied here.
Key words: atomic data - atomic processes
For electron impact excitation of V-like ions (Mn III, Fe IV, Co V and Ni VI), new astronomical observations are revealing the presence of trace metals in many types of astronomical objects. High-dispersion IUE observations of the brightest of the hot stars showed absorption features from photospheric Fe and Ni (Holberg et al. 1994); identifications included V-like Fe and Ni ions; i.e. Fe IV and Ni VI lines. From these observations Ni became the second iron group element to be positively identified in the photosphere of the hot DA white dwarfs. Adelman and co-workers (Adelman et al. 1994) have analysed the abundances of elements such as Cr, Mn, Fe, Co and Ni in early type stars from IUE high-dispersion spectrograms. Ruiz-Lapuente et al. (1995) reviewed observations of Type Ia supernovae at late phases, which range from the UV to the infrared region. Calculations of spectra of different Type Ia models have shown the need for further computations of collision strengths for forbidden transitions of Fe I-IV (Ruiz-Lapuente et al. 1995). In supernovae 1992A among the identified forbidden transitions giving rise to UV emission lines in Hubble Space Telescope (HST) spectra are the following V-like ions Fe IV (-), Fe IV (-) and Mn III (-). In the Orion nebulae, the first detection of an Fe IV line in a H II region has been made using the Goddard High-Resolution Spectrograph on the Hubble Space Telescope, where the flux of the [Fe IV]( ), Å line has been measured (Rubin et al. 1997). Fe IV lines have also been detected in symbiotic nova such as RR TELESCOPII (RR Tel) based on International Ultraviolet Explorer (IUE) observations (Penston et al. 1983) and more recently by the telescope of the Cerro Tololo Inter-American Observatory (McKenna et al. 1997). A recent reappraisal of the chemical composition of the Orion nebulae (Estan et al. 2004) based on Very Large Telescope (VLT) UVES echelle spectromphotometery illustrated vividly the need to have accurate atomic data on several of the Fe-peak elements, namely low ionization stages of Fe, Ni and Co. Furthermore, accurate electron impact excitation rates for low ionization stages of Fe-ions (Fe II-Fe V) are required for non-LTE calculations in hot stars atmospheres (Becker & Butler 1995) and winds. The present work on the Fe-peak element Fe IV attempts to provide accurate atomic data suitable for relevant applications.
(1) |
(2) |
(3) |
(4) |
(5) |
For many applications the rate coefficient, in cm^{3} s^{-1}, is
required as a function of electron temperature.
The rate coefficient can be determined for transition
corresponding to de-excitation (when E_{j} > E_{i})
from the effective collision strength
via the relationship (Eissner et al. 1969),
(6) |
(7) |
(8) |
Figure 1: Observed Fe IV levels in cm associated with the three configurations , and from the NIST tables. All of the levels of the manifold are observed whereas only 23 of the 24 levels for and 67 of the 68 levels of the manifolds areobserved. | |
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As an indication of the complexity of the problem for electron-impact collisions with Fe IV ions we show in Fig. 1 the number of LS - coupled target states which arise from the three configurations; , and . We note that the sheer size of the problem doubles (both in the number of states and coupled channels) by including those states arising from the inclusion of the configuration, none of which have been observed (cf. NIST tables, http://physics.nist.gov/cgi-bin/AtData/main_asd, Sugar & Corliss 1985). These states were omitted as structure calculations indicated they lay sufficiently higher than the rest. In our work we retained in the R-matrix expansion all 108 LS-coupled states which arise from the , and configurations of Fe IV. Our recent investigation on this complex ion dealt with transitions within the manifold (McLaughlin et al. 2005b). In that work is was seen that with the inclusion of suitably correlated target and scattering wavefunctions the effective collision strengths were enhanced by a factor of two, particularly at temperatures below 100 000 Kelvin. The main thing to note from our recent work on Fe IV was that it was essential to include the two electron promotions in the target wavefunctions in order to have an adequate representation of the target energies (Hibbert et al. 2004; Quintet & Hansen 1995). It should be pointed out that the number of coupled scattering channels and target states would vastly increase if fine structure effects are included in the calculation as does the computational complexity. Prior to our investigation on electron impact excitation of Fe IV (McLaughlin et al. 2004,2005b), previous work (Sawey & Berrington 1992; Berrington & Pelan 1995a,b; Zhang & Pradhan 1997), included only a limited number (5 and 49 states respectively) of the 108 states which may arise from the three Fe IV configurations , , in scattering calculations. We note that in our work we include all of the terms which can arise from each of the configuration which is necessary to obtain reliable results.
Table 1: Term energies (Rydbergs) for the 108-states of Fe IV relative to the state. Theoretical energies (7 configuration model) are compared with observed values and the theoretical adjustment to reproduce experimental values.
In the current study, results are presented for forbidden transitions between the manifolds and . As in our recent work (McLaughlin et al. 2005b) on this complex ion, the 108 states of Fe IV are represented by multi-configuration interaction wavefunctions in the corresponding close-coupling calculations. Hartree-Fock orbitals of the ground state configuration augmented with two spectroscopic orbitals namely, the 4s and 4p and correlation orbital are employed. The 1s, 2s, 2p, 3s, 3p and 3d orbitals used were taken from the the work of Clementi & Roetti (1974). The additional orbitals used are determined from the structure codes CIV3 (Hibbert 1975). Using a seven configuration model; , , , , , and we found that this gave a compact and adequate CI representation for all of the 108 levels of Fe IV arising from the , and configurations (see Table 1), with term energies differing from experiment by approximately a few percent. These compact CI target wavefunctions for Fe IV were then used in our scattering calculations. All the cross section and effective collision strengths were obtained with this seven configuration model; , , , , , and as outlined in our recent work. The relevant collision calculations were performed with the PRMAT suite of codes (Sunderland et al. 1999, 2002; Noble 2004; Burke et al. 2004; and Noble et al. 2005). Cross section calculations for total scattering angular momentum for all spin symmetries 2S+1 equal to 1, 3, 5 and 7, i.e. for singlets, triplets, quintets and septets were then carried out for both odd and even parities of the collision system. Further details of the collision calculations can been found in our recent work (McLaughlin et al. 2005b) on this system and will not be expanded upon here.
Table 1 gives the theoretical energies of the 108 states included in the present approximation (7 configuration model) and includes the adjustment required to the theoretical values so as to reproduce the available observed values (NIST tables, http://physics.nist.gov/cgi-bin/AtData/main_asd, Sugar & Corliss 1985). It should be pointed out that some of the 108 states of Fe IV included in the present approximation have not been observed but are present due to LS-coupling and they will play an important role as intermediate states in the calculation. Hence, where no observed values are available for a specific term we have made a similar adjustment to its theoretical value as that made to the ground-state term. The same labelling of the states is used to identify transitions from state i to state j for the effective collision strengths tabulated in Tables 2-17.
In Figs. 3-6 we illustrate a sample of our effective collision results for transitions between manifolds obtained from the 7 configuration model. Figure 3 is for the transitions and , Fig. 4 for the transitions and . Whereas Fig. 5 is for the transitions and and finally Fig. 6 is for the transitions and .
In Figs. 3 and 4 we include for comparison purposes the Fe IV effective collision
results from the calculations of Zhang & Pradhan (1997), averaged over fine-structure levels.
From this comparison it is seen that our present effective collision results
for non-spin changing forbidden transitions between manifolds give a major
enhancement of the rates at all temperatures, whereas for the spin-changing forbidden transitions
our present results are comparable to the findings of Zhang & Pradhan (1997).
Our recent findings on Fe IV effective collision strengths for transitions
within the
manifold, McLaughlin et al. (2005b) with the calculations
of Zhang & Pradhan (1997), showed that rates were dramatically
increased at temperatures below about 100 000 Kelvin.
Therefore given our recent results (McLaughlin et al. 2005b) together with the
present findings clearly indicates that the effecive collision strengths data
from our calculations should be used in preference to those available
in the literature for applications.
Figure 2: Fe IV collision strength for the scattering symmetry as a function of scattering energy. The scattering energy is given in scaled Rydberg units, where for Fe IV the effective charge z= N-Z =3. The results from the 7 configuration model B, allow for the important core-excitations in the target and scattering wavefunctions whereas those from the 3 configuration model A do not. Note, model B gives strong resonance enhancement at threshold (Z) and in regions of higher lying thresholds (X). The background collision strength (Y) is also seen to be enhanced. | |
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Figure 3: Fe IV effective collision strength for a sample of transitions between the ground-state to low-lying states in the manifolds. The present results were obtained with the 7 configuration model (Model B) which allows for the important core-excitations in the target and scattering wavefunctions. ZP are the results for the same transitions from the work of Zhang & Pradhan (1997) averaged over fine-structure levels. | |
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Figure 4: Fe IV effective collision strength for a sample of transitions between the ground-state to low-lying states in the manifolds. The present results were obtained with the 7 configuration model (Model B) which allows for the important core-excitations in the target and scattering wavefunctions. ZP are the results for the same transitions from the work of Zhang & Pradhan (1997) averaged over fine-structure levels. | |
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Figure 5: Fe IV effective collision strength for a sample of transitions between the excited state and low-lying states in the manifolds. The present results were obtained with the 7 configuration model (Model B) which allows for the important core-excitations in the target and scattering wavefunctions. | |
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Tables 2-17 present all of the non-zero effective collision strengths for the forbidden transitions between the manifolds; i.e., and , over the temperature range 2000-1 000 000 degrees Kelvin. All of the Fe IV effective collision strength data from Tables 2-17 are available electronically from CDS.
Figure 6: Fe IV effective collision strength for a sample of transitions between the excited state and low-lying states in the manifolds. The present results were obtained with the 7 configuration model (Model B) which allows for the important core-excitations in the target and scattering wavefunctions. | |
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Acknowledgements
Financial support from the UK Particle Physics and Astronomy Research Council (PPARC), under the auspices of a UK Rolling Grant (PPA/G/O/2002/00004) is gratefully acknowledged. The computations were carried out on the HPCX, IBM-Power 4 (SP4), at Daresbury Laboratory, UK, the Cray T3E-1200 and SGI/Origin 2000 CSAR HPC facilities at Manchester University in the UK.