A&A 483, 339-359 (2008)
DOI: 10.1051/0004-6361:20079333

Extended analysis of the Eu III spectrum

J.-F. Wyart¹ - W.-Ü L. Tchang-Brillet² - S. S. Churilov³ - A. N. Ryabtsev³

1 - Laboratoire Aimé Cotton (CNRS UPR3321), bâtiment 505, Université Paris-Sud, 91405 Orsay Cedex, France
2 - Laboratoire d'Étude du Rayonnement et de la Matière en Astrophysique (LERMA), Observatoire de Paris-Meudon, Université Pierre et Marie Curie-Paris 6, 92190 Meudon, France
3 - Institute of Spectroscopy, Russian Academy of Sciences, 142190 Troitsk, Moscow region, Russia

Received 27 December 2007 / Accepted 5 February 2008

Abstract
Aims. We create an Eu  III new atomic data set for interpreting the spectra of chemically peculiar stars by an extended analysis of the doubly-ionized europium.
Methods. We classified Eu  III spectral lines from a laboratory wavelength list with the support of energy and transition probability predictions in the Racah-Slater approach, using the Cowan codes and generalized least-squares fit (GLS) studies along the sequence of doubly-ionized lanthanides.
Results. More than thirty new levels and ninety classified lines are established in Eu  III. Improved prediction of the Eu  III spectrum was achieved by using scaling factors for ab initio energy integrals, as well as effective configuration interaction parameters supplied by GLS studies. Transition probabilities, oscillator strengths, and Landé g-factors are calculated for the lines in the region 2000-9995 Å.

Key words: atomic data - stars: atmospheres - stars: chemically peculiar - stars: variables: general

   
1 Introduction

The spectra of doubly-charged lanthanide ions are of current interest for modelling stellar atmospheres. Their importance in stellar spectra and the relevant advances in laboratory studies have been reviewed recently (Wahlgren 2002; Biémont & Quinet 2003). The spectrum of doubly-charged europium Eu  III  is especially important among the third spectra of the rare-earth elements (REE), since europium shows prominent overabundances in the atmospheres of hot magnetic chemically peculiar stars (CP2) where Eu²⁺ is its dominant ionization stage (Ryabchikova et al. 1999). The ground configuration of Eu  III is 4f⁷. For this ion, Sugar & Spector (1974) published a list of 890 observed lines but only one third of them were classified. These lines were transitions involving nine levels of 4f⁷ and ninety-six levels of the 4f⁶(⁷F)5d, 4f⁶(⁷F)6s and 4f⁶(⁷F)6p sub-configurations built on the lowest term ⁷F of the 4f⁶ core. Several levels with low J values, assumed to give rise to weak transitions, were missing in these sub-configurations.

First estimates of the oscillator strengths in Eu  III spectrum were made by Ryabchikova et al. (1999) from the spectra of some CP2 stars. Using europium abundances obtained from Eu  II transition at 6645.11 Å and assuming local thermodynamic equilibrium (LTE), they were able to derive ``astrophysical'' oscillator strengths for four Eu  III lines. Later, Mashonkina et al. (2002) calculated oscillator strengths and transition probabilities for the 4f⁷ - (4f⁶5d + 4f⁶6s) transitions in Eu  III using the Cowan (1981) code. Relativistic Hartree-Fock (HFR) energies were modified by a fitting to the experimental ones but transition integrals were kept at their HFR values in the calculations. These calculations led to transition probabilities lower than the astrophysical transition probabilities by about two orders of magnitude. However, in a comparison with the lifetime measurements of the 5d ⁸P term levels (Zhang et al. 2000; Den Hartog et al. 2002), it was concluded that the calculated absolute transition probabilities could be overestimated by a factor of 3. Later, calculations of the Eu  III spectrum were performed by Quinet & Biémont (2003). In addition to the approach by Mashonkina et al. (2002), the core polarisation effects were included in the calculations leading to a modification of ab initio transition integrals. As a result, about 10% deviation of calculated lifetimes for the 5d ⁸P term levels from the most accurate measurements (Den Hartog et al. 2002) was achieved. Calculated by Quinet & Biémont (2003), oscillator strengths for about 900 lines can be found in the DREAM data base created at Mons University (Biémont et al. 1999).

Table 1: Additional new classifications for Eu  III.

We present here the results of new calculations of the Eu  III spectrum. Improved predictions of the energy levels and relative transition probabilities were performed using scaling factors for HFR integrals and a set of effective parameters accounting for the interactions with the far lying configurations obtained from the generalized least-squares fit (GLS) studies along the sequence of doubly-ionized lanthanides. An absolute scale of transition probabilities was established by scaling of transition integrals by the factors extrapolated from the lanthanide ion spectra where lifetime measurements are available. Starting from the known levels and unclassified lines of Sugar & Spector (1974) and based on our calculations of transition probabilities, new energy levels of Eu  III were determined.

Table 2: Newly found energy levels of Eu  III.

   
2 Results and discussion

As mentioned above, a limited number of levels are known in the ground 4f⁷ configuration and the 4f⁶(⁷F)5d, 4f⁶(⁷F)6s, and 4f⁶(⁷F)6p sub-configurations built on the lowest term ⁷F of the 4f⁶ core in the Eu  III spectrum. In the parametric Racah-Slater approach the configurations 4f^N (N = 6 and 7) are described at the first order of perturbation theory by F^k(4f, 4f) Slater integrals (k = 0, 2, 4, 6) to which effective parameters are added for considering the second-order configuration interaction effects, usually the $\alpha L(L+1) +\beta G(G2) + \gamma G$(R7) correction, accounting for double excitations (Rajnak & Wybourne 1963). The spin-dependent interactions are limited to the spin-orbit operator. The F^k(4f, nl) and G^k(4f, nl) Slater integrals are added in the 4f⁶nl configurations. Second-order configuration interactions for the 4f-nl space in the Cowan code (Cowan 1981) are treated using F^k(4f, nl) and G^k(4f, nl) Slater integrals of illegal ranks as parameters. The most important interactions are expected with the levels of the doubly-excited group 4f⁵ (5d², 5d6s, 6s²). According to Brewer (1971), they should be located above 102 000 $\pm$ 6000 cm^-1 and therefore their influence can be treated in effective configuration interaction parameter approach. But direct application of the parametric Racah-Slater method could not be provided for a reliable interpretation of the high-lying new energy levels in Eu  III  since the electrostatic energy parameters could only be determined from nine levels of three terms in the 4f⁷ configuration and only from one parent term ⁷F in the 4f⁶nl configurations. However, the predictions of the 4f^N high levels could be improved with the support of semi-empirical regularities within the Ln  III period (Ln is a common name for all lanthanides), i.e. the N-dependence of radial integrals along the period, similar to Shadmi's simultaneous treatment of several iron-group elements of the same ionic charge (Shadmi et al. 1968). This GLS fit method had already been applied to the 4f^N-15d and 4f^N-16s configurations in the second, third, and fourth spectra (Wyart & Bauche-Arnoult 1981). Previous works for the opposite parity had also shown its relevance for the 4f^N-16p (Wyart 1978) and 4f^N (Wyart 1977) configurations. More recently, the first analysis of Dy  III (Spector et al. 1997) and an extension in the Er  III analysis (Wyart et al. 1997) brought additional levels, so we updated the GLS studies for 4f^N and 4f^N-16p. Detailed theoretical results will be reported in another publication.

Introduction of an extended set of effective parameters ( $\alpha, \beta$, and $\gamma$ in the 4f^N configurations and F¹(4f, 5d) in 4f⁶5d) with values predicted from GLS studies, as well as GLS scaling factors for electrostatic parameters resulted in more accurate predictions of the Eu  III spectrum than in previous calculations by Mashonkina et al. (2002). With these calculations, it was possible to extend the analysis of Eu  III spectrum using the list of unclassified lines from the publication by Sugar & Spector (1974).

Table 3: Classified lines of the level newly found at 83928.16 cm^-1 and from the level at 83959.93 cm^-1.

	Figure 1: Upper panel: comparison of the ratios of transition probabilities calculated in this work and taken from the DREAM database for all 34 lines of the 4f7-4f65d transitions listed in DREAM in the region 4600-9660 Å.  The lower panel shows the same, but for the 4f65d-4f66p (filled squares) and 4f66s-4f66p (hollow squares) lines in the regions 2000-2100 Å and 3000-3100 Å.
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A total of ninety-three new classifications, extending those of Sugar & Spector (1974), are collected in Table 1. The general agreement between line intensities and gA transition probabilities supports the classifications. The present calculations helped to derive new levels given in Table 2. Among those levels are

-

two levels that make the sub-configuration 4f⁶(⁷F)6p now complete;

-

eight out of the nine levels of 4f⁶(⁷F)5d that were still missing (the level 4f⁶5d ⁶F_1/2 should be found from only one transition near 2501 Å where several lines are present);

-

twenty seven levels of 4f⁶5d belonging to parent terms other than ⁷F of the 4f⁶ sub-configuration with energies in the range 64 800-75 000 cm^-1 decaying to two or three levels of the terms 4f^{7 6}I and ⁶P;

-

the level 4f^{7 6}D_9/2 determined from its three most probable transitions in the scheme of known levels;

-

the level 4f^{7 4}₄G, where the subscript is a seniority number, whose identification needs some discussion.

A search from unclassified lines (Sugar & Spector 1974) had led to a new level at 83 928.16 cm^-1 with unambiguous J-value of 11/2 based on transitions to some sextets and octets of the 4f⁶(⁷F)5d configuration. In its vicinity, only a 4f⁶(⁷F₆)6p ⁸D_11/2 was predicted, but had already been found by Sugar & Spector (1974) at a well-established value of 83 959.93 cm^-1 with three first components in LS coupling 76% ⁸D, 10% ⁶F, and 8% ⁸F. Therefore, the unique plausible identification of the new level at 83 928.16 cm^-1, was some high-lying term of the ground configuration 4f⁷. However a study of the 4f⁷ configuration, in which parameters were either fitted from ten known levels or fixed to values derived from GLS studies, shows that the high-lying terms of 4f⁷ comprise mostly doublets and a few quartets and should not decay to the sextets and octets of the 4f⁶(⁷F)5d configuration. The 25th to 27th levels with J=11/2 in Eu  III 4f⁷ are predicted at 79 512, 83 769 and 85 412 cm^-1 which indicates that the Eu  III level at 83 928 cm^-1 is quite likely the 26th one. It must be 4f^{7 4}₄G with three main LS components 44% ⁴₄G, 22% ⁴₂G, and 8% ²H. Comparison of the classified lines for the two levels at 83 928 cm^-1 and 83 959 cm^-1 listed in Table 3 suggests that both levels have the same trends in branching ratios and that the level at 83 928 cm^-1 borrows its radiative properties from its neighbour. Such a mixing behaviour, in the absence of a common LS term in the eigenfunctions, can only come from higher order CI effects, and it is usual, in these cases, that the parametric method fails to reproduce it adequately. Indeed, the present calculations of 4f⁷ + 4f⁶6p and 4f⁶5d + 4f⁶6s by means of the Cowan codes (Cowan 1981) lead to a configuration-sharing that underestimates the transition probabilities for the level at 83 928 cm^-1. Consequently the theoretical radiative data for this level should not be considered as reliable for diagnostic purposes.

Table 4 lists energy parameters of known configurations in Eu  III obtained from the fitting with all known levels except for the questioned ones. In a comparison with Mashonkina et al. (2002), parameter $\gamma$, with a fixed value taken from GLS studies, was added to the set of effective parameters of the f^N shells, along with electrostatic direct interaction parameter of illegal rank F¹(4f, 5d) in the 4f⁶5d configuration. Parametric calculations of the 4f⁶6p configuration were not published by Mashonkina et al. (2002), but reported by Quinet & Biémont (2003) using only electrostatic Slater and spin-orbit parameters. In our present calculations of the 4f⁶6p configuration, the same set of effective parameters as in 4f⁶5d was used. An increased number of known terms in the 4f⁷ and 4f⁶ shells permitted all F^k(4f, 4f) (k=2, 4, 6) parameters to be fitted in the 4f⁷ and 4f⁶5d configurations. In the 4f⁶6p and 4f⁶6s configurations where the levels of only the ⁷F parent term are known, these parameters were fixed at Hartree-Fock ratios to the same parameters respectively in 4f⁷ and 4f⁶5d. The effective parameters $\alpha$, $\beta$, and $\gamma$ were fixed at the predetermined values, whereas F¹(4f, nl) were free at the fitting and converged to the well-defined values. In result, 48 even levels were fitted with 11 parameters and 97 odd levels with 15 parameters with the average deviations 26 and 72 cm^-1, respectively.

	Figure 2: Comparison between the observed spectrum of HD 144897 in the region of Eu  III $\lambda$ 7750.59 Å line (double line) and synthesized spectrum with the atomic parameters derived in the present work (full line).
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Table 4: Fitted (FIT) and Hartree-Fock (HFR) energy parameters (cm^-1) of the 4f⁷+4f⁶6p and 4f⁶5d+4f⁶6s configurations of Eu  III and their ratios.

An analysis of the data for lanthanide atoms and first ions (Komarovskii 1991) has shown that ab initio calculations usually overestimate the transition probabilities by two or more times as was also the case in the calculations by Mashonkina et al. (2002), where HFR values were adopted for the dipole matrix elements. Substantial improvement in the calculations can be achieved by taking the core polarisation effects into account. But this technique does not work for transitions 4f^N-4f^N-15d because of a collapse of the 4f orbital inside the 5s²5p⁶ closed subshells (Biémont et al. 2001). Therefore, Quinet & Biémont (2003) calculated 4f⁶6p-4f⁶(5d + 6s) transition probabilities accounting for core polarisation, while a scaling of HFR dipole matrix element was applied for 4f⁷-4f⁶5d bringing into agreement calculated and measured lifetimes (Zhang et al. 2000) for the 4f⁶(⁷F)⁸P levels. In the present work, we corrected the HFR values of the transition integrals calculated by means of the RCN code by Cowan (1981) using scaling factors as an effective treatment of core polarisation effects for all transitions. The chosen scaling factors are 0.55 for the 4f-5d transitions and 0.86 for the 6s-6p and 5d-6p transitions. The first scaling factor agrees with the Eu  III experimental lifetimes measured by Zhang et al. (2000) and Den Hartog et al. (2002) (same as Quinet & Biémont 2003), while the second one fits measured values of the lifetimes for the 5d-6p transitions in the second spectra of several lanthanides, for example, in Nd  III (Zhang et al. 2002a; calculations by Ryabchikova et al. 2006) and in Dy  III (Zhang et al. 2002b; calculations by the present authors).

The results of our calculations for the known levels are presented in Table 5, which can be found after the references. For each transition between 2000-9000 Å, we give wavelength calculated from the experimental level energies (Ritz wavelength); weighted transition probability $g_{\rm u}$A (higher than 10⁵ s^-1 for 2000-3360 Å and higher than 10⁴ s^-1 for 3360-9000 Å region) and logarithm of the oscillator strength $\log(g_{\rm l}f)$ (where $g_{\rm u}$ and $g_{\rm l}$ are the statistic weights of the upper and lower levels, respectively); cancellation factor CF; energy of the lower level with its parity, g-factor Landé, level designation and J-value; the same for the upper level. A comparison of the results of our calculations for transition probabilities with those by Quinet & Biémont (2003) is shown in Fig. 1.

In the upper panel, the ratios of transition probabilities calculated in this work ( $g_{\rm u} A_{\rm pres}$) and by Quinet & Biémont (2003) ($g_{\rm u}$ $A_{\rm DREAM}$) for all 34 lines of the 4f⁷-4f⁶5d transitions listed in DREAM for the region 4600-9660 Å are given as a function of their transition probabilities. The same quantities are shown in Fig. 1 (lower panel) but for the 4f⁶5d-4f⁶6p and 4f⁶6s-4f⁶6p lines, taken from the regions 2000-2100 Å and 3000-3100 Å. Very good agreement for the strong lines of the 4f⁶5d-4f⁶6p and 4f⁶6s-4f⁶6p transitions implies that core polarisation approach and a scaling of the transition integrals are equivalent in the calculation of the transition probabilities. Good agreement for the strong lines in the 4f⁷-4f⁶5d case is expected due to using the same approach in treating the transition integrals in both calculations. Substantial differences in calculations are revealed for weak lines of all transition arrays. It should be noted that all lines with different $g_{\rm u} A$ values in our calculations and those in Quinet & Biémont's (2003) have small cancellation factors CF < 0.2 (for a definition of CF see Cowan 1981, p. 432), and therefore the results of calculations depend critically on the accuracy of calculated composition of the levels in intermediate coupling. We hope that by using a larger set of energy parameters and having a larger number of levels for the fitting, our values for the transition probabilities for weak lines are more reliable. Calculated Landé g-factors listed in Table 5 are in good agreement with calculations by Quinet & Biémont (2004). More than a 5% difference exists only for two levels: 38 050.11 cm^-1 4f⁶5d J=0.5 (19%) and 84 510.34 cm^-1 4f⁶6p J=1.5 (12%). It is interesting to note that the g-factor of the first level is very sensitive to the calculation scheme. It has the value 2.568 in this work but 2.072 and 1.774 respectively in the calculations by Quinet & Biémont (2004) and Mashonkina et al. (2002). It has to be noted further that in these two publications an even level at 39574.00 cm^-1 is listed by mistake. Indeed, it was a value calculated by Mashonkina et al. (2002). This level was found only in this work with the value 39 361.13 cm^-1 (Table 2).

3 Astrophysical applications

Table 5 contains 1150 transitions only between experimentally known levels of Eu  III. These data are very important for the abundance study of the rare-earth elements and, in particular, non-equilibrium line formation in the atmospheres of the chemically peculiar (Ap) stars (see Mashonkina et al. 2002, 2005). One of the newly classified Eu  III lines, $\lambda$ 7750.59 Å, has already been identified and used in Eu abundance determination in Ap star HD 144897 (Ryabchikova et al. 2006), supporting +5 dex Eu overabundance in its atmosphere. This line, together with four other strongest Eu  III lines in the red spectral region at 6666.347, 6976.028, 7221.838, and 8379.183 Å, are the indicators of the Eu anomalies. Moreover, spectroscopic observations of the sharp-lined stars with strong magnetic fields help a lot in justifying the spectral line classification via the comparison of the resolved Zeeman patterns. Figure 2 shows a comparison between the observed and synthesized spectra for HD 144897 whose surface magnetic field is 8.8 kG. (For details of the observations and calculations see Ryabchikova et al. 2006.) Although Eu  III $\lambda$ 7750.59 Å is weak, a fairly good agreement between the observed and calculated spectral features supports the line classification and the calculated atomic parameters.

For some applications, such as a search for new levels, a full account of the line opacities in model atmosphere calculations, or non-LTE calculations (Mashonkina et al. 2002), an extended list of transitions including predicted levels can be a big help. Therefore we made a list of 23 827 lines in the region 2000-9995 Å available with transition probabilities for all transitions from the levels below 91 000 cm^-1 on the websites http//das101.isan.troitsk.ru/files/spectra/Eu_III and http://molat.obspm.fr.

   
4 Conclusions

Recommended scaling factors of HFR integrals and average values of the two-body effective parameters derived by means of GLS techniques applied to the Ln  III spectra are shown to be useful in the calculation of the Eu  III spectrum. These new calculations support extensions of the Eu  III analysis including two levels of 4f^{7 6}D and ⁴₄G terms and more than ninety classified lines. The accidental perturbation shown in the two levels at 83 928 and 83 959 cm^-1 should be a warning to users oftheoretical $g_{\rm u} A$ values that low levels of excited configurations can be strongly perturbed by upper unknown levels of lower configurations. However, most of the oscillator strengths reported here should be useful for modelling astrophysical plasmas. For further extensions in this very complex spectrum, a much longer line list than the present one (Sugar & Spector 1974) would be needed.

Acknowledgements

This collaborative work were supported by the DRI-CNRS Project No.12254 and by the Russian Academy of Sciences. A. Bachelier and J. Sinzelle are acknowledged for making atomic structure calculations possible at the Laboratoire Aimé Cotton. We thank T. Ryabchikova and O. Kochukhov for providing us with the observations of HD 144897 and synthetic spectrum calculations.

References

• Biémont, E., & Quinet, P. 2003, Phys. Scr., T105, 38 [NASA ADS] [CrossRef] (In the text)
• Biémont, E., Palmeri, P., & Quinet, P. 1999, Ap&SS, 269, 635 [NASA ADS] [CrossRef] (DREAM: http://www.umh.ac.be/astro/dream/shtml) (In the text)
• Biémont, E., Garnir, H. P., Palmeri, P., et al. 2001, Phys. Rev. A, 64, 022503 [NASA ADS] [CrossRef] (In the text)
• Brewer, L. 1971, JOSA, 61, 1666 [NASA ADS] (In the text)
• Cowan, R. D. 1981, The Theory of Atomic Structure and Spectra (Berkeley, CA, USA: Univ. California Press) (In the text)
• Den Hartog, E. A., Wickliffe, M. E., & Lawler, J. E. 2002, ApJS, 141 255 (In the text)
• Komarovskii, V. A. 1991, Opt. Spectr., 71, 322 [NASA ADS] (In the text)
• Mashonkina, L. I., Ryabtsev, A. N., & Ryabchikova, T. A. 2002, Astron. Lett., 28, 34 [NASA ADS] [CrossRef] (In the text)
• Mashonkina, L. I., Ryabchikova, T. A., & Ryabtsev, A. N. 2005, A&A, 441, 309 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
• Quinet, P., & Biémont, E. 2003, MNRAS, 340, 463 [NASA ADS] [CrossRef] (In the text)
• Quinet, P., & Biémont, E. 2004, At. Data Nucl. Data Tables, 87, 207 [NASA ADS] [CrossRef] (In the text)
• Rajnak, K., & Wybourne, B. G. 1963, Phys. Rev., 132, 280 [NASA ADS] [CrossRef] (In the text)
• Ryabchikova, T., Piskunov, N., Savanov, I., Kupka, F., & Malanushenko, V. 1999, A&A, 343, 229 [NASA ADS] (In the text)
• Ryabchikova, T., Ryabtsev, A., Kochukhov, O., & Bagnulo, S. 2006, A&A, 456, 329 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
• Shadmi, Y., Oreg, J., & Stein, J. 1968, JOSA, 58, 909 [NASA ADS] (In the text)
• Spector, N., Sugar, J., & Wyart, J.-F. 1997, JOSA B, 14, 511 [NASA ADS] (In the text)
• Sugar, J., & Spector, N. 1974, JOSA, 64, 1484 [NASA ADS] (In the text)
• Wahlgren, G. 2002, Phys. Scr., T100, 22 [NASA ADS] [CrossRef] (In the text)
• Wyart, J.-F. 1977, Spectroscopie des éléments de transition et des éléments lourds dans les solides (Colloques Internationaux du CNRS 255, Paris), 45 (In the text)
• Wyart, J.-F. 1978, JOSA, 68, 197 [NASA ADS] (In the text)
• Wyart, J.-F., & Bauche-Arnoult, C. 1981, Phys. Scr., 22, 583 [NASA ADS] [CrossRef] (In the text)
• Wyart, J.-F., Blaise, J., Cowley, C., & Bidelman, W. C. 1997, Phys. Scr., 56, 446 [NASA ADS] [CrossRef] (In the text)
• Zhang, Z. G., Li, Z. S., Lundberg, H., et al. 2000, J. Phys. B, 33, 521 [NASA ADS] [CrossRef] (In the text)
• Zhang, Z. G., Svanberg, S., Palmeri, P., Quinet, P., & Biémont, E. 2002a, A&A, 385, 724 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
• Zhang, Z. G., Svanberg, S., Palmeri, P., Quinet, P., & Biémont, E. 2002b, MNRAS, 334, 1 [NASA ADS] [CrossRef] (In the text)

 

Table 5: Spectrum of Eu  III.