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Rare-earth elements in the atmosphere of the magnetic chemically peculiar star HD 144897. New classification of the Nd III spectrum

We have obtained a UVES spectrum of a slowly rotating strongly magnetic Ap star, HD 144897, that exhibits very large overabundances of rare-earth elements. Here we present a detailed spectral analysis of this object, also taking into account effects of non-uniform vertical distribution (stratification) of chemical elements. We have determined the photospheric abundances of 40 ions. For seven elements (Mg, Si, Ca, Ti, Cr, Mn, Fe), we have obtained a stratification model that allow us to produce a satisfactory fit to the observed profiles of spectral lines of various strength. REEs abundances, that for the first time in the literature have been determined from the lines of the first and second ions, have been found typically four dex larger than solar abundances. Our analysis of REE spectral lines provide a strong support to the laboratory line classification and determination of the atomic parameters. The only remarkable exception is Nd III, for which spectral synthesis was found to be inconsistent with the observations. We have therefore performed a revision of the Nd III classification. We have confirmed the energies for 11 out of 24 odd energy levels classified previously, and we have derived the energies for additional 24 levels of Nd III, thereby increasing substantially the number of classified Nd III lines with corrected wavelengths and atomic parameters.

first few most abundant elements, like La, Ce, Nd, Sm in some cases, and Eu, which has few prominent lines in the optical region. The lines of the dominant second ionization stage (REE3) were rarely studied quantitatively because of the lack of atomic data, although their presence in the spectra of Ap stars was known for a long time (see, for example, the pioneering work by Swings (1944) on the REE3 line variations in α 2 CVn). A significant progress in the laboratory works on the energy level classifications provides an opportunity for theoretical calculations of the transition probabilities and other atomic parameters of spectral lines. The most extensive calculations were done by the Belgium group at Mons University, who created a Database on Rare Earths at Mons University -DREAM (Biémont et al. 1999). Other groups, which will be mentioned below, have also performed theoretical calculations of the REE3 atomic structure, and this gives a possibility of comparing different results. At present, we have transition probabilities for all but unstable Pm . Additionally, thanks to great efforts of the Wisconsin University group (references will be given in the corresponding Section), high precision laboratory measurements of the radiative lifetimes and transition probabilities for the first REE ions became available. These data give us a possibility for the detailed study of the REE in Ap atmospheres.
However, the first applications of the REE3 atomic data have revealed some inconsistencies between laboratory and calculated data (wavelengths, oscillator strengths) and the observed lines in stellar spectra. In particular, wavelengths of few Nd  lines calculated from the Nd  energy levels (Martin et al. 1978) differ from the stellar ones by up to 0.1 Å and even more (see line identification list of HD 122970 spectrum in Ryabchikova et al. 2000). This problem was resolved in a study of the laboratory Nd  spectrum by Aldenius (2001), who corrected several energy levels based on high precision wavelength measurements. However, calculated oscillator strengths give discordant abundance results for some Nd  lines in HgMn stars (Dolk et al. 2002).
Ap stars provide a perfect natural laboratory for REE study. First, they have extreme overabundances of these elements, therefore their spectra contain a large number of spectral lines of both ionization stages. Second, magnetic splitting may give extra information to verify line classification. And third, rapidly oscillating roAp stars have an outstanding pulsational characteristic: in most stars only REE lines show large radial velocity pulsation amplitudes (Savanov et al. 1999;Kochukhov & Ryabchikova 2001a, therefore we can double-check whether a certain spectral feature belongs to REEs by looking at its pulsational characteristics. We chose HD 144897 as a template. This star has a surface magnetic field B s varying between 8.5 and 9.5 kG over the period 48.43 d. (Mathys et al. 1997). This field is strong enough to produce clear Zeeman splitting of the spectral lines in unpolarized spectrum of the slowly rotating star, and not too large to produce an overlapping of the Zeeman components from nearby spectral lines. The quick look at the HD 144897 spectrum shows resolved Zeeman split features at the positions of strong Pr  and Nd  lines. Furthermore, HD 144897 was never studied for abundances, therefore our analysis will provide additional information for Ap-star chemistry.
Our paper is structured as follows. Observations and data reduction are described in Sect. 2, the determination of the fundamental stellar parameters is presented in Sect. 3. The results of the magnetic spectrum synthesis in the homogeneous, as well as in chemically stratified, atmosphere are given in Sect. 4. Sect. 5 revises classification of the Nd  spectrum. Discussion and conclusions are given in Sects. 6 and 7, respectively.

Observations and data reduction
High resolution, high signal to noise ratio UVES spectra of HD 144897 were obtained with the UVES instrument of the ESO VLT on 26 February 2002 within the context of program 68.D-0254. The UVES instrument is described by Dekker et  al. (2000). The observations were carried out using both available dichroic modes. The detailed log of the observations is given in Table 1. In both the blue arm and the red arm the slit width was set to 0.5 ′′ , for a spectral resolution of about 80 000. The slit was oriented along the parallactic angle, in order to minimize losses due to atmospheric dispersion. Almost the full wavelength interval from 3030 to 10400 Å was observed except for a few gaps, the largest of which are at 5760-5835 Å and 8550-8650 Å. In addition, there are several small gaps, about 1 nm each, due to the lack of overlapping between theéchelle orders in the 860U setting. The UVES data have been reduced with the automatic pipeline described in Ballester et al. (2000). For all settings, science frames are bias-subtracted and divided by the extracted flat-field, except for the 860 setting, where the 2D (pixel-topixel) flat-fielding is used, in order to better correct for the fringing. Because of the high flux of the spectra, we used the UVES pipeline average extraction method.
All spectra were normalized to the continuum with the help of an interactive procedure, which employed either a lowdegree polynomial or a smoothing spline function.

Fundamental parameters
Initial estimate of the effective temperature and surface gravity of HD 144897 was derived using photometric data in the Geneva system. The measurements were taken from the online catalogue maintained at Geneva Observatory (Burki et al. 2005) 1 . Hipparcos parallax, π = 4.77 ± 1.28 mas, (Perryman et al. 1997) and galactic coordinates of the star suggest that its reddening is significant. From a variety of sources (Lucke 1978;Hakkila et al. 1997;Schlegel et al. 1998) we obtained E(B − V) in the range from 0.13 to 0.48. Large reddening is confirmed by the presence of very strong NaD interstellar absorption lines. In this situation, the best approach is to make use of the reddening-free X, Y parameters of the Geneva photometry. Using the calibration of Künzli et al. (1997), we determined T eff = 12051 K and log g = 4.34. Subsequent correction for the anomalous flux distribution of Ap stars (Hauck & Künzli 1996) yields T eff = 11100 K. Stellar parameters were further adjusted to fit the hydrogen Hα and Hβ lines. Finally, we have obtained T eff = 11250 K and log g = 4.0. Model atmosphere of HD 144897 was calculated with the ATLAS9 code (Kurucz 1993), using ODF with 10 times solar metallicity and micro-turbulent velocity 4 km s −1 to mimic the enhancement of line opacity due to magnetic intensification.
We estimated the averaged surface magnetic field B s by measuring distance between the resolved Zeeman components of either pure doublets (Fe  3303.46,6149.48 Å,Nd  6145.07 Å,Cr  6231.68,6275.87 Å). Zeeman components were approximated by the sum of Gaussians. The results for both groups are similar, and the final value is B s = 8.79±0.10 kG. Our observations (HJD=2452331.83) correspond to a rotation phase 0.13 for the ephemeris given in Mathys et al. (1997), and the derived B s is fully consistent with their magnetic curve for HD 144897.
The projected rotational velocity was estimated using rather weak magnetically insensitive line Fe  6586.70 Å (mean Landé factor g eff =0.02) and medium intensity Fe  4491.40 Å (g eff =0.4). Both lines indicate v e sin i ≈ 4 km s −1 which seems a little too large to reproduce clearly visible Zeeman structure of many weak lines. A better fit of the synthetic spectrum to the observations is provided by v e sin i = 3 km s −1 , therefore we adopted this value in all abundance analysis calculations.

Abundance analysis
A very important part of all abundance calculations is accurate atomic parameters of spectral lines. Most atomic data in our study are taken from the  database (Kupka et al. 1999), which has been updated recently to include the new line lists: Ti  (Pickering et al. 2001), Cr , Fe , Co  (Raassen & Uylings 1998), Mn  (Kling & Griesmann 2000;Kling et al. 2001). The  REE line database (Biémont et al. 1999) is also made accessible via the  extraction procedures. For the second REE ions Landé factors were calculated by Quinet et al. (2004). For Sr, Y, Zr, Ba, Re Landé factors were taken from the "Atomic Energy Levels" tables by Moore (1971). For light elements O, Mg, Si Landé factors were calculated in the LS approximation. For Si  new experimental data on the Stark broadening and transition probabilities are available (Wilke 2003), which allows us to increase the number of Si  lines included in the abundance analysis. The new Si  oscillator strengths are smaller by 0.05 dex on average compared to the values in  (see also Ryabchikova et al. 2005). This difference does not influence the results of both standard and stratification analysis. Detailed description of the REE atomic parameters will be given below.

Spectrum synthesis
Computations of the synthetic spectra of HD 144897 were carried with the help of the magnetic spectrum synthesis code  , which represents an improved version of the program described by Piskunov (1999). In this spectrum synthesis approach, the polarized radiative transfer equation is solved numerically for seven values of the angle between the line of sight and the normal to the stellar surface. Resulting intensity spectra are integrated for a given rotational velocity.   uses a simplified model of the stellar magnetic field geometry with a homogeneous surface distribu- tion of both the field strength and field orientation. Although not suitable for detailed analysis of polarization spectra, this model is adequate for the purpose of fitting magnetically enhanced and splitted lines in the Stokes I spectrum. In our study   was used to calculate spectra both for homogeneous and stratified vertical distribution of chemical abundances. The modelling of the lines with different Zeeman patterns require a mean inclination of the magnetic vector to the stellar surface ∼ 50-60 • to reproduce relative intensities of the π and σ components. The final abundances calculated for the magnetic field B s =8.8 kG are presented in Table 2. Full list of the measured lines is available in electronic form only (Table 5 of Online material). In Table 2 abundances derived for HD 144897 are compared with the recently published abundances of the two stars with similar effective temperatures: HD 170973 (Kato 2003), and HD 116458 (Nishimura et al. 2004). The recent solar photospheric abundances (Asplund et al. 2005) are given in the last column. With a few exceptions abundances in all 3 Ap stars are similar, in particular, for the REE.

Abundance stratification
Preliminary analysis of the HD 144897 spectrum revealed presence of Fe lines in three ionization stages, with plenty of strong high-excitation Fe  lines. It was impossible to fit them with the same abundance. Also, lines of Si  and Si  are present, and again it is not possible to explain them with the same abundance. Therefore, we performed a stratification analysis of a few chosen elements which have enough spectral lines of different strength, ionization (where possible), excitation, sensitivity to Stark effect, and lying on both sides of the Balmer Jump (BJ). For Mn hyperfine splitting was taken into account using the data from Holt et al. (1999). The same step function approximation of the abundance distribution which was adopted by Ryabchikova et al. (2005) in their analysis of HD 204411 was used here. The details of stratification anal- ysis are given in the cited paper. The only difference is that we used magnetic spectrum synthesis for HD 144897 instead of a regular spectrum synthesis for HD 204411. Stratification calculations were performed for Mg, Si, Ca, Ti, Cr, Mn and Fe. First, we derived a mean abundance which gives the best fit for all chosen line profiles, treated the same way as in stratification procedure, but with a chemically homogeneous atmosphere. These homogeneous abundances are presented in Table 2 together with number of lines used in the analysis, and they were used as initial guess for the stratification study. We also calculated mean deviation between the observed and calculated line profiles, which may be considered as a measure of the standard error. The obtained element distributions are shown in Fig. 1. An example of the fits to a sample of Fe line profiles representing a variety of Zeeman patterns is given in Fig. 2. We do not expect to get a better fit of the Zeeman components due to a crude magnetic geometry used in the magnetic spectrum synthesis. The improvement of the fit with the stratified abundances over that with the homogeneous element distribution is also shown in Fig. 10. Co  lines are very strong in HD 144897, especially in spectral region below BJ. They indicate an overall Co abundance of log(Co/N tot ) = −4.2:−5.0, i.e. more than 3 dex above the solar photospheric abundance. However, the lack of hyperfine splitting (hfs) data for Co  lines does not allow us to perform a detailed analysis for this element.
All stratified elements but Cr show a steep decrease of concentration towards the upper atmospheric layers. The position of the abundance jump varies from log τ 5000 ≈ −1 (Mg, Si, Ti and Fe) to −2.5 (Mn). The Mg distribution in HD 144897 differs from the distribution derived in HD 204411 ) and in HD 133792 (Kochukhov et al. 2006), where a slow increase of the Mg abundance towards the upper atmosphere was obtained. We cannot consider our present results for Mg as conclusive because of small number of Mg lines available for HD 144897. More stars in a large temperature range should be investigated to get a better picture of the abundance distribution variations with effective temperature and other stellar parameters. In HD 144897 the abundance jumps for Cr, Mn and Fe are not very large, ∼1-2 dex. The jump is larger for Fe than for Cr and Mn. As demonstrated by Shulyak et al. (2004), similar Fe distribution in the hotter star CU Vir (12750 K) leads to a better modelling of the observed energy distribution, in particular, the λ 5200 Å depression. Similar Ca and Cr distributions, but with slightly smaller abundance jumps, were derived in the atmospheres of cooler and more evolved stars HD 204411 (8400 K) and HD 133792 (9400 K). Ca has the largest jump in all three stars. Si abundance jump is smaller than in HD 204411 and HD 133792. It is roughly comparable with the Si distribution in slightly hotter star HD 10221 (Glagolevskij et al. 2005).
For all elements except Mg and Ca abundances are never below solar over the part of the atmosphere where we can consider our results to be reliable. This atmospheric part is limited by the line formation sensitivity to temperature and pressure. We cannot say much about abundances above log τ 5000 = −4.

Rare-earth elements
HD 144897 is the second object after the famous Przybylski's star (HD 101065) for which abundances of all REEs but Pm are derived, and the first star in which abundances for most REEs are derived from the lines of the first and second ions. For odd isotopes hyperfine splitting is known and can be taken into account. However, in the presence of magnetic field, the coupling between the Zeeman and hfs components changes shape of spectral line and should be taken into account in spectral synthesis. However, we noticed that in most cases the line profiles are fitted reasonably well with the pure Zeeman splitting. The lines of the first ions of the REE are rather weak in HD 144897 spectrum, and the derived abundance should not be affected much by the hfs effects. Consequently, we did not use the hfs  Table 2. data in our analysis, with the exception of Pr , Eu  and Lu . Below we discuss briefly each element.
When no specific reference is given for atomic data, it means that all relevant parameters are extracted from  (Kupka et al. 1999).
Lanthanum. The oscillator strengths and hfs constants for La  lines are taken from Lawler et al. (2001a). Two lines of La  at λ 3171.69 and 3517.16 are seen in our spectrum, but the lines are rather wide and are obviously affected by hfs, which is unknown.
Cerium. Oscillator strength for Ce  and Ce  lines are taken from Palmeri et al. (2000) and from Biémont et al. (2002a), respectively. All lines are nicely reproduced with adopted magnetic field. Figure 3 shows a fit of the synthesized Ce  3470.92 Å line to the observed one. Most Ce lines in HD 144897 are well represented with the available atomic data.
Praseodymium. Atomic data from  and hfs constants from Ginibre (1989) were used in the Pr  analysis, which was based on two relatively weak lines at λλ 4206.72, 5322.77 Å. Other Pr  lines are in blends. For Pr  lines new calculations by one of us (AR) based on the extended energy levels given by Wyart et al. (2006) were applied. New calculations contain transition probabilities for the 4f 3 4 F term, which is missing in the  list (Biémont et al. 2001c). However, a number of intermediate strength lines from this term are observed in our spectrum. In general, a difference between 's and present oscillator strengths for 10 lines in common does not exceed 0.08 dex. Calculated Landé factors represent nicely the observed Zeeman patterns (see Fig. 4   Nd  classification will be considered in Sect. 5. We based our abundance determinations on the lines whose Zeeman patterns are well reproduced by the Landé factors given in three independent sets of theoretical calculations: Bord (2000), Zhang et al. (2002b) and the present study (Sect. 5). An example of the fit for the Nd  5845.02 Å line is shown in Fig. 4. Samarium. Accurate experimental data are available now for 958 Sm  lines (Lawler et al. 2006), and we used them in our analysis. Note, that for the 4 lines studied here, the data by Lawler at al. agree perfectly with the line parameters included in . For Sm  lines oscillator strengths are taken from Biémont et al. (2003). The authors give 3 sets of data: experimental transition probabilities for a limited number of lines, relativistic Hartree-Fock (HF) calculations combined with the experimental branching ratios (BR), and HF calculations with the core polarization effects included. The last data are available for the larger number of spectral lines, and was 6 T. Ryabchikova et al.: Rare-earth  used in our abundance analysis (Table 2). With experimental data only we get log(Sm/N tot ) = −7.03 ± 0.23 from 3 spectral lines. The HF calculations with the experimental BR give log(Sm/N tot ) = −6.90±0.14 for 8 spectral lines. Abundance determinations with 3 sets of oscillator strengths agree within the error limits. Calculated Landé factors for the lines used in abundance analysis represent the observed Zeeman patterns well. Europium. Experimental oscillator strengths and hfs constants for Eu  lines are taken from Lawler et al. (2001b). For the Eu  lines we again used the new transition probabilities and Landé factors calculations, which are based on the extended analysis of the Eu  energy levels (Wyart et al. 2006). Generally, the new line parameters do not differ significantly from the  data. Eu is the only rare-earth element for which more than 1.0 dex difference between abundances from the lines of the first and second ions is obtained.   al. 2002). NLTE effects of the same order are expected for Nd. However, under the LTE assumption, Nd  lines should provide lower abundances to Nd  (L. Mashonkina, private communication), but we do not find this discrepancy for HD 144897.
Gadolinium. The Gd  oscillator strengths are taken from Biémont et al. (2002b). The two lines, λλ 3118.04 and 3176.66 Å, although partially blended, are synthesized satisfactorily with the theoretical Landé factors.
Terbium. Experimental data for Tb  lines are adopted from Lawler et al. (2001c). For Tb  the transition probabilities and Landé factors were calculated by one of us (AR) based on the extended analysis of the Tb  energy levels (Wyart et al. 2006). Figure 4 gives an example of the fit to the observed Tb  5847.23 Å line. All other unblended lines in our analysis are also fitted perfectly with the current atomic data. The Tb  transition probabilities were also calculated by Biémont et al. (2002c), and the two sets of parameters agree within 0.05 dex.
Dysprosium. Experimental data for Dy  lines (Wickliffe et al. 2000) and theoretical calculations for Dy  lines  were used in the present study. Figure 6 shows the fit for one of the Dy  lines at λ 3669.66 Å. Although a standard deviation in abundance obtained from Dy  lines is larger than for other species, a good agreement between abundances derived from both ionization stages provides a support for relatively accurate theoretical atomic parameters of Dy  lines.
Holmium. Experimental data for Ho  lines are taken from Lawler et al. (2004). Improved partition function for Ho  (Bord & Cowley 2002) were implemented in . Ho  lines were synthesized using oscillator strengths calculated by Zhang et al. (2002a) and normalized to the measured lifetimes. Figure 7 demonstrates the fit of the calculated Ho  3581.45 Å line (the strongest in our study) to the observed spectrum. Obviously, hfs effects are not significant. The fit of similar quality is obtained for other Ho  lines.
Erbium. For Er  calculations we used oscillator strength from Biémont et al. (2001a). Figure 8 illustrates the quality of existing Er  data.
Thulium. Experimental data for Tm  lines (Wickliffe & Lawler 1997)   Nevertheless, good agreement of the synthesized lines with the observed Zeeman splitting confirms reliability of the atomic data (see Fig. 9 for Tm  3629.09 Å). Ytterbium. Theoretical oscillator strengths (Biémont et al 2001b) were used in Yb  analysis. It was possible to model only one line for each Y ion. These lines are weak, but provide consistent abundance.
Lutecium. The only line which is suitable for the Lu abundance determination is Lu  6221.89 Å. It is weak, but in order to fit the line profile we have to account for both the Zeeman and hfs splittings. At the same time, derived abundance is not affected by these effects. Oscillator strength for this line is taken from Den Hartog et al. (1998) and hfs constants -from Brix & Kopfermann (1952). Our synthesis confirmed the revised wavelength of this line, λ 6221.86 Å, as derived by Bord et al. (1998) from the analysis of the solar spectrum.
Spectral synthesis of the REEs in HD 144897 provides a strong support for the calculated atomic parameters for the second ions of most of these elements and, hence, for the correct line classification. Only for Nd  we obtained inconsistencies between the theoretical calculations and few rather strong observed features, which disagree either in the Zeeman pattern  Fig. 9. The same as in Fig. 4 but for Tm  line. No strong feature is observed at 3626.12 Å corresponding to a strong Nd  line predicted by Zhang et al. (2002b) on the basis of Martin et al. (1978) energy levels.
( Fig. 5) or in the intensity (Fig. 9). Taking into account the fact that for all second ions of REE calculations provide quite reliable atomic data, we may conclude that poor knowledge of the Nd  spectrum rather than a problem with the theoretical line profile calculations is the reason for the observed inconsistencies in the case of Nd  lines.

Nd  classification
The Nd  spectrum is very poorly known. Martin et al. (1978) compiled 5 levels of the 4f 4 5 I ground term and 24 levels of the 4f 3 5d configuration using unpublished material by Crosswhite (1976). The latter list of Nd  lines was not published but widely circulates in the astrophysical community. Recent study of the Nd  spectrum was made by Aldenius (2001) (2000) and Zhang et al. (2002b). In the last paper the experimental lifetimes of five 4f 3 5d levels were also reported. Aldenius (2001) classified 38 Nd  lines and suggested an identification of 20 new Nd  lines based on the laboratory spectrum, but did not provide their classification. In our classification work we used 27 the most intensive lines from her list of 38 classified lines and 9 lines from the list of unclassified ones. Rejected are the lines of low intensity (less than 3 in Aldenius' intensity scale) and the line 4781.014 Å (intensity 10), which is practically invisible in spectra of Ap and roAp stars. These spectra provide us with additional wavelength data. We mentioned in the Sect. 1 that Nd  lines show outstanding pulsational characteristics in roAp stars, which we 8 T. Ryabchikova et al.: Rare-earth   consider as a necessary (but not sufficient) condition for a spectral feature to belong to Nd . We chose a set of unidentified lines in the spectra of roAp stars γ Equ (Kochukhov et al. 2004) and HD 24712 (Sachkov et al. 2005), which have pulsational amplitudes and phases similar to those for classified Nd  lines, and measured wavelengths of these lines. Because of the large magnetic field, the spectrum of HD 144897 is not suitable for precise wavelength measurements, therefore we carried out line position determinations using the spectrum of roAp HD 217522. Moderate magnetic field ( B s <2 kG) and slow rotation (v e sin i≤3 km s −1 ) of this star provide an accuracy ∼0.005 Å for unblended lines. The spectrum of HD 217522 was obtained during the same observational program 68.D-0254 and was reduced in the same way as our data on HD 144897. Then we applied a classification procedure to the whole line sample using the code  (Azarov 1993) for identification of atomic spectra.
As in previous studies (Bord 2000;Zhang et al. 2002b), our calculations of the Nd  atomic structure were made with the Cowan code (Cowan 1981). For the prediction of the effective energy parameters and electrostatic parameters in the 4f 4 and 4f 3 shells we took advantage of the generalized parametric studies of doubly-ionized lanthanides (Wyart et al. 2006). Table 6 (Online material) lists the energy parameters of the 4f 4 and 4f 3 5d configurations after fitting to all observed levels. 4f 4 + 4f 2 5d 2 + 4f 3 6p configurations were included in the even system of levels. 4f 3 5d + 4f 3 6s + 4f 2 5d6p configurations form the energy matrix of the odd set of levels. All electrostatic parameters for unknown configurations as well as the parameters of configuration interactions were fixed at the 0.85 level relative to the corresponding Hartree-Fock values. Average deviation σ =55 cm −1 of our fitting is the same as in the previous calculations, but due to introduction of the effective energy parameters (α, β, γ and F 1 (4f,5d)) and scaling factors for F k (4f,4f), the Slater integrals predictions for unknown energy levels are expected to be more accurate than in previous studies by Bord (2000) and Zhang et al. (2002b).
A list of identified Nd  lines is given in Table 4 and found energy levels are presented in Table 7 (Online material). First column of Table 4 contains recommended wavelengths for 71 lines. They coincide with the Aldenius' wavelengths where available (column 2). Column 3 shows the wavelengths from the Crosswhite's list. In the 4th column the wavelengths measured in the spectrum of roAp star HD 217522 are given. For the lines absent in Aldenius' list but originated from the levels defined at least by one wavelength from Aldenius' list we recommend the wavelengths calculated from the level energies (Ritz values). We also give Ritz values for transitions from some levels established by Crosswhite's wavelengths (where Aldenius' measurements were not available). In other cases recommended wavelengths coincide with the stellar measurements.
An agreement between the theoretical Zeeman structure and intensity of the lines from Table 4 and the observed features in HD 144897 was accepted as a sufficient condition for correct Nd  classification. Mean abundance obtained for 39 newly classified lines is log(Nd/N tot ) = −6.60 ± 0.20 and it agrees very well with the abundance derived from the known lines (Table 2). Figure 10 gives an example how newly classified Nd  lines fit the observed spectra in the 4900-4915 Å region. The top panel displays this spectral part in HD 144897, and the spectrum of roAp star HD 24712 (Sachkov et al. 2005) is shown in the bottom panel. Dashed line in the bottom panel represents scaled pulsation pattern in roAp stars (standard deviation of the time-series spectra from the averaged spectrum) where double-peaks show a position of the lines with pulsation radial velocity variations. Only one pulsating line, Nd  4903.24 Å, was previously known and classified, and another line 4914.09 Å was listed (but not classified) as Nd  by Aldenius (2001). Previous classification of the Nd  4903.24 Å line does not correspond to the observed magnetic splitting (dashed line in the upper panel of Fig. 10). Two other lines, 4911.65 and 4912.94 Å, with the same pulsation signature are also seen in Fig. 10. All 4 lines are classified in this work and validity of the identification is proved by Zeeman calculations in the spectrum of HD 144897 (upper panel in Fig. 10). A good fit to the stellar spectrum for one more newly classified Nd  5851.542 Å line is shown in Fig. 4. Table 7 (Online material) contains the energies of all levels of the 4f 3 5d configuration with J = 3-10 below 33000 cm −1 . The energies of 35 levels were determined. We were able to confirm the energies only for 11 out of 24 levels compiled by Martin et al. (1978). Oscillator strengths of 23 transitions from these 11 levels to the lower 4f 4 5 I term, calculated by Zhang et al. (2002b) and in the present work agree within 0.14 dex in average. The energies of almost all levels with J = 4-8 are based now on the identification of 2 or 3 lines. The levels with J = 3 are defined by one line and need further confirmation. Calculated composition of the levels (column 4) shows that some of the levels are highly mixed, and leading contribution is given by the same LS term. To avoid possible ambiguities, we supplied designations of such levels by additional letters A or B in Table 4 (see also Table 7 (Online material)).
Previous identification was changed for a few strong lines. For example, the changes were made for the ( 4 I) 5 I o J=5,6,8 levels.
( 4 I) 5 I o 5 : New value 20348.715 cm −1 is supported by 3 lines, 5203.9236, 4912.946 and 5566.022 Å, observed in stellar spectra with the intensities corresponding to the calculated g f values. Previous energy of the level 20388.980 cm −1 was based on two lines 5193.0397 and 4903.2410 Å, but Zeeman structure calculated from this classification does not fit the observed spectrum of HD 144897. With the new classification these two lines perfectly match a transition array from the ( 4 I) 5 H o 4 level (Fig. 10).
( 4 I) 5 I o 6 : Aldenius (2001) found only one line 4781.0141 Å (mentioned above) as the 5 I 5 -( 4 I) 5 I o 6 transition to support the value 22048 cm −1 (Martin et al. 1978). Another expected transition to the 5 I o 6 level at 5084.927 Å with 10 times larger transition probability was not measured by Aldenius. A rather strong line at 5085.0 Å is present in stellar spectra, but the predicted Zeeman pattern based on Martin et al. energy levels does not fit the observed feature. There is no observable feature at 4781.014 Å in any of our stars (HD 144897, γ Equ, HD 24712 or HD 217522) which may be compared to rather strong theoretically predicted line based on previous identification. Therefore, we reject previous energy for ( 4 I) 5 I o 6 and propose instead two other lines 4796.4999 and 5102.4258 (blended by Nd ) for the transitions from the upper ( 4 I) 5 I o 6 level to 5 I 5,6 lower levels. Both lines are fitted fairly well with the new transition probabilities and Landé factors (Fig. 11). The identification is supported by the third weak line to the 5 I 7 level at 5473.14 Å. The corrected ( 4 I) 5 I o 6 energy for the level is 21980.505 cm −1 .
( 4 I) 5 I o 6 : For previous value 24686.4 cm −1 (Martin et al. 1978) Aldenius (2001) found two lines at 5102.4278 and 4766.9971 Å. Theoretical calculations (Zhang et al. (2002b) predict strong line at 4766.9971 Å, while no feature is observed in stellar spectra at this wavelength. We attributed the first line to the ( 4 I) 5 I o 6 level (see above). The energy 24592.234 cm −1 of ( 4 I) 5 I o 6 level was derived based on the 5127.0441 and 4788.465 Å lines.
Few relatively strong lines from Aldenius' list lines remain unclassified, although for three of them (4514.128, 4711.333, 5028.520 Å) the Nd  identification is supported by pulsational observations in roAp stars.

Discussion
An extended abundance analysis of the magnetic Ap star HD 144897 strongly demonstrated a possibility of the adequate fit of the observed spectrum to the theoretical calculations when atmospheric (temperature, magnetic field, etc.) and atomic line parameters are correctly known. In particular, it concerns the rare-earth elements in the first and second ionization stages, which dominated the spectra of some cool roAp stars, for example, famous Przybylski's star (HD 101065). Unfortunately, an extended laboratory analysis of some REEs in the second ionization stage is not complete. In such cases stellar data play an important role in spectrum classification. Usually, the quality of the theoretical atomic structure calculations are checked by comparison the observed and calculated lifetimes. For Nd  the lifetime measurements were made for 5 levels of the 5d (4F) 5 H configuration having strong mixture with almost overlapping 5d (4F) 5 D levels (Zhang et al. 2002b). The mixture results in the presence of two close lying levels with the (4F) 5 H character, which were distinguished by additional letters A and B in our Table 4. Because of the mixture, small variation of the energy parameters leads to drastic change of the calculated lifetimes. A comparison between the observed and theoretical lifetimes calculated by Zhang et al. (2002b) and in the present work is given in Table 3. It should be mentioned that we suggested new energies for the 5d (4F) 5 H levels with J = 3, 5 and 6. Each level with J = 5 or 6 is now based on two lines with appropriate Zeeman structure checked using the HD 144897 spectrum. The J = 3 level is defined by one relatively narrow line in accordance with the g-factor of this level. New classification corresponds better to the observed feature, although the calculated line is still narrower then the observed one. As a result we have to interchange the observed wavelengths and energies for J = 3, 5 and 6 levels according to new line classification.
One can notice an apparently better agreement between measured and calculated lifetimes in Zhang et al. (2002b). However, there is a difficulty in the calculations of the oscillator strengths for the 5p 6 4f n -5p 6 4f n−1 5d transitions related to the fact that the 4f electrons are deeply embedded inside the 5p 5 core as discussed by Biémont et al. (2001c). As a result, the relativistic Hartree-Fock calculated lifetimes for the 4f n−1 5d levels are shorter than the measured ones. For example, in Eu  a ratio of measured and calculated lifetimes is equal to 3 (Mashonkina et al. 2002). In view of this property, the relation between calculated and measured lifetimes has an expected tendency in the present work, but not in the Zhang et al. (2002b) study.

Conclusions
We presented an extensive abundance analysis, with the emphasis on REEs, in the atmosphere of the tepid magnetic Ap   Fig. 11. The Nd  lines from the 4 I 5 I 5,6 -4 I 5 I o 6 transition array. Calculations with the old classification for λ 5102.44 line are shown by the dotted line. Table 3. Comparison between the measured and calculated lifetimes of the 5d (4F) 5 H J levels in a framework of new identifications. Zhang et al. (2002b) Present work Lifetime (ns) star HD 144897. Thanks to the extremely large wavelength coverage of our observational material, all stable REEs but La and Lu are studied using spectral lines of the first and second ionization stages, thus giving more confidence to the REE abundance results. The spectrum of HD 144897 is very complex because of the large overabundance of the Fe-peak elements and Zeeman splitting of lines in a 8.8 kG magnetic field. Therefore, a careful abundance and, in particular, stratification analysis of the most prominent elements, like Cr and Fe, was performed to minimize blending problems in the REE analysis.
Comparison of the atmospheric abundances in HD 144897 and in the other two tepid Ap stars, HD 170973 (Kato 2003) and HD 116458 (Nishimura et al. 2004), shows close similarity, in particular, in the REE abundances. On average, REEs are overabundant by 4 dex compared to the solar abundances, and no serious violation of odd-even effect is observed. Using a spectrum of the star where clearly resolved Zeeman patterns for most spectral lines are observed, we were able to check an accuracy of the experimental (first REE ions) and theoretical (second REE ions) data: energy level classification, transition probabilities and Landé factors. We found that for all ions but Nd , the profiles of unblended or partially blended REE lines in the spectrum of HD 144897 are well synthesized adopting for the mean magnetic field modulus the value 8.8 kG. In contrast, less than half of the previously classified Nd  lines could be fitted. Using two criteria for the Nd  line identification -pe-culiar pulsational characteristics in rapidly oscillating stars and a correspondence between the calculated and observed Zeeman pattern in magnetic star HD 144897 -we performed a revision of Nd  classification. We were able to confirm the energies only for 11 out of 24 levels compiled by Martin et al. (1978), and we derived energies for additional 24 levels of the 4f 3 5d configuration increasing a total number of classified Nd  lines with corrected wavelengths and atomic parameters. Our classification of the Nd  energy levels was partially based on stellar measurements. Therefore, precise laboratory measurements in wide spectral region are required to confirm our results.       T. Ryabchikova et al.: Rare-earth elements in the atmosphere of the magnetic chemically peculiar star HD 144897, Online Material p 7