Zoran Simić and Milan S. Dimitrijević Astronomical Observatory, Volgina 7, Belgrade, Serbia

Motivation --Spectral lines of rare-earth elements are present in Solar as well as in stellar spectra (see e.g. Grevesse & Blanquet 1969, Molnar 1972, Adelman 1987, Mathys & Cowley 1992, Sadakane 1993, Bidelman et al. 1995, Cowley et al. 1996, etc.). --Principally, these lines originate in layers of stellar atmospheres with higher electron density (photosphere or subphotosphere). --Consequently, electron-impact broadening mechanism can be important, especially for hot (A and B) stars as well as for white dwarfs. So, it is important to have a set of electron-impact broadening data for the lines of ionized rare-earth elements.

--For example, the reliability of the element abundance determinations in stellar atmospheres depends on a number of factors, where atomic data (transition probabilities, collisional widths, etc.) are among the most important. --One of the needed set of atomic data for line synthesis are the electron- impact widths. They are needed in order to solve various problems in astrophysics and physics, for example, diagnostics and modeling of laboratory and stellar plasma, investigation of its physical properties and for abundance determination.

Rare-earth elements in the atmosphere of the magnetic chemically peculiar star HD High overabundances of the rare-earth elements (REE) are the most typical characteristic of the upper main-sequence, magnetic, chemically peculiar (Ap) stars. In the past, REE studies were based on the lines of the first ions, which are rather weak even in the spectra of REE-rich stars with Teff > K, which makes blending a severe problem. In normal stars with these tempe- ratures, the lines of singly ionized REE are not visible at all. Therefore, the REE study was limited by the first few most abundant elements, such as La, Ce, Nd, Sm in some cases, and Eu, which has a 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 has been known for a long time (for exa- mple, Swings (1944) in α2 CVn).

--The 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 needed to verify line classification. *Third, rapidly oscillating roAp stars have the outstanding pulsational characteristic that in most stars only REE lines show large radial velocity pulsation amplitudes (Savanov et al. 1999; Kochukhov & Ryabchikova 2001a,b), therefore we can doublecheck whether a certain spectral feature belongs to REEs by looking at its pulsational characteristics.

Abundances of HD144897

Example1: spectral lines of REE in HD (T. Ryabchikova et al. 2006)

Example2: new Nd III classification in HD (T. Ryabchikova et al. 2006)

HD144897: -- Ryabchikova et al. determined the photospheric abundances of 40 ions. --The REEs abundances, which have been determined for the first time from the lines of the first and second ions, have been found typically four dex higher than solar abundances. --They therefore performed a revision of the Nd III classification. They con- firmed the energies for 11 out of 24 odd energy levels that were classified previously, and derived the energies for additional 24 levels of Nd III, thereby substantially increasing the number of classified Nd III lines with corrected wavelengths and atomic parameters.

Our Aim “In order to provide atomic data needed for astrophysical investigations, a set of electron-impact broadening parameters for ionized rare-earth element lines should be calculated. We are going to calculate the electron-impact broade- ning parameters for transitions of ionized rare-earth elements. Taking into account that the spectra of these elements are very complex, for calculation we can use the modified semi-empirical approach -- MSE or simplified MSE. Also, we can estimate these parameters on the basis of regu- larities and systematic trends.”

MODIFIED SEMIEMPIRICAL THEORY (Dimitrijević & Konjević, 1980; Dimitrijević & Kršljanin, 1986)

Here we present our plans and specify the number of lines for which we may calculate electron-impact broadening parameters with a satisfying accuracy and discuss the difficulties which may appear in the calculation.

--Due to the very complex spectra of ionized rare-earth elements we have to improve the existing software. It means that calculations within intercoupling approximation have to be performed. Example: Ce III, 4f6p  jj coupling approximation, while 4f6d well described by  jl coupling approximation. Also, a numerical experiment about the influence of this effect on calculated parameters should be done.

(L. Č. Popović, M. S. Dimitrijević & T. Ryabchikova, 1999) --The electron-impact widths and shifts for six Eu II lines and widths for three La II, and six La III multiplets have been calculated by using the modified semiempirical method. Estimation for Stark widths of nm (Eu II) and nm (Eu III) lines are given as well. The influence of the electron-impact mechanism on line shapes and equivalent widths in hot star atmospheres has been considered.

Example : Eu II

--The influence of the Stark broadening mechanism on line shapes and equiva- lent widths in stellar atmospheres was considered. The test of this influence was done for 38 astrophysically important Nd II lines for different types of stellar atmospheres. Moreover, the electron-impact widths for 284 Nd II lines are given. For calculation of the electron-impact widths we use the modified semiempirical method.

A Part of the full table for Nd II

Consequently, electron-impact broadening mechanism can be important, especially for hot (A and B) stars as well as for white dwarfs. So, it is important to have a set of electron-impact broa- dening data for the lines of ionized rare-earth elements.

Ce II, Pr II, Sm II, Tm II Pr III, Nd III, Ho III, Er III, Tm III La IV, Yb IV

Thank you for attention!