Non-LTE line formation for Pr II and Pr III is considered through a range of effective temperatures between 7250 K and 9500 K. A comprehensive model atom for Pr II/III is based on the measured and the predicted energy levels, in total, 6708 levels of
Pr II and Pr III. We describe calculations of the Pr II energy levels and oscillator strengths for the transitions in Pr II and Pr III. The influence of departures from LTE on Pr abundance determinations is evaluated. At Teff >= 8000 K departures from LTE lead to overionization of Pr II and to systematically depleted total absorption in the line and positive abundance corrections. At the lower temperatures, different lines of Pr II may be either weakened or amplified depending on the line strength. The non-LTE effects strengthen the Pr III lines and lead to negative abundance corrections. Non-LTE corrections grow with effective temperature for the Pr II lines, and, in contrast, they decline for the Pr III lines. The Pr II/III model atom is applied to determine the Pr abundance in the atmosphere of the roAp star HD 24712 from the lines of two ionization stages. In the chemically uniform atmosphere with [Pr/H] = 3, the departures from LTE may explain only small part (0.3 dex) of the difference between the LTE abundances derived from the Pr II and Pr III lines (2 dex). We find that the lines of both ionization stages are described for the vertical distribution of the praseodymium where the Pr enriched layer with [Pr/H] > 4 exists in the outer atmosphere at log tau_5000 < -4. The departures from LTE for Pr II/III are strong in the stratified atmosphere and have the opposite sign for the Pr II and Pr III lines. Using the revised partition function of Pr II and experimental transition probabilities, we determine the solar non-LTE abundance of Pr as log (Pr/H) = -11.15pm0.08.
Stellar parameters and abundances of Na, Mg, Al, K, Ca, Sr, Ba, and Eu are determined for four very metal-poor stars (-2.66 < [Fe/H] < -2.15) based on non-LTE line formation and analysis of high-resolution (R ~60000 and 90000) high signal-to-noise (S
/N > 200) observed spectra. A model atom for H I is presented. An effective temperature was obtained from the Balmer Halpha and Hbeta line wing fits, the surface gravity from the Hipparcos parallax if available and the non-LTE ionization balance between Ca I and Ca II. Based on the hyperfine structure affecting the Ba II resonance line, the fractional abundance of the odd isotopes of Ba was derived for HD 84937 and HD 122563 from a requirement that Ba abundances from the resonance line and subordinate lines of Ba II must be equal. For each star, non-LTE leads to a consistency of Teff from two Balmer lines and to a higher temperature compared to the LTE case, by up to 60 K. Non-LTE effects are important in spectroscopic determination of surface gravity from Ca I/Ca II. For each star with a known trigonometric gravity, non-LTE abundances from the lines of two ionization stages agree within the error bars, while a difference in the LTE abundances consists of 0.23 dex to 0.40 dex for different stars. Departures from LTE are found to be significant for the investigated atoms, and they strongly depend on stellar parameters. For HD 84937, the Eu/Ba ratio is consistent with the relative solar system r-process abundances, and the fraction of the odd isotopes of Ba, f_odd, equals 0.43+-0.14. The latter can serve as a constraint on r-process models. The lower Eu/Ba ratio and f_odd = 0.22+-0.15 found for HD 122563 suggest that the s-process or the unknown process has contributed significantly to the Ba abundance in this star.
