We present atmospheric models of red giant stars of various metallicities, including extremely metal poor (XMP, [Fe/H]<-3.5) models, with many chemical species, including, significantly, the first two ionization stages of Strontium (Sr) and Barium (Ba), treated in Non-Local Thermodynamic Equilibrium (NLTE) with various degrees of realism. We conclude that 1) for all lines that are useful Sr and Ba abundance diagnostics the magnitude and sense of the computed NLTE effect on the predicted line strength is metallicity dependent, 2) the indirect NLTE effect of overlap between Ba and Sr transitions and transitions of other species that are also treated in NLTE non-negligibly enhances NLTE abundance corrections for some lines, 3) the indirect NLTE effect of NLTE opacity of other species on the equilibrium structure of the atmospheric model is not significant, 4) the computed NLTE line strengths differ negligibly if collisional b-b and b-f rates are an order of magnitude smaller or larger than those calculated with standard analytic formulae, and 5) the effect of NLTE upon the resonance line of Ba II at 4554.03 AA is independent of whether that line is treated with hyperfine splitting. As a result, the derivation of abundances of Ba and Sr for metal-poor red giant stars with LTE modeling that are in the literature should be treated with caution.
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