Barium isotopic ratios in metal-poor stars: calibrating the method with globular clusters

Identifying the nucleosynthesis processes behind heavy-element enrichment in stellar atmospheres is challenging. It typically relies on comparing observed abundance-to-iron ratios with theoretical predictions relative to the Sun, but this method is prone to uncertainty due to limitations of classical 1D hydrostatic models. One promising but still underexplored approach is to measure the isotopic composition of stellar atmospheres by focusing on elements that have both slow (s)-process and rapid (r)-process contributions. While the study of total elemental abundances offers a simplified view, isotopic ratios are directly linked to the underlying nucleosynthesis processes. Our aim is to provide a reliable method for quantifying the contributions of the s- and r-processes to barium in stellar atmospheres. This is achieved by determining barium isotopic ratios using 1D atmospheric models in combination with a carefully calibrated microturbulence, based on the comparison between subordinate and resonance Ba lines. In this initial study, we use member stars of the globular cluster NGC 6752 to calibrate the microturbulence ($v_{mic}$) value for both subordinate and resonance barium lines across different stellar evolutionary stages. This allows us to provide a reliable estimate of $v_{mic}$ that can be applied to accurately determine barium abundances and isotopic ratios in stars ranging from the main sequence to the upper red giant branch. The $v_{mic}$ scale adapted for barium subordinate lines is consistent with that derived from 3D model atmospheres, and thus the $T_{\mathrm{eff}}$-log $g$ dependent relations of the later can be used safely. The $v_{mic}$ for the resonance line at $\lambda$4934 Angstrom -- for the determination of the isotopic ratio -- is higher, and depends on the equivalent width (EW). We provide calibrated relations between $v_{mic}$ and EW for measuring isotopic ratios.