Barium isotopic ratios in metal-poor stars: Calibrating the method with globular clusters: I. Dwarf and giant stars in NGC 6752

Context. In recent years, the abundances of heavy elements have been proven essential in several major topics in astrophysics, ranging from stellar age determinations to constraining the origins of gravitational wave events, such as neutron star mergers. However, 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 the limitations of classical 1D hydrostatic models that neglect chromospheric effects. One promising, but still underexplored approach is to measure the isotopic composition of stellar atmospheres by focussing 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. Aims. Our aim is to provide a reliable method for quantifying the contributions of the s- and r-processes to the abundance of barium in stellar atmospheres. This can be 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. Methods. In this initial study, we used member stars of the globular cluster NGC 6752, assuming a low spread in the Ba abundance, to calibrate the microturbulence (υ_mic) value for both subordinate and resonance barium lines across different stellar evolutionary stages. This allowed us to provide a reliable estimate of υ_mic that can be used to accurately determine barium abundances and isotopic ratios in stars ranging from the main sequence (MS) to the upper red giant branch (RGB). Results. The microturbulence scale adapted for barium subordinate lines for the determination of Ba abundances is consistent with that derived from hydrodynamic (3D) model atmospheres; thus, the T_eff-log g dependent relations of the later can be used safely. The microturbulence for the resonance line at λ4934 Å for the determination of the isotopic ratio is higher and depends on the equivalent width (EW). Here, we provide calibrated relations between υ_mic and EW for measuring isotopic ratios. Regarding the chemical characterisation of the cluster, stars across all evolutionary stages exhibit a clear dominance of the s-process. Conclusions. Measuring the abundance of heavy elements has proved increasingly necessary, especially in anticipation of new surveys and instruments. In this work, we have provided a practical tool for measuring both the abundance and isotope ratios of Ba, directly related to the EW intensity, and applicable to 1D model atmospheres.