We re-analysed the carbon and oxygen isotopic ratios in the atmospheres of the two bright K giants Arcturus and Aldebaran. Previous determinations of their 16O/18O ratios showed a rough agreement with FDU expectations; however, the estimated 16O/17O and 12C/13C ratios were lower than in the canonical predictions. These anomalies are interpreted as signs of the occurrence of non-convective mixing episodes. We re-investigated this issue in order to verify whether the observed data can be reproduced in this hypothesis and if the well determined properties of the two stars can help us in fixing the uncertain parameters characterizing non-convective mixing and its physical nature. We used high-resolution infrared spectra to derive the 12C/13C and 16O/17O/18O ratios from CO molecular lines near 5 mu. We also reconsidered the determination of the stellar parameters to build the proper atmospheric and evolutionary models. We found that both the C and the O isotopic ratios for the two stars considered actually disagree with pure FDU predictions. This reinforces the idea that non-convective transport episodes occurred in them. By reproducing the observed elemental and isotopic abundances with the help of parametric models of nucleosynthesis and mass circulation, we derived constraints on the properties of non convective mixing. We find that very slow mixing is incapable of explaining the observed data, which require a fast transport. Circulation mechanisms with speeds intermediate between those typical of diffusive and of convective mixing should be at play. We however conclude with a word of caution on the conclusions possible at this stage, as the parameters for the mass transport are rather sensitive to the stellar mass and initial composition.
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