  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.
