Aims: We investigate the change in the surface abundance of 12C during the evolution along the AGB, aiming to constrain third dredge-up models.
Methods: High-resolution, near-infrared spectra of a sample of AGB stars in the LMC cluster NGC 1846 were obtained. A cluster sample ensures a high level of homogeneity with respect to age, metallicity, and distance. The C/O ratio and the ratio of 12C/13C were measured and compared with our evolutionary models.
Results: For the first time, we show the evolution of the C/O and 12C/13C ratios along a cluster AGB. Our findings allow us to check the reliability of the evolutionary models and, in particular, the efficiency of the third dredge up. The increase in both C/O and 12C/13C in the observed O-rich stars is reproduced by the models well. However, the low carbon isotopic ratios of the two C-stars in our sample indicate the late occurrence of moderate extra mixing. The extra mixing affects the most luminous AGB stars and is capable of increasing the abundance of 13C, while leaving unchanged the C/O ratio, which has been fixed by the cumulative action of several third dredge-up episodes. We find indications that the F abundance also increases along the AGB, supporting an in situ production of this element.