We present the N, O, F and Na abundance and 12C/13C isotopic ratio measurements or upper limits for a sample of 10 C-rich, metal-poor giant stars, eight enhanced in s-process (CEMP-s) elements and two poor in n-capture elements (CEMP-no). The abundances are derived from IR, K-band, high-resolution CRIRES@VLT spectra obtained. The metallicity of our sample ranges from [Fe/H]=-3.4 to -1.3. F abundance could be measured only in two CEMP-s stars. With [F/Fe]=0.64, one is mildly F-overabundant, while the other is F-rich, at [F/Fe]=1.44. For the remaining eight objects, including both CEMP-no in our sample, only upper limits on F abundance could be placed. Our measurements and upper limits show that there is a spread in [F/C+N] ratio in CEMP-s stars as predicted by theory. Predictions from nucleosynthetic models for low-mass, low-metallicity Asymptotic Giant Branch stars, account for the derived F abundances, while the upper limits on F content derived for most of the stars are lower than the predicted values. The measured Na content is accounted for by AGB models in the 1.25 to 1.7 Msun range, confirming that the stars responsible for the peculiar abundance pattern observed in CEMP-s stars are low-mass, low-metallicity AGB stars, in agreement with the most accepted astrophysical scenario. We conclude that the mechanism of F production in current state-of-the-art low-metallicity low-mass AGB models needs further scrutiny and that F measurements in a larger number of metal-poor stars are needed to better constraint the models.
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