  Despite a rich observational background, few spectroscopic studies have dealt
with the measurement of the carbon isotopic ratio in giant stars. However, it
is a key element in understanding the mixing mechanisms that occur in the
interiors of giant stars. We present the CNO and $^{12}$C/$^{13}$C abundances
derived for 71 giant field stars. Then, using this new catalogue and
complementary data from the Kepler and Gaia satellites, we study the efficiency
of mixing occurring in the giant branch as a function of the stellar
properties. We have determined the abundances of CNO and more specifically
12C/13C using the FIES Spectrograph on the Nordic Optical Telescope, for 71
giant field stars. In addition, asteroseismology is available for all stars,
providing their mass, age as well as the evolutionary states. Finally,
astrometry from Gaia data is also available for the majority of the sample. We
compare these new determinations with stellar evolution models taking into
account the effects of transport processes. To exploit the complete potential
of our extensive catalogue and considering both the Galactic evolution and the
impact of stellar evolution, we built mock catalogues using the Besancon Galaxy
model in which stellar evolution models taking into account the effects of
thermohaline instability are included. We confirm that 12C/13C at the surface
of core He-burning stars is lower than that of first ascent RGB stars. 12C/13C
measured at the surface of the core He-burning stars increases with [Fe/H] and
mass while it decreases with age. These trends are all very well explained by
the thermohaline mixing that occurs in red giants. We have shown that our
models can explain the behaviour of 12C/13C versus N/O, although the
observations seem to show a lower N/O than the models. We also note that more
constraints on the thick disc core He-burning stars are needed to understand
this difference.
