  We present the results of a study aimed at determining the 12C/13C ratio in
two samples of planetary nebulae (PNe) by means of millimeter wave observations
of 12CO and 13CO. The first group includes six PNe which have been observed in
the 3He+ hyperfine transition by Balser et al. (1997); the other group consists
of 22 nebulae with rich molecular envelopes. We have determined the carbon
isotopic ratio in 14 objects, 9 of which are new detections. The results
indicate a range of values of 12C/13C between 9 and 23. We estimate the mass of
the progenitors of the PNe of our sample and combine this information with the
derived 12C/13C isotopic ratios to test the predictions of stellar
nucleosynthesis models.
  We find that the majority of PNe have isotopic ratios below the values
expected from current standard asymptotic giant branch models in the mass range
of interest. We suggest that the progenitors of the PNe must have undergone a
non-standard mixing process during their red giant phase and/or asymptotic
giant phase, resulting in a significant enhancement of the 13C abundance in the
surface layers. Our study confirms a similar behaviour inferred from
spectroscopic observations of field population II stars and globular cluster
giants, and extends it to the final stages of stellar evolution. Finally, we
discuss the implications of our results on models of Galactic chemical
evolution of 3He and 12C/13C.
