  The elemental abundances of ten planetary nebulae, derived with high accuracy
including ISO and IUE spectra, are analysed with the aid of synthetic
evolutionary models for the TP-AGB phase. Model prescriptions are varied until
we achieve the simultaneous reproduction of all elemental features, which
allows placing important constraints on the characteristic masses and
nucleosynthetic processes experienced by the stellar progenitors. First of all,
it is possible to separate the sample into two groups of PNe, one indicating
the occurrence of only the third dredge-up during the TP-AGB phase, and the
other showing also the chemical signature of hot-bottom burning. The former
group is reproduced by stellar models with variable molecular opacities (see
Marigo 2002), adopting initial solar metallicity, and typical efficiency of the
third dredge-up 0.3-0.4. The latter group of PNe, with extremely high He
content 0.15<=He/H<=0.20 and marked oxygen deficiency, is consistent with
original sub-solar metallicity (i.e. LMC composition). Moreover, we are able to
explain quantitatively both the N/H-He/H correlation and the N/H-C/H
anti-correlation, thus solving the discrepancy pointed out long ago by Becker &
Iben (1980). This is obtained only under the hypothesis that intermediate-mass
TP-AGB progenitors (M > 4.5-5.0 Mo) with LMC composition have suffered a number
of very efficient, carbon-poor, dredge-up events. Finally, the neon abundances
of the He-rich PNe can be recovered by invoking a significant production of
22Ne during thermal pulses, which would imply a reduced role of the
22Ne(alpha,n)25Mg reaction as neutron source to the s-process nucleosynthesis
in these stars.
