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 .
The accuracy on the observed abundances is essential in order to make a reliable comparison with the models .
The advantages of the infrared spectra in achieving this accuracy are discussed .
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 , \lambda \sim 0.3 - 0.4 .
The latter group of PNe , with extremely high He content ( 0.15 \leq He/H \leq 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 \ga 4.5 - 5.0 M _ { \odot } ) 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 ^ { 22 } Ne during thermal pulses , which would imply a reduced role of the ^ { 22 } Ne ( \alpha , n ) ^ { 25 } Mg reaction as neutron source to the s-process nucleosynthesis in these stars .