  The envelope of thermally pulsing AGB stars undergoing periodic third
dredge-up episodes is enriched in both light and heavy elements, the ashes of a
complex internal nucleosynthesis involving p, alpha and n captures over
hundreds of stable and unstable isotopes. In this paper, new models of low-mass
AGB stars (2 Msun), with metallicity ranging between Z=0.0138 (the solar one)
and Z=0.0001, are presented. Main features are: i) a full nuclear network (from
H to Bi) coupled to the stellar evolution code, ii) a mass
loss-period-luminosity relation, based on available data for long period
variables, and ii) molecular and atomic opacities for C- and/or N-enhanced
mixtures, appropriate for the chemical modifications of the envelope caused by
the third dredge up. For each model a detailed description of the physical and
chemical evolution is presented; moreover, we present a uniform set of yields,
comprehensive of all chemical species (from hydrogen to bismuth). The main
nucleosynthesis site is the thin 13C pocket, which forms in the core-envelope
transition region after each third dredge up episode. The formation of this 13C
pockets is the principal by-product of the introduction of a new algorithm,
which shapes the velocity profile of convective elements at the inner border of
the convective envelope: both the physical grounds and the calibration of the
algorithm are discussed in detail. The final surface compositions of the
various models reflect the differences in the initial iron-seed content and in
the physical structure of AGB stars belonging to different stellar populations.
The agreement with the observed [hs/ls] index observed in intrinsic C stars at
different [Fe/H] is generally good.
