At the end of their life, stars of low- and intermediate-mass evolve along the Asymptotic Giant Branch, where they experience recurrent thermal instabilities and substantial mass loss. During this phase, the stars undergo a very rich and unique nucleosynthesis. Moreover, recurrent dredge-up events enrich the stellar surface with the freshly synthesized nuclides which are then ejected into the interstellar medium through the strong winds. The thermally pulsing AGB stars thus play a crucial role in the chemical evolution of galaxies.
On the other hand, AGB stars are important contributors to the integrated luminosity of stellar systems in a wide range of ages. A coverage of this phase is needed in particular for the treatment of the luminosity functions and color magnitude diagrams of star clusters. Last but not least, the corresponding stellar models are basic tools to study carbon stars, OH/IR stars, planetary nebulae and their central objects (white dwarfs).
In the last 15 years, extensive observational data has become available that
changed and highly constrained the theoretical view of the AGB evolution.
Most of the progresses came from Magellanic Cloud studies, which revealed
for example the absence of very luminous carbon stars (which were previously
predicted to originate from stars with initial masses between 5 and
), and the unexpected existence of relatively faint and lower mass
carbon stars (Blanco et al. 1980; Mould & Aaronson 1982, 1986;
Wood et al.
1983; Reid & Mould 1984; Aaronson & Mould 1985;
Smith & Lambert 1989).
This so-called ``carbon star mystery'' (Iben 1981) has led to the concept of
hot-bottom convective envelope burning (Iben 1975; Sackmann et al. 1974;
Scalo et al. 1975; Sackmann & Boothroyd 1992). This mechanism, which
reconverts C-rich to O-rich envelopes and produces 
, was
confirmed by the existence of lithium enriched AGB stars (Smith & Lambert
1989, 1990b; Plez et al. 1993; Smith et al. 1995). On the other hand, the
discovery, inside meteorites, of interstellar grains which have been formed
in the wind of cool carbon stars (see e.g. Zinner et al. 1991a),
complemented the stellar abundance analysis, and brought crucial
informations on AGB star nucleosynthesis. In spite of important
improvements, many important issues of AGB evolution still remain to be
addressed, observationally as well as theoretically.
This paper is the first of a series aimed at examining all the physical
processes that may induce abundance anomalies in the surface of evolved AGB
stars. In the present work, we specifically investigate the case of
intermediate-mass stars. Stars with initial masses between 3 and 
and with metallicities Z of 0.02 and 0.005 have been evolved, starting
from the pre-main sequence until they had gone through a number of
helium-shell flashes along the TP-AGB. The 
(6 and 
) stars
with Z = 0.02 (0.005) ignite off-center carbon burning and will not be
discussed in detail. For each other stellar mass, full evolutionary models
were computed up to the fourth ``full amplitude'' thermal pulse in the
so-called ``asymptotic regime''. Synthetic evolution was then used to follow
global surface properties and nucleosynthesis up to the planetary nebula
ejection. This self-consistent and extended set of models is particularly
relevant for population synthesis and chemical evolution models. Very
complete figures and tables containing informations about the center and
surface evolution of the structure and chemical composition for all our
models are available.
In the present computations, which include the latest input physics, the evolution of the chemical composition is followed by only taking into account nuclear reactions and mixing inside convective zones (we assume instantaneous mixing, except when hot-bottom burning occurs, which requires a time-dependent convective diffusion algorithm). We neglect all other mixing mechanism of non-convective origin which may contribute to transport chemical elements in radiative regions, like rotation-induced mixing or diffusion. In the stellar mass range we consider, this approximation is supported by the observed surface abundances at different evolutionary stages. This is however certainly not the case for lower mass stars, for which some ``non-standard'' mixing processes have to be invoked to explain various chemical anomalies.
The physical ingredients of our models and numerical aspects of the computations are presented in Sects. 2 and 3, respectively. The general properties of the stars and their chemical evolution during the phases prior to the TP-AGB one are summarized in Sects. 4 and 5, respectively.
In Sect. 6, we briefly present the structural features of the thermal pulses and discuss the occurrence of the third dredge-up in our models. We derive a core-mass luminosity relation for our less massive stars that do not undergo hot-bottom burning. We then present the extrapolation procedure that we use to follow both the evolution and the nucleosynthesis in the ``asymptotic regime" up to the TP-AGB tip. We also give the initial mass-final mass relation resulting from our models, that appears to be in good agreement with the observed one.
In Sect. 7, we review the various nucleosynthesis sites inside TP-AGB stars,
namely the burning shells (He, 
and H), the convective tongue
that develops during a thermal runaway and the base of hot convective
envelopes. We investigate in detail the nucleosynthetic processes that
involve the Li, CNO, F, NeNa and MgAl elements and neutrons. We then discuss
which specific nuclear region, inside a TP-AGB star, mainly contributes to
the surface abundance change of each nuclide when a third dredge-up occurs.
In Sect. 8, we finally present our predictions concerning (i) the
evolution of all the surface isotopic ratios by including our evolutionary
models and synthetic extrapolations up to the convective envelope removal
and (ii) the chemical yields ejected at different ages for all the
species up to 
. As in the previous sections, comparisons
between our predictions and observations are attentively performed.