Presumably all main sequence stars with initial masses between 
and 
8 
pass through a double-shell burning phase at the
end of their lifetime, also referred to as the asymptotic giant branch
(AGB) phase. During this phase, intermediate mass stars lose most of
their envelope mass while they contribute substantially to the
interstellar abundances of He, C, N, and s-process elements (e.g.\
Renzini & Voli 1981; Iben & Renzini 1983;
Dopita & Meatheringham 1991).
The most quoted work with respect to the yields of intermediate mass stars is that of Renzini & Voli (1981; hereafter RV) who calculated the amount of matter returned to the ISM by AGB stars in the form of e.g. He, C, N, and O. Their well known results have been widely used to compare the predicted abundances in the ejecta of AGB stars with the abundances observed in planetary nebulae (see Clegg 1991 and references therein) and have been often applied in Galactic chemical evolution models (e.g. Matteucci et al. 1989; Rocca-Volmerange & Schaeffer 1990).
In this paper, we use a synthetic evolution model similar in approach to that presented by RV to follow the chemical evolution of stars on the AGB. However, our model differs substantially from that described by RV, both in the various aspects of AGB evolution considered as well as in the parameters that best fit the observations (in particular the mass loss rate on the AGB). The model has been described in detail by Groenewegen & de Jong (1993; hereafter GJ) and applied to various observational aspects of AGB evolution, both for AGB stars in the Galactic disk and Magellanic Clouds (GJ; Groenewegen et al. 1995, hereafter GHJ).
An important aspect of AGB evolution largely neglected in previous studies is the metallicity dependence of the evolutionary algorithms used. Observations show that the luminosity function and relative number ratios of carbon and oxygen-rich AGB stars in the Large and Small Magellanic Clouds are different (see e.g. GJ). One of the explanations for this is the different metallicity in these galaxies. In the actual model, we use a nearly complete metallicity dependent treatment of the evolution of AGB stars covering the first, second, and third dredge up. In addition, in GJ/GHJ take into account several new physical ingredients including the variation of the luminosity during the interpulse period, the fact that the first few pulses are not yet at full amplitude, and the detailed inclusion of mass loss and chemical evolution prior to the AGB.
Before reaching the AGB phase, the main sequence stellar composition has changed during the first dredge-up (experienced by all stars on the red giant branch (RGB)) and during the second dredge-up (experienced by stars with initial mass larger than some certain critical mass). The first dredge up occurs when the convective envelope moves inwards as a star becomes a red giant for the first time so that helium and CNO processed material are brought to the surface. Several tenths of solar masses can be lost in this phase for low mass stars (e.g. Sweigart et al. 1990; Rood 1973).
The second dredge-up is associated with the formation of the electron-degenerate CO core after central helium exhaustion and occurs on the early-AGB (hereafter E-AGB). In this case, helium and nitrogen may be dredged up towards the stellar surface. We use the comprehensive set of metallicity dependent stellar evolution tracks provided by the Geneva group (e.g. Schaller et al. 1992) to describe the evolution prior to the AGB. However, to study in detail the influence of the first and second dredge up on the AGB yields, we also consider a metallicity dependent theoretical treatment of these phases (cf. Sect. 3) according to the recipes outlined in GJ. In both cases, the stellar evolution prior to the AGB is coupled consistently to the thermal pulsing AGB phase.
During the third dredge up, carbon is dredged up to the stellar
surface by convection of the carbon-rich pocket formed after each
helium shell flash (or thermal pulse (TP)). By mixing additional
carbon to the envelope, the star may undergo a transition from M-star
(oxygen-rich), to S-star (carbon roughly equal to oxygen), and C-star
(carbon outnumbering oxygen). For stars with 
, this
transition is affected by HBB when both carbon already present and
newly dredged-up carbon are processed at the base of the convective
envelope according to the CNO cycle. We account for the effect of HBB
in an approximate way since the details of this process are not well
understood. Abundance variations during the AGB of individual
elements heavier than oxygen are not taken into account.
The free parameters in our calculations are the mass loss scaling
parameter 
for stars on the AGB (using a Reimers law),
the minimum core mass for dredge-up 
, and the
third dredge-up efficiency 
. We will discuss the effect of
these parameters as well as the effect of HBB on the stellar yields in
Sect. 4. For AGB stars both in the Galactic disk and Magellanic
Clouds, models with 
, 
, and 
including HBB are in best agreement with
the observations. Part of the argumentation for this specific set of
parameter values can be found in GJ and GHJ and references therein.
For this set, we compute the stellar yields of H, 
He, 
C,
C, 
N, and 
O of AGB stars with initial mass
between 0.8 and 8 
, and initial metallicity Z = 0.001, 0.004, 0.008,
0.02 and 0.04, as presented at the end of this paper.
This paper is organized as follows. In Sect. 2, we define the stellar yields used throughout this paper. In Sect. 3, we briefly describe the basic ingredients of the synthetic evolution model related to the chemical evolution of stars on the AGB. In Sect. 4, resulting stellar yields are presented and their dependence on the main model assumptions is examined. In Sect. 5, we discuss the preferred set of stellar yields with respect to earlier theoretical work and compare the abundances predicted during the final stages of the AGB with those observed in planetary nebulae (PNe) in the Galactic disk.