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Astron. Astrophys. 333, 926-941 (1998)

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2. Computer codes used in the paper

To calculate the evolution of a [FORMULA] star from the ZAMS through to the core helium flash we used the code described by Raffelt & Weiss (1992), which, in the meantime, has been updated with respect to new opacity data (Rogers & Iglesias 1992; Iglesias & Rogers 1996) and plasma neutrino emission (Haft et al. 1994). The mass fraction of heavy elements was taken as [FORMULA] ([FORMULA]) to approximately match the metallicities of M 13 ([Fe/H] = -1.49) and [FORMULA]  Cen ([FORMULA] [Fe/H] [FORMULA]), whereas the initial helium abundance was [FORMULA] as in the big bang composition (Walker et al. 1991). The adopted value of the mixing length parameter [FORMULA] (times the pressure scale height, [FORMULA]) came from calibrating a solar model.

A number of selected red giant models were used to interpolate temperature and density distributions as well as to follow the movements in mass of the HBS and the BCE as the star ascends the RGB. Following the procedures described in Denissenkov & Weiss 1996 (Paper I), mixing in the radiative zone between the HBS and the BCE was modelled by introducing diffusion terms into the standard equations of nuclear kinetics. Results of these deep mixing calculations depend on a choice of two parameters: the depth of mixing [FORMULA] determined as a relative mass coordinate of the deepest radiative layer involved in the mixing (measured from the HBS in units of the mass separating the HBS and the BCE), and the diffusion coefficient [FORMULA]. The latter may not be chosen arbitrarily large because there are some estimates of its "reasonable" upper limit values which yield [FORMULA] [FORMULA] cm2 s-1 (see Paper I). The nuclear kinetics network used in the deep mixing calculations includes all important nuclides participating in the reactions of the CNO-, NeNa- and MgAl-cycles as well as those in a few reactions of the pp-chains (to follow changes of the 3 He abundance) and numbers 26 particles coupled by 30 reactions.

To estimate nucleosynthesis yields from intermediate mass AGB stars we employed an algorithm developed by Denissenkov et al. (1997, hereafter Paper II) which is very similar to the scheme used by Renzini & Voli (1981). The algorithm takes into account nuclear processing in the HBS (in an AGB star!) and at the BCE (hot bottom burning, hereafter HBB) between pulses as well as the convective shell He burning nucleosynthesis during a pulse in a simplified parameterized manner. A number of parameters are not well constrained in these calculations. For instance, the temperature of the HBB and the amount of material dredged up after finishing every pulse remain very uncertain (Lattanzio et al. 1997). Therefore, in Sect. 4 we shall concentrate only on those results of our nucleosynthesis calculations in intermediate mass AGB stars which weakly depend on the choice of such parameters or, otherwise, specially emphasize which values of parameters lead to a particular result supported by observations. Unfortunately, mainly because of uncertainties in the current treatment of convective overshoot in stars (Frost & Lattanzio 1996), such an approach seems to be the only one possible at present. Our nuclear kinetics network applied in AGB stars includes the same nuclides and reactions as those in the deep mixing code plus Si isotopes; 3 [FORMULA] -reaction; [FORMULA] -reactions on 12 C, 14 C, 14 N, 15 N, 16 O, 17 O, 18 O, 20 Ne, 21 Ne, 22 Ne, 24 Mg, 25 Mg and 26 Mg; [FORMULA],n)-reactions on 13 C, 17 O, 18 O, 21 Ne, 22 Ne, 25 Mg and 26 Mg; neutron captures by 12 C, 13 C, 16 O, 19 F, 20 Ne, 21 Ne, 22 Ne, 23 Na, 24 Mg, 25 Mg, 26 Mg, 27 Al, 28 Si, 29 Si, 30 Si and by an averaged neutron-sink heavy "nucleus" 31 X14 ; as well as the reactions 14 C(p, [FORMULA] N, 14 N(n,p)14 C, 19 F([FORMULA],p)22 Ne, 26 [FORMULA] (n,p)26 Mg, 21 Ne(n, [FORMULA] O and 26 [FORMULA] (n, [FORMULA] Na. The total numbers of nuclides and reactions in this network are 26 and 69, respectively.

To check the degree to which the s-process nucleosynthesis can contribute to the yields of heavy nuclei from intermediate mass AGB stars at low metallicity we have prepared a code which allows all the reactions mentioned above plus neutron captures by numerous heavier nuclides and solves a nuclear kinetics network for the total of 409 particles coupled by 1273 reactions. Neutrons are assumed to have their local equilibrium abundances in every mesh point within the He convective shell.

In all nucleosynthesis codes we used the same input data for the reaction rates. For reactions between charged particles the tables of Caughlan & Fowler (1988, hereafter CF88) were usually used. Exceptions are the reactions 17 O(p, [FORMULA] N and 17 O(p, [FORMULA] F for which the rates proposed by Landré et al. (1990) with the uncertainty factors [FORMULA] and [FORMULA] recommended by Boothroyd et al. (1995) were preferred, and the reaction 12 C [FORMULA] O whose CF88 rate was multiplied by a constant 1.7 as suggested by Woosley & Weaver (1995). For the NeNa-cycle we also considered the latest nuclear reaction rates advocated by El Eid & Champagne (1995) but did not include them in our main calculations (see Sect. 3). Below, where these new rates for the NeNa-cycle are used instead of those of CF88 we note this explicitly.

Neutron capture cross sections were taken from summaries published by Fowler et al. (1967), Holmes et al. (1976), Woosley et al. (1978), Bao & Käppeler (1987), Ratynski & Käppeler (1988), Beer et al. (1989), Cowan et al. (1991) and Schatz et al. (1995). Beta-decay rates were interpolated in temperature and density using the tables of Takahashi & Yokoi (1987).

Finally, to calculate the structure of a low metallicity massive ZAMS star (Sect. 4) we employed a modified version of Paczyski's code (1970) described by Denissenkov (1990).

Thus, in total, we made use of five different stellar evolution/nucleosynthesis codes in this work.

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© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998

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