The branchings of the main s-process: their sensitivity to α-induced reactions on 13C and 22Ne and to the uncertainties of the nuclear network

This paper provides a detailed analysis of the main component of the slow neutron capture process (the s-process), which accounts for the solar abundances of half of the nuclei with 90 less than or similar to A less than or similar to 208. We examine the impact of the uncertainties of the two neutron sources operating in low-mass asymptotic giant branch (AGB) stars: the C-13(alpha, n)O-16 reaction, which releases neutrons radiatively during interpulse periods (kT similar to 8 keV), and the Ne-22(alpha, n)Mg-25 reaction, partially activated during the convective thermal pulses (TPs). We focus our attention on the branching points that mainly influence the abundance of s-only isotopes. In our AGB models, the C-13 is fully consumed radiatively during interpulse. In this case, we find that the present uncertainty associated with the C-13(alpha, n)O-16 reaction has marginal effects on s-only nuclei. On the other hand, a reduction of this rate may increase the amount of residual (or unburned) C-13 at the end of the interpulse: in this condition, the residual C-13 is burned at higher temperature in the convective zone powered by the following TP. The neutron burst produced by the Ne-22(alpha, n) Mg-25 reaction has major effects on the branches along the s-path. The contributions of s-only isotopes with 90 less than or similar to A <= 204 are reproduced within solar and nuclear uncertainties, even if the Ne-22(alpha, n)Mg-25 rate is varied by a factor of 2. Improved beta-decay and neutron capture rates of a few key radioactive nuclides would help to attain a comprehensive understanding of the solar main component.