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≲ A ≲ 208. We examine the impact of the uncertainties of the two neutron sources operating in low-mass asymptotic giant branch (AGB) stars: the 13C(α, n)16O reaction, which releases neutrons radiatively during interpulse periods (kT ~ 8 keV), and the 22Ne(α, n)25Mg 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 13C is fully consumed radiatively during interpulse. In this case, we find that the present uncertainty associated with the 13C(α, n)16O 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) 13C at the end of the interpulse: in this condition, the residual 13C is burned at higher temperature in the convective zone powered by the following TP. The neutron burst produced by the 22Ne(α, n)25Mg reaction has major effects on the branches along the s-path. The contributions of s-only isotopes with 90 ≲ A ≤ 204 are reproduced within solar and nuclear uncertainties, even if the 22Ne(α, n)25Mg rate is varied by a factor of 2. Improved β-decay and neutron capture rates of a few key radioactive nuclides would help to attain a comprehensive understanding of the solar main component.