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.