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This paper provides a detailed analysis of the main component of the slowneutron capture process (the s-process), which accounts for the solarabundances of half of the nuclei with 90 <~ A <~ 208. We examine the impact ofthe uncertainties of the two neutron sources operating in low-mass asymptoticgiant branch (AGB) stars: the 13C(alpha, n)16O reaction, which releasesneutrons radiatively during interpulse periods (kT ~ 8 keV), and the22Ne(alpha, n)25Mg reaction, partially activated during the convective thermalpulses (TPs). We focus our attention on the branching points that mainlyinfluence the abundance of s-only isotopes. In our AGB models, the 13C is fullyconsumed radiatively during interpulse. In this case, we find that the presentuncertainty associated to the 13C(alpha, n)16O reaction has marginal effects ons-only nuclei. On the other hand, a reduction of this rate may increase theamount of residual (or unburned) 13C at the end of the interpulse: in thiscondition, the residual 13C is burned at higher temperature in the convectivezone powered by the following TP. The neutron burst produced by the 22Ne(alpha,n)25Mg reaction has major effects on the branches along the s path. Thecontributions of s-only isotopes with 90 <~ A <= 204 are reproduced withinsolar and nuclear uncertainties, even if the 22Ne(alpha, n)25Mg rate is variedby a factor of two. Improved beta-decay and neutron capture rates of a few keyradioactive nuclides would help to attain a comprehensive understanding of thesolar main component.

The Branchings of the Main s-process: Their Sensitivity to alpha-induced Reactions on 13C and 22Ne and to the Uncertainties of the Nuclear Network