  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(alpha, n)16O reaction, which releases
neutrons radiatively during interpulse periods (kT ~ 8 keV), and the
22Ne(alpha, 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 to the 13C(alpha, 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(alpha,
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(alpha, n)25Mg rate is varied
by a factor of two. 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.
