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We have investigated the characteristics of the distribution of neutron exposures (“DNE” hereafter) in the He-shell nucleosynthesis regions in the model of s-process nucleosynthesis in low-mass AGB (Asymptotic Giant Branch) stars in 13C radiatively burning conditions. The result indicates that although the DNE obtained with this model is still approximately exponential, like those of the previous convective s-process scenarios, the relation between the neutron exposure Δτ of each pulse and the mean neutron exposure τ0 is no longer τ0 = −Δτ/ln r, rather, it is now approximately τ0 = −Δτ/ ln{q[1.0020 + 0.6602(r − q) + 4.6125(r − q)2− 10.8962(r − q)3+ 13.9138(r − q)4]} (r is the overlap factor, q is the mass ratio of the 13C shell to the He shell). This formula unifies the stellar model of radiative s-process with the classical model from the angle of DNE.

Taking account of the metallicity dependence of the s-process nucleosynthesis in the AGB stars, we adopted the wind accretion model with the condition of total angular momentum conservation and used the Monte-Carlo method to study the variations and the distributions of the orbital elements of the mild and strong Ba stars. The calculated results show that the level of heavy-element overabundance in a Ba star depends on the orbital period. Since there is a strong dependence of s-process yields on the initial stellar metallicity of the AGB star and a strong increase of the s-process yields in AGB stars with decreasing metallicity, the calculated results strongly suggest that the initial metallicity of the Ba star systems is another important parameter for the level of heavy-element overabundance in a Ba star. The strong Ba stars generally have lower metallicities than mild Ba stars. The masses of AGB progenitor and Ba star are other two parameters which also have some impact on the heavy-element overabundance in the Ba star.