In order to get a broader view of the s-process nucleosynthesis we study the abundance distribution of heavy elements of 35 barium stars and 24 CEMP-stars, including nine CEMP-s stars and 15 CEMP-r/s stars. The similar distribution of [Pb/hs] between CEMP-s and CEMP-r/s stars indicate that the s-process material of both CEMP-s and CEMP-r/s stars should have a uniform origin, i.e. mass transfer from their predominant AGB companions. For the CEMP-r/s stars, we found that the r-process should provide similar proportional contributes to the second s-peak and the third s-peak elements, and also be responsible for the higher overabundance of heavy elements than those in CEMP-s stars. Which hints that the r-process origin of CEMP-r/s stars should be closely linked to the main r-process. The fact that some small $r$ values exist for both barium and CEMP-s stars, implies that the single exposure event of the s-process nucleosynthesis should be general in a wide metallicity range of our Galaxy. Based on the relation between $C_{r}$ and $C_{s}$, we suggest that the origin of r-elements for CEMP-r/s stars have more sources. A common scenario is that the formation of the binary system was triggered by only one or a few supernova. In addition, accretion-induced collapse(AIC) or SN 1.5 should be the supplementary scenario, especially for these whose pre-AGB companion with higher mass and smaller orbit radius, which support the higher values of both $C_{r}$ and $C_{s}$.
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