  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 $C_{s}$.
