Investigation of the single neutron exposure model for the s-process: the primary nature of the neutron source

The primary nature of the $^{13}$C neutron source is very significant for the studies of the s-process nucleosynthesis. In this paper we present an attempt to fit the element abundances observed in 16 s-rich stars using parametric model of the single neutron exposure. The calculated results indicate that almost all s-elements were made in a single neutron exposure for 9 sample stars. Although a large spread of neutron exposure is obtained, the maximum value of the neutron exposure will reach about 7.0 mbarn$^{-1}$, which is close to the theoretical predictions by the AGB model. The calculated result is a significant evidence for the primary nature of the neutron source. Combining the result obtained in this work and the neutron exposure-initial mass relations, a large spread of neutron exposure can be explained by the different initial stellar mass and their time evolution. The possibility that the rotationally induced mixing process can lead to a spread of the neutron exposure in AGB stars is also existent.