Calculating Method and Characteristics of the Distribution of Neutron Exposures in the Radiative S-process Nucleosynthesis Model for AGB Stars

A study on the distribution of neutron exposures in a low-mass asymptotic giant branch (AGB) star is presented, according to the s-process nucleosynthesis model with the 12C(α, n)16O reaction occurred under radiative conditions in the interpulse phases. The model parameters, such as the over- lap factor r of two successive convective thermal pulses, the mass ratio q of the 13C shell with respect to the He intershell, and the effective mass of 13C in the 13C shell, vary with the pulse number. Considering these factors, a calculating method for the distribution of neutron exposures in the He intershell has been presented. This method has the features of simplicity and universality. Using this method, the exposure distribution for the stellar model of a star with the mass of 3 Mʘ and the solar metallicity has been calculated. The results suggest that under the reasonable assumption that the number density of neutrons is uniform in the 13C shell, the final exposure distribution approaches to an exponential distribution. For a stellar model with the definite initial mass and metallicity, there is a definite relation between the mean neutron exposure τ0 and the neutron exposure Δτ of each pulse, namely τ0 = 0.434λ(q1, q2, …, qmmax +1, …, r1, r2, …, rmmax +1)Δτ, where mmax is the total number of thermal pulses with the third dredge-up episode, and the proportional coeffcient λ(q1, q2, …, qmmax +1, …, r1, r2, …, rmmax +1) can be determined by an exponential curve fitting to the final exposure distribution. This new formula quantitatively unifies the classical model with the s-process nu- cleosynthesis model by means of neutron exposure distribution, and makes the classical model continue to offer guidance and constraints to the s-process nu- merical calculations of stellar models.