ALGORITHMS FOR NEUTRON DENSITY AND S-PROCESS NUCLEOSYNTHESIS IN A LOW-MASS ASYMPTOTIC GIANT BRANCH STAR

Algorithms for calculating neutron-capture nucleosynthesis in the context of low-mass asymptotic giant branch (AGB) stars are presented. The primary neutron source is the 13C(α, n) 16O reaction which is activated in the convective shell of an AGB star having the characteristics found in stellar model calculations. We show that a one-zone model is useful for obtaining estimates of the consequence of neutron-capture nucleosynthesis; for a typical pulse, this zone has a temperature of ∼136 × 106 K and a density of ∼34,400 g cm-3. This compares with a temperature of 150 × 106 K and a density of 40,000 g cm-3 at the base of the convective shell. Each neutron release episode lasts for ∼10 yr and, if 13C is introduced into the convective shell at a constant rate, the mean neutron number density during most of this episode is given approximately by n̄n≃ Ñ13/[τinΣ′], where Ñ13 is the total number of 13C nuclei introduced into the convective shell over the time interval τin, and Σ′ = ΣkNk〈σν〉k, where Nk is the total number in the convective shell of the kth isotope (if it does not recycle neutrons), σ is a neutron-capture cross section, ν is a relative velocity, and 〈σν〉k is σν for the /cth isotope averaged over a Maxwell-Boltzmann distribution; finally, 〈σν〉k is an average of 〈σν〉k over the convective shell, weighted by a function defined in the text. Not to be included in Σ′ is the possibly important neutron absorber 12C; also not to be included in Σ′ is 14N, which enters the convective shell toward the end of the introduction episode. Neutron capture on both of these nuclei may lead to the formation of 13C, and thence to another neutron. The time scale for the build up and decay of n̄n is given by 7.5 τ13(0)Σ/Σ′, where Σ = Σ′ + N12〈σν〉12 + N14〈σν〉14 and τ13(0) is the time scale for destruction of 13C by α capture at the base of the convective shell. The abundances of certain interesting isotopes will "freeze out" after all the 13C has been introduced into the convective shell, and the neutron density during freeze out is inversely proportional to the time scale for the decay of n̄n. The precise value of n̄n at any time is influenced by uncertain cross sections for neutron capture by 12C, 14N, 22Ne, and 25Mg, and the present formulation provides a means for easily assessing the effects of changes in experimental estimates of these important cross sections.