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Jakub Skowronski
Reaction ratesThe s-process, explained

Reaction rates

s-process: what if?

In the s-process iron captures neutrons from 13C(α,n) and 22Ne(α,n) and climbs up to lead. Choose a site, change a reaction or a neutron poison and see how the heavy isotopes change.

13C pocket90 MKthermal pulse270 MKHe core250 MK

AGB star, 13C pocket between pulses90 million K · 3500 g/cm3 · 100 thousand years

1What the burn made, from iron to bismuth

N = 50Sr Y ZrN = 82Ba La CeN = 126Pb10−210−11101021031046080100120140160180200Mass number Atimes more than at the start?
stable isotopes-onlybelow a hundredth of the start (burnt)needs a stellar decay this network lacks

AGB star, 13C pocket between pulses: about 15 neutrons captured by every iron seed.

Each dot is a stable isotope: how much more of it there is at the end of the burn than at the start, which is the solar mix. In this small layer, not in the whole star. Squares are s-only isotopes, made by the s-process alone; the shaded bands are the closed neutron shells, where the flow piles up. The s-process peaks: strontium, yttrium, zirconium (A ≈ 88), barium, lanthanum, cerium (A ≈ 138) and lead (A = 208), where nuclei with closed neutron shells capture slowly and pile up.

Neutron exposurehow many neutrons a nucleus has met, per millibarn of its target area (1 mb = 10−27 cm2)
0.247 mb−1
Peak neutron density
1.1 × 107 cm−3
Neutrons captured per seedper heavy nucleus from iron up
15.3

How to read it

The neutron exposure τ measures how many neutrons each nucleus was offered during the burn: the neutron density times their speed, added up over time, in neutrons per millibarn. A nucleus with a cross section (the MACS) of 100 mb captures about 100 τ of them. An exposure of a few tenths per millibarn is enough to carry iron up to barium and lead.

Making a source faster in the 13C pocket changes little: the 13C burns completely anyway, only sooner. What matters more is how much 13C there is, and how many neutrons the poisons take: raise the initial 14N, or 14N(n,p)14C, and the lead falls. In a thermal pulse, instead, 22Ne(α,n) burns only partly, and its rate directly decides how many neutrons there are.

The model is one zone: fixed temperature and density, one initial composition per site, the network integrated in your browser with the same implicit method as the rates page, and checked against pynucastro. It shows how sources, poisons and seeds move the distribution, not the yields of a star.

Credits, licences and sources

Reaction rates: the JINA REACLIB database (Cyburt et al. 2010), snapshot of 30 March 2025 as distributed with pynucastro; each rate's own source is listed with it in the specialist tables. REACLIB is free to use with citation. reaclib.jinaweb.org

The networks, the rate sources, the solar composition and the screening were exported with pynucastro (Smith et al. 2023; Willcox & Zingale 2018), BSD 3-Clause licence. The browser's solver is checked against pynucastro's own integration of the same networks. github.com/pynucastro/pynucastro

References

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