Eur. Phys. J. A (2026) 62: 53
https://doi.org/10.1140/epja/s10050-026-01810-x

Review

s-process nucleosynthesis in low-mass AGB stars by the $_{}^{13}$C($\alpha$,n)$_{}^{16}$O neutron source

¹ Dpt. Física Teórica y del Cosmos, University of Granada, 18071, Granada, Spain
² Department of Physics and Geology, University of Perugia, via A. Pascoli s/n, 06125, Perugia, Italy
³ INFN Section of Perugia, via A. Pascoli s/n, 06125, Perugia, Italy
⁴ INAF, Osservatorio Astronomico di Roma, via Frascati 33, Monte Porzio Catone, 00078, Rome, Italy
⁵ INAF, Osservatorio Astronomico d’Abruzzo, Via Mentore Maggini, 64100, Teramo, Italy
⁶ INFN, Sezione di Roma, Piazzale A. Moro 2, 00185, Rome, Italy

^a This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 8 December 2025
Accepted: 5 February 2026
Published online: 13 March 2026

Abstract

In this review we outline the temporal growth of our knowledge on slow neutron captures (the so-called s-process), concentrating on its main part occurring during the final stages of stellar evolution for low or intermediate-mass stars when they approach for the second time the Red Giant Branch and are therefore called Asymptotic Giant Branch, or AGB, stars. In particular, we focus our attention on how, in this field, studies passed from a first era of inquiries based on nuclear systematics (now often referred to as the the phenomenological approach), to numerical nucleosynthesis computations performed in stellar codes. We then discuss how these last were forced, by observational constraints, to almost abandon, for the synthesis of nuclei between Sr and Pb (i.e. the maincomponent), the rather naturally activated $_{}^{22}$Ne($\alpha$,n)$_{}^{25}$Mg neutron source (operating efficiently at T$\gtrsim$ 3.5 $·$ 10$_{}^8$ K, i.e. 30 keV, and producing a neutron density $n_n\gtrsim 5·{10}^8$${\text{cm}}^{-3}$). This implied considering the alternative reaction $_{}^{13}$C($\alpha$,n)$_{}^{16}$O, that can be activated locally after each of the recurring mixing episodes from the envelope (collectively referred to as the Third Dredge Up, or TDU). The mentioned crucial reaction occurs at a relatively low temperature ($T\simeq 8-9·{10}^7$ K., i.e. less than 8 keV), in the time intervals separating two subsequent thermalinstabilities of the He shell (also named ThermalPulses, or TP). The layers where $_{}^{13}$C($\alpha$,n)$_{}^{16}$O operates are characterized by a radiative equilibrium and their low temperature also yields low values for the neutron density ($n_n\lesssim {10}^7$${\text{cm}}^{-3}$). The activation of such a neutron source is unfortunately not straightforward, as little $_{}^{13}$C is left behind by shell H burning in the zone bracketed by the two alternatively burning shells of AGB stars. One has therefore to discover the proper mixing mechanisms providing further proton captures on the abundant $_{}^{12}$C there present. Despite this difficulty, the modelling of s-process as provided by this alternative neutron-producing reaction was crucial to clarify the origin and the distribution of nuclei from Sr up to Pb and Bi in the Galaxy, hence we outline the various (mainly non-convective) mixing processes so far considered for this purpose and their relative efficiency. We conclude by accounting for the extensive observations and measurements on several sources, from low-metallicity stellar objects to presolar grains, from normal AGB stars to post-AGB sources and binary systems, which motivated the crucial change of paradigm from the $_{}^{22}$Ne($\alpha$,n)$_{}^{25}$Mg to the $_{}^{13}$C($\alpha$,n)$_{}^{16}$O neutron source.