Production of n-rich nuclei in red giant stars

We outline a partial historical summary of the steps through which the nucleosynthesis phenomena induced by slow neutron captures (the s-process) were clarified, a scientific achievement in which Franz Käppeler played a major role. We start by recalling the early phenomenological approach, which yielded a basic understanding of the subject even before models for the parent stellar evolutionary stages were developed. Through such a tool, rough limits for the neutron density and exposure were set, and the crucial fact was understood that more than one nucleosynthesis component is required to account for solar abundances of s-process nuclei up to the Pb-Bi region. We then summarize the gradual understanding of the stellar processes actually involved in the production of nuclei from Sr to Pb (the so-called Main Component, achieved in the last decade of the past century and occurring in red giants of low and intermediate mass, M $\lesssim$ 8 M${}_{\odot }$) populating, in the HR diagram, the Asymptotic Giant Branch or AGB region. We conclude by giving some details on more recent research concerning mixing mechanisms inducing the activation of the main neutron source, ${}^{13}$C(α,n)${}^{16}$O.