Low mass Asymptotic Giant Branch stars are among the most important polluters of the interstellar medium. In their interiors, the main component (A>90) of the slow neutron capture process (the s-process) is synthesized, the most important neutron source being the 13C(alpha,n)16O reaction. In this paper we review its current experimental status discussing possible future synergies between some experiments currently focused on the determination of its rate. Moreover, in order to determine the level of precision needed to fully characterize this reaction, we present a theoretical sensitivity study, carried out with the FUNS evolutionary stellar code and the NEWTON post-process code. We modify the rate up to a factor of two with respect to a reference case. We find that variations of the 13C(alpha,n)16O rate do not appreciably affect s-process distributions for masses above 3 Msun at any metallicity. Apart from a few isotopes, in fact, the differences are always below 5%. The situation is completely different if some 13C burns in a convective environment: this occurs in FUNS models with M<3 Msun at solar-like metallicities. In this case, a change of the 13C(alpha,n)16O reaction rate leads to non-negligible variations of the elements Surface distribution (10% on average), with larger peaks for some elements (as rubidium) and for neutron-rich isotopes (as 86Kr and 96Zr). Larger variations are found in low-mass low-metallicity models, if protons are mixed and burnt at very high temperatures. In this case, the surface abundances of the heavier elements may vary by more than a factor 50.
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