Some metal-poor stars have abundance patterns which are midway between the slow (s) and rapid (r) neutron capture processes. We show that the helium shell of a fast rotating massive star experiencing a jet-like explosion undergoes two efficient neutron capture processes: one during stellar evolution and one during the explosion. It eventually provides a material whose chemical composition is midway between the s- and r-process. A low metallicity 40~$M_{odot}$ model with an initial rotational velocity of $sim 700$~km~s$^{-1}$ was computed from birth to pre-supernova with a nuclear network following the slow neutron capture process. A 2D hydrodynamic relativistic code was used to model a $E = 10^{52}$~erg relativistic jet-like explosion hitting the stellar mantle. The jet-induced nucleosynthesis was calculated in post-processing with a network of 1812 nuclei. During the stars life, heavy elements from $30 lesssim Z lesssim 82$ are produced thanks to an efficient s-process, which is boosted by rotation. At the end of evolution, the helium shell is largely enriched in trans-iron elements and in (unburnt) $^{22}$Ne, whose abundance is $sim 20$ times higher than in a non-rotating model. During the explosion, the jet heats the helium shell up to $sim 1.5$ GK. It efficiently activates ($alpha,n$) reactions, such as $^{22}$Ne($alpha,n$), and leads to a strong n-process with neutron densities of $sim 10^{19} - 10^{20}$~cm$^{-3}$ during $0.1$~second. This has the effect of shifting the s-process pattern towards heavier elements (e.g. Eu). The resulting chemical pattern is consistent with the abundances of the carbon-enhanced metal-poor r/s star CS29528-028, provided the ejecta of the jet model is not homogeneously mixed. This is a new astrophysical site which can explain at least some of the metal-poor stars showing abundance patterns midway between the s- and r-process.
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