  Extremely metal-poor low-mass stars experience an ingestion of protons into
the helium-rich layer during the core He-flash, resulting in the production of
neutrons through the reactions
^{12}C(p,\gamma)^{13}N(\beta)^{13}C(\alpha,n)^{16}O. This is a potential site
for the production of s-process elements in extremely metal-poor stars not
occurring in more metal-rich counterparts. Observationally, the signatures of
s-process elements in the two most iron deficient stars observed to date,
HE1327-2326 & HE0107-5240, still await for an explanation. We investigate the
possibility that low-mass EMP stars could be the source of s-process elements
observed in extremely iron deficient stars, either as a result of
self-enrichment or in a binary scenario as the consequence of a mass transfer
episode. We present evolutionary and post-processing s-process calculations of
a 1Msun stellar model with metallicities Z=0, 10^{-8} and 10^{-7}. We assess
the sensitivity of nucleosynthesis results to uncertainties in the input
physics of the stellar models, particularly regarding the details of convective
mixing during the core He-flash. Our models provide the possibility of
explaining the C, O, Sr, and Ba abundance for the star HE0107-5240 as the
result of mass-transfer from a low-mass EMP star. The drawback of our model is
that if mass would be transferred before the primary star enters the AGB phase,
nitrogen would be overproduced and the ^{12}C/^{13}C abundance ratio would be
underproduced in comparison to the observed values. Our results show that
low-mass EMP stars cannot be ruled out as the companion stars that might have
polluted HE1327-2326 & HE0107-5240 and produced the observed s-process pattern.
However, more detailed studies of the core He-flash and the proton ingestion
episode are needed to determine the robustness of our predictions.
