  Models of primordial and hyper-metal-poor stars with masses similar to the
Sun experience an ingestion of protons into the hot core during the core helium
flash phase at the end of their red giant branch evolution. This produces a
concurrent secondary flash powered by hydrogen burning that gives rise to
further nucleosynthesis in the core. We perform post-process nucleosynthesis
calculations on a one-dimensional stellar evolution calculation of a star of 1
solar mass and metallicity [Fe/H] = -6.5 that suffers a proton ingestion
episode. Our network includes 320 nuclear species and 2,366 reactions and
treats mixing and burning simultaneously. The mixing and burning of protons
into the hot convective core leads to the production of 13C, which then burns
via the 13C(alpha,n)16O reaction releasing a large number of free neutrons.
During the first two years of neutron production the neutron poison 14N
abundance is low, allowing the prodigious production of heavy elements such as
strontium, barium, and lead via slow neutron captures (the s process). These
nucleosynthetic products are later mixed to the stellar surface and ejected via
stellar winds. We compare our results with observations of the hyper-metal-poor
halo star HE 1327-2326, which shows a strong Sr overabundance. Our model
provides the possibility of self-consistently explaining the Sr overabundance
in HE 1327-2326 together with its C, N, and O overabundances (all within a
factor of ~4) if the material were heavily diluted, for example, via mass
transfer in a wide binary system. The model produces at least 18 times too much
Ba than observed, but this may be within the large modelling uncertainties. In
this scenario, binary systems of low mass must have formed in the early
Universe. If true then this puts constraints on the primordial initial mass
function.
