  We present models for the slow neutron-capture process (s process) in
asymptotic giant branch (AGB) stars of metallicity [Fe/H]=-2.3 and masses 0.9
Msun to 6 Msun. We encountered different regimes of neutron-capture
nucleosynthesis increasing in importance as the stellar mass decreases: the
22Ne(alpha,n)25Mg reaction activated during the thermal pulses, the
13C(alpha,n)16O reaction activated in radiative conditions during the
interpulse periods, and the 13C(alpha,n)16O reaction activated during the
thermal pulses, also as a result of mild proton ingestion episodes. The models
where the 13C burns radiatively (masses ~ 2 Msun) produce an overall good match
to carbon-enhanced metal-poor (CEMP) stars showing s-process enhancements
(CEMP-s), except they produce too much Na and F. On the other hand, none of our
models can provide a match to the composition of CEMP stars also showing
rapid-process enhancements (CEMP-s/r). The models fail to reproduce the
observed Eu abundances, and they also fail to reproduce the correlation between
the Eu and Ba abundances. They also cannot match the ratio of heavy to light
s-process elements observed in many CEMP-s/r stars, which can be more than ten
times higher than in the solar system. To explain the composition of CEMP-s/r
stars we need to invoke the existence of a different "s/r" neutron-capture
process either with features in-between the s and the r processes, or generated
by superpositions of different neutron-capture processes in the same
astrophysical site or in sites linked to each other - for example, in multiple
stellar systems.
