  The detailed chemical composition of most metal-poor halo stars has been
found to be highly uniform, but a minority of stars exhibit dramatic
enhancements in their abundances of heavy neutron-capture elements and/or of
carbon. The key question for Galactic chemical evolution models is whether
these peculiarities reflect the composition of the natal clouds, or if they are
due to later mass transfer of processed material from a binary companion. If
the former case applies, the observed excess of certain elements was implanted
within selected clouds in the early ISM from a production site at interstellar
distances. Our aim is to determine the frequency and orbital properties of
binaries among these chemically peculiar stars. This information provides the
basis for deciding whether mass transfer from a binary companion is necessary
and sufficient to explain their unusual compositions. This paper discusses our
study of a sample of 17 moderately (r-I) and highly (r-II) r-process-element
enhanced VMP and EMP stars. High-resolution, low signal-to-noise spectra of the
stars were obtained at roughly monthly intervals over 8 years with the FIES
spectrograph at the Nordic Optical Telescope. From these spectra, radial
velocities with an accuracy of ~100 m/s were determined by cross-correlation
against an optimized template. 14 of the programme stars exhibit no significant
RV variation over this period, while 3 are binaries with orbits of typical
eccentricity for their periods, resulting in a normal binary frequency of
~18+-6% for the sample. Our results confirm our preliminary conclusion from
2011, based on partial data, that the chemical peculiarity of the r-I and r-II
stars is not caused by any putative binary companions. Instead, it was
imprinted on the natal molecular clouds of these stars by an external, distant
source. Models of the ISM in early galaxies should account for such mechanisms.
