  The abundances of r-process elements of very metal-poor stars capture the
history of the r-process enrichment in the early stage of the Milky Way
formation. Currently, various types of astrophysical sites including neutron
star mergers, magneto-rotational supernovae, and collapsars, are suggested as
the origin of r-process elements. The time delay between the star formation and
the production of r-process elements is the key to distinguish these scenarios
with the caveat that the diffusion of r-process elements in the interstellar
medium also induces the delay in r-process enrichment because r-process events
are rare. Here we study the observed Ba abundance data of very metal-poor stars
as the tracer of the early enrichment history of r-process elements. We find
that the gradual increase of [Ba/Mg] with [Fe/H] requires a significant time
delay (100 Myr -- 1 Gyr) of r-process events from star formation rather than
the diffusion-induced delay. We stress that this conclusion is robust to the
assumption regarding s-process contamination in the Ba abundances because the
sources with no delay would overproduce Ba at very low metallicities even
without the contribution from the s-process. Therefore we conclude that sources
with a delay, possibly neutron star mergers, are the origins of r-process
elements.
