  Several globular clusters (GCs) in the Galaxy are observed to show internal
abundance spreads in r-process elements (e.g., Eu). We here propose a new
scenario which explains the origin of these GCs (e.g., M5 and M15). In this
scenario, stars with no/little abundance variations first form from a massive
molecular cloud (MC). After all of the remaining gas of the MC is expelled by
numerous supernovae, gas ejected from asymptotic giant branch stars can be
accumulated in the central region of the GC to form a high-density
intra-cluster medium (ICM). Merging of neutron stars then occurs to eject
r-process elements, which can be efficiently trapped in and subsequently mixed
with the ICM. New stars formed from the ICM can have r-process abundances quite
different from those of earlier generations of stars within the GC. This
scenario can explain both (i) why r-process elements can be trapped within GCs
and (ii) why GCs with internal abundance spreads in r-process elements do not
show [Fe/H] spreads. Our model shows that (i) a large fraction of Eu-rich stars
can be seen in Na-enhanced stellar populations of GCs, as observed in M15, and
(ii) why most of the Galactic GCs do not exhibit such internal abundance
spreads. Our model demonstrates that the observed internal spreads of
$r$-process elements in GCs provide strong evidence for prolonged star
formation (~10^8 yr).
