  Observations of pulsars in globular clusters (GCs) give evidence that more
>10-20% of neutron stars (NSs) ever formed in GCs were retained there. However,
the velocity distribution of field pulsars peaks at 5-10 times the escape
velocities of GCs. Consequently, only a small fraction of GC-NSs should have
been retained, even accounting for low-velocity NSs formed through
electron-capture supernovae. Thus, too few low-velocity NSs should have been
retained in GCs, giving rise to the NS retention problem in GCs. Here we
suggest a novel solution, in which the progenitors of most GC-NSs were ONe
white-dwarfs (WDs) that accreted ambient intra-cluster gas and formed
low-velocity NSs through accretion induced collapse (AIC). The existence of an
early gas-enriched environment in GCs is supported by observations of GC
multiple stellar populations. It is thought that 10s-100s of Myrs after the
formation of the first generation of stars, and after ONe-WDs were already
formed, GCs were replenished with gas which formed a second generation of
stars. Accretion of such replenished gas onto the ONe-WDs catalyzed the AIC
processes. The number of AIC-formed NSs is then sufficient to explain the large
number of NSs retained in GCs. Similar processes might also drive CO-WDs to
produce type-Ia SNe or to merge and form NSs, and similarly drive NSs to AIC
and mergers producing BHs. Moreover, the wide variety of gas-catalyzed binary
mergers and explosive transients suggest to occur in the gas-rich environments
of AGN disk could similarly, and even more efficiently, occur in
second-generation gas in GCs.
