  We investigate evolutionary pathways leading to neutron star formation
through the collapse of oxygen-neon white dwarf (ONe WD) stars in interacting
binaries. We consider (1) non-dynamical mass transfer where an ONe WD
approaches the Chandrasekhar mass leading to accretion-induced collapse (AIC)
and (2) dynamical timescale merger-induced collapse (MIC) between an ONe WD and
another WD. We present rates, delay times, and progenitor properties for two
different treatments of common envelope evolution. We show that AIC neutron
stars are formed via many different channels and the most dominant channel
depends on the adopted common envelope physics. Most AIC and MIC neutron stars
are born shortly after star formation, though some have delay times >10 Gyr.
The shortest delay time (25-50 Myr) AIC neutron stars have stripped-envelope,
compact, helium-burning star donors, though many prompt AIC neutron stars form
via wind-accretion from an asymptotic giant branch star. The longest delay time
AIC neutron stars, which may be observed as young milli-second pulsars among
globular clusters, have a red giant or main sequence donor at the time of NS
formation and will eventually evolve into NS + helium WD binaries. We discuss
AIC & MIC binaries as potential gravitational wave sources for LISA. Neutron
stars created via AIC undergo a LMXB phase, offering an electromagnetic
counterpart for those shortest orbital period sources that LISA could identify.
The formation of neutron stars from interacting WDs in binaries is likely to be
a key mechanism for the production of LIGO/Virgo gravitational wave sources
(NS-NS and BH-NS mergers) in globular clusters.
