  We propose a new formation mechanism (direct-supernova) for low-mass X-ray
binaries (LMXBs) that does not involve any prior phase of mass transfer.
Survival through the supernova (SN) explosion and shrinkage of the orbit is
achieved by a kick velocity of appropriate magnitude and direction imparted to
the neutron star at its birth. We present analytical population synthesis
calculations of LMXBs forming via both the direct-SN and the helium-star SN
mechanisms, and compare the results. We find that the direct-SN channel
contributes a non-negligible fraction of the total LMXB population, depending
strongly on the r.m.s. magnitude of the kick velocity. More importantly, the
direct-SN mechanism provides a natural way for the formation of low-mass binary
pulsars in nearly circular orbits with orbital periods in excess of about 100
days, which cannot have been formed via the helium-star SN mechanism.
