X-ray binaries and their descendants: binary radio pulsars; evidence for   three classes of neutron stars?
  An important recent discovery by Pfahl et al. (2002) is that there are two classes of Be X-ray binaries: one with orbits of small eccentricity (<0.25), in which the neutron stars received hardly any kick velocity at birth and a class with substantial orbital eccentricities, in which the neutron stars received a kick velocity of order 100 km/s at birth. Also many of the double neutron stars (5 out of 7) have a low orbital eccentricity (0.09 to 0.27), which indicates that their second-born neutron stars received hardly any velocity kick at birth. These second-born neutron stars tend to have low masses (1.25 to 1.35 Msun). It is proposed that the low-mass, low-kick neutron stars are formed by the electron capture of degenerate O-Ne-Mg cores of stars with initial masses below about 12-14 Msun, while the high-kick neutron stars originated from the photo-disintegration collapse of the iron cores of stars which started out with masses larger than this limit. The latter group may be further subdivided into two classes of different mass. 
E.P.J. van den Heuvel