The binaries PSR J1141-6545 and PSR B2303+46 each appear to contain a white
dwarf which formed before the neutron star. We describe an evolutionary pathway
to produce these two systems. In this scenario, the primary transfers its
envelope onto the secondary which is then the more massive of the two stars,
and indeed sufficiently massive later to produce a neutron star via a
supernova. The core of the primary produces a massive white dwarf which enters
into a common envelope with the core of the secondary when the latter evolves
off the main sequence. During the common envelope phase, the white dwarf and
the core of the secondary spiral together as the envelope is ejected. The
evolutionary history of PSR J1141-6545 and PSR B2303+46 differ after this
phase. In the case of PSR J1141--6545, the secondary (now a helium star)
evolves into contact transferring its envelope onto the white dwarf. We propose
that the vast majority of this material is in fact ejected from the system. The
remains of the secondary then explode as a supernova producing a neutron star.
Generally the white dwarf and neutron star will remain bound in tight, often
eccentric, systems resembling PSR J1141-6545. These systems will spiral in and
merge on a relatively short timescale and may make a significant contribution
to the population of gamma ray burst progenitors. In PSR B2303+46, the
helium-star secondary and white dwarf never come into contact. Rather the
helium star loses its envelope via a wind, which increases the binary
separation slightly. Only a small fraction of such systems will remain bound
when the neutron star is formed (as the systems are wider). Those systems which
are broken up will produce a population of high-velocity white dwarfs and
neutron stars.Comment: 9 pages, 10 figures; MNRAS in pres
