At least one, but more likely two or more, eccentric neutron star, carbon-o
xygen white dwarf binaries with an unrecycled pulsar have been observed. Ac
cording to the standard scenario for evolving neutron stars that are recycl
ed in common envelope evolution, we expect to observe greater than or simil
ar to 50 such circular neutron star, carbon-oxygen white dwarf binaries, si
nce their formation rate is roughly equal to that of the eccentric binaries
and the time over which they can be observed is 2 orders of magnitude long
er, as we shall outline. We observe at most one or two such circular binari
es, and from that we conclude that the standard scenario must be revised. I
ntroducing hypercritical accretion into common envelope evolution removes t
he discrepancy by converting the neutron star into a black hole which does
not emit radio waves, and therefore would not be observed.