  Central compact objects (CCOs) are a handful of young neutron stars found at
the center of supernova remnants (SNRs). They show high thermal X-ray
luminosities but no radio emission. Spin-down rate measurements of the three
CCOs with X-ray pulsations indicate surface dipole fields much weaker than
those of typical young pulsars. To investigate if CCOs and known radio pulsars
are objects at different evolutionary stages, we carried out a census of all
weak-field (<1e11 G) isolated radio pulsars in the Galactic plane to search for
CCO-like X-ray emission. None of the 12 candidates is detected at X-ray
energies, with luminosity limits of 1e32-1e34 erg/s. We consider a scenario in
which the weak surface fields of CCOs are due to rapid accretion of supernova
materials and show that as the buried field diffuses back to the surface, a CCO
descendant is expected to leave the P-Pdot parameter space of our candidates at
a young age of a few times 10kyr. Hence, the candidates are likely to be just
old ordinary pulsars in this case. We suggest that further searches for
orphaned CCO, which are aged CCOs with parent SNRs dissipated, should include
pulsars with stronger magnetic fields.
