  A large number of neutron stars (NSs), ~10^9, populate the Galaxy, but only a
tiny fraction of them is observable during the short radio pulsar lifetime. The
majority of these isolated NSs, too cold to be detectable by their own thermal
emission, should be visible in X-rays as a result of accretion from the
interstellar medium. The ROSAT all sky survey has however shown that such
accreting isolated NSs are very elusive: only a few tentative candidates have
been identified, contrary to theoretical predictions that up to several
thousands should be seen. We suggest that the fundamental reason for this
discrepancy lies in the use of the standard Bondi formula to estimate the
accretion rates. We compute the expected source counts using updated estimates
of the pulsar velocity distribution, realistic hydrogen atmosphere spectra, and
a modified expression for the Bondi accretion rate as suggested by recent MHD
simulations, and supported by direct observations in the case of accretion
around supermassive black holes in nearby galaxies and in our own. We find
that, whereas the inclusion of atmospheric spectra partly compensates for the
reduction in the counts due to the higher mean velocities of the new
distribution, the modified Bondi formula dramatically suppresses the source
counts. The new predictions are consistent with a null detection at the ROSAT
sensitivity.
