Log N -- Log S distributions of accreting and cooling isolated neutron   stars
  We model populations of isolated neutron stars in the Galaxy following their orbital and magneto-rotational evolution. It is shown that accretors become more abundant than coolers at fluxes below $\sim 10^{-13}$ erg cm$^{-2}$ s$^{-1},$ and one can predict that about one accreting neutron star per square degree should be observed at the {\it Chandra} and {\it Newton} flux limits of $\sim 10^{-16}$ erg cm$^{-2}$ s$^{-1}.$ The soft ROSAT sources associated with isolated neutron stars can be relatively young cooling objects only if the neutron star birth rate in the Solar vicinity during the last $\sim 10^6$ yr is higher than that inferred from radiopulsar observations. 
S.B. Popov (SAI), M. Colpi (Univ. of Milan), M.E. Prokhorov (SAI), A.   Treves (Univ. of Como) and R. Turolla (Univ. of Padova)