Deep searches for isolated radio-quiet neutron stars

Using ROSAT seven isolated neutron stars have been discovered characterised by blackbody spectra at temperatures of 400-800 thousand K and the absence of radio and high energy emissions. Observations with Keck, HST and VLT show faint optical counterparts (m ∼ 24-29) with Rayleigh-Jeans-type spectra (∼ν ^{2}) and large proper motions. These objects are believed to be cooling neutron stars. They are of great interest from the point of view of neutron star astrophysics and nuclear physics. In particular, they allow us to measure neutron star radii and thus to constrain the equation of state at very high densities. We discuss the possibility of discovering larger samples of these objects with future sensitive X-ray sky surveys and follow-up optical observations with extremely large telescopes.