Non-equilibrated post-freeze-out distributions

We discuss freeze-out on the hypersurface with time-like normal vector, trying to answer how realistic it is to assume thermal post-freeze-out distributions for measured hadrons. Using simple kinetic models for gradual freeze-out we are able to generate a thermal post-FO distribution, but only in a highly simplified situation. In a more advanced model, taking into account rescattering and re-thermalization, the post-FO distribution gets more complicated. The resulting particle distributions are in qualitative agreement with the experimentally measured pion spectra. Our study also shows that the obtained post-FO distribution functions, although analytically very different from the Juettner distribution, do look pretty much like thermal distributions in some range of the parameters. (orig.)