N ov 2 00 7 Bjorken model with Freeze Out

The freeze out of the expanding systems, created in relativistic heavy ion collisions, is discussed. We combine Bjorken scenario with earlier developed freeze out equations into a unified model. The important feature of the proposed model is that physical freeze out is completely finished in a finite time, which can be varied from 0 (freeze out hypersurface) to ∞. The dependence of the post freeze out distribution function on this freeze out time will be studied. As an example model is completely solved and analyzed for the gas of pions. In the ultrarelativistic heavy ion collisions at RHIC the total number of the produced particles exceeds several thousands, therefore one can expect that the produced system behaves as a " matter " and generates collective effects. Indeed strong collective flow patterns have been measured at RHIC, which suggests that the hydrodynamical models are well justified during the intermediate stages of the reaction: from the time when local equilibrium is reached until the freeze out (FO), when the hydrodynamical description breaks down. In the recent works [1] it has been shown that the basic assumptions of the Boltzman Transport Equation (BTE) are not satisfied during FO and therefore its description has to be based on Modified BTE, suggested in [1]. When the characteristic length scale, describing the change of the distribution function, becomes smaller than mean free path (this always happens at late stages of the FO), then the basic assumptions of the BTE get violated,