Volodymyr Magas, University of Bergen, Norway

Title:  Idealized freeze out models

Authors: V. Magas, (University of Bergen); L.P. Csernai (University of Bergen, KFKI Research Institute for Particle and Nuclear Physics, Hungary), H. Stocker, W. Greiner (Institut fur Theoretische Physik, Universitat Frankfurt, Germany)

Abstract: Freeze out of particles across a three dimensional space-time hypersurface is discussed in fluid dynamical and kinetic models.  The calculation of final momentum distribution of emitted particles is described for freeze out surfaces, with both space-like and time-like normals, taking into account conservation laws across the freeze out discontinuity.  The important point here is that the post freeze out (FO) distribution need not be a thermal distribution! In fact the post-FO distribution should contain only particles which cross the FO-front outwards, so if the FO-surface is space-like this seriously constrains the shape of post-FO distribution.  We can describe the freeze out kinetics assuming that we have two components of our momentum distribution, free and interacting components. Rescattering within the interacting  component will lead to rethermalization and re-equilibration of this component. Thus the evolution of the interacting component is determined by drain terms and the re-equilibration. We use the  relaxation time approximation to simplify the description of the dynamics. Due to the collision or relaxation terms energy-momentum tensor and baryon current change, and this should be considered in the modified interacting distribution function. We can get a change of temperature, baryon density and flow velocity from the conservation laws.  When we assume that re-thermalization is much faster than particles freezing out, (or much faster than parameters,  n, T and v change). The interacting component can be approximate by the spherical Juttner form. Then, the change of conserved quantities due to particle drain or transfer can be  evaluated.  We apply this model to the baryonfree and massless gas to simplify the equations. The final momentum distribution of emitted particles, for freeze out surface with space-like normal, shows a non-exponential  transverse momentum spectrum. The slope parameter of the transverse momentum distribution increases with increasing transverse momentum, in agreement with recently measured SPS pion and h^- spectra.