Non-ideal Particle Distributions from Kinetic Freeze Out Models.pdf

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Non-ideal Particle Distributions from Kinetic Freeze Out Models.pdf

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Non-ideal Particle Distributions from Kinetic Freeze Out Models

a r X i v : n u c l - t h / 9 8 0 8 0 2 4 v 1 1 1 A u g 1 9 9 8 Non-ideal Particle Distributions from Kinetic Freeze Out Models Cs. Anderlik,1 Zs.I. La?za?r,1 V.K. Magas,1 L.P. Csernai,1,2 H. Sto?cker3 and W. Greiner3 1 Section for Theoretical Physics, Department of Physics University of Bergen, Allegaten 55, 5007 Bergen, Norway 2 KFKI Research Institute for Particle and Nuclear Physics P.O.Box 49, 1525 Budapest, Hungary 3 Institut fu?r Theoretische Physik, Universita?t Frankfurt Robert-Mayer-Str. 8-10, D-60054 Frankfurt am Main, Germany Abstract: In fluid dynamical models the freeze out of particles across a three dimensional space-time hypersurface is discussed. 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. 1. Introduction The freeze out of particle distributions is an essential part of continuum or fluid dynamical reaction models. From the point of view of observable consequences this is one of the most essential parts of the model. On the other hand this step is not based on fluid dynamical principles and governed by a large variaty of ad hoc assumptions. The freeze out can be considered as a discontinuity across a hypersurface in space-time. The general theory of discontinuities in relativistic flow was not worked out for a long time, and the 1948 work of A. Taub1 discussed discontinuities across propagating hypersurfaces only (which have a space-like normal vector, dσμdσμ = ?1). Events happening on a propagating, (2 dimensional) surface belong to this category. Another type of change in a continuum is an overall sudden change in a finite volume. This is represented by a hypersurface with a time-like normal, dσμdσμ = +1, called confusingly both space-like and time-like surface in the literature. In 1987 Taubs approach was generalized to both types of surfaces,2 making it possible