Freeze-Out Problem in Hydrokinetic Approach toA+ACollisions

Abstract

A new method for evaluating spectra and correlations in the hydrodynamic approach is proposed. It is based on an analysis of the Boltzmann equations (BE) in terms of probabilities for constituent particles to escape from the interacting system. The conditions of applicability of the Cooper-Frye freeze-out prescription are considered within the method. The results are illustrated with a nonrelativistic exact solution of BE for an expanding spherical fireball as well as with approximate solutions for ellipsoidally expanding ones.

Covariant description of kinetic freeze-out through a finite time-like layer

“…The basis of the gradual FO method is to separate the "full" f = f (x, p) distribution function into still interacting and already frozen out parts, f = f i + f f , and describe the evolution of both components in a self consistent way [4,5,6,7,8]. This can be achieved by introducing the so-called escape rate, P esc (s, p), used to drain particles, which no longer collide from the interacting component, f i , and to gradually build up the free component, f f .…”

Particle emission in hydrodynamics: a problem needing a solution

“…The formalism that we presented for continuous emission needs improvements, for example the ansatz of immediate rethermalization is not realistic. An example of such an attempt is [23]. Finally, it is also necessary to think of ways to include continuous emission in hydrodynamics.…”

“…Comparison with data was performed in [11][12][13][14][15][16][17]. The emission mechanism was considered in [18][19][20][21][22][23]. In this paper, I concentrate on the problem of particle emission in hydrodynamics.…”

Sudden Freeze-Out vs. Continuous Emission: Duality in Hydro-Kinetic Approach to <i≯A</i≯+<i≯A</i≯ Collisions

“…Since f esc (x, p) is formed from the particles suffering last collisions at space-time point x it is associated with term P F gain and form the emission function S [7] …”

“…[7] and express the observables through both distribution and emission functions of expanding systems. We start from the Boltzmann equations (BE) as more general than the hydrodynamic ones.…”