On freeze-out problem in relativistic hydrodynamics
- PDF / 622,771 Bytes
- 7 Pages / 612 x 792 pts (letter) Page_size
- 99 Downloads / 183 Views
ELEMENTARY PARTICLES AND FIELDS Theory
On Freeze-Out Problem in Relativistic Hydrodynamics* Yu. B. Ivanov** and V. N. Russkikh† Gesellschaft fur ¨ Schwerionenforschung mbH, Darmstadt, Germany; Russian Research Centre “Kurchatov Institute”, Moscow Received November 5, 2008
Abstract—A finite unbound system which is equilibrium in one reference frame is in general nonequilibrium in another frame. This is a consequence of the relative character of the time synchronization in the relativistic physics. This puzzle was a prime motivation of the Cooper–Frye approach to the freeze-out in relativistic hydrodynamics. Solution of the puzzle reveals that the Cooper–Frye recipe is far not a unique phenomenological method that meets requirements of energy–momentum conservation. Alternative freeze-out recipes are considered and discussed. PACS numbers: 24.10.Nz, 25.75.-q DOI: 10.1134/S1063778809070187
1. INTRODUCTION Hydrodynamics is now a conventional approach to simulations of heavy-ion collisions. Even review papers [1–6] do not comprise a complete list of numerous applications of this approach. The hydrodynamics is applicable to description of hot and dense stage of nuclear matter, when the mean free path is well shorter than the size of the system. However, as expansion proceeds, the system gets dilute, the mean free path becomes comparable to the system size, and hence the hydrodynamic calculation should be stopped at some instant. All hydrodynamic calculations are terminated by a freeze-out procedure, while these freeze-out prescriptions are somewhat different in different models. Moreover, the freeze-out prescriptions include recipes to calculate spectra of produced particles which are of prime experimental interest. Historically, the first method for freeze-out was suggested by Milekhin [7] in the context of the Landau hydrodynamic model of multiple production of particles in high-energy hadron collisions [8]. Later, Milekhin’s approach was criticized by Cooper and Frye [9]. Cooper and Frye pointed out that Milekhin’s approach does not conserve energy and proposed their own recipe of the freeze-out. In this paper we would like to discuss a puzzle which was in fact a prime motivation of the Cooper–Frye approach [9] to the freeze-out in the relativistic hydrodynamics. This ∗
The text was submitted by the authors in English. Deceased. ** E-mail: [email protected] †
puzzle is closely related to the definition of the relativistically invariant distribution function as it was for the first time advanced by Belyaev and Budker [10]. 2. THE PUZZLE Let us consider a droplet of matter (for simplicity consisting of only nucleons), which is characterized by a total baryon number N , a total energy E, and a total momentum P, and occupies a volume V . To be precise, we assume that this droplet is a closed system. Let this droplet be described by an equilibrium distribution (in configuration and momentum space) 1 g (1) f (x, p) = 3 µ (2π) exp {(pµ u − µ) /T } + 1 in the reference frame characterized by 4-velocity uµ . Let us call this frame as
Data Loading...
