# Kinetics vs hydrodynamics: generalization of Landau/Cooper-Frye prescription for freeze-out

Source: [Kinetics vs hydrodynamics: generalization of Landau/Cooper-Frye prescription for freeze-out](<https://www.sota2.com/research/paper/68fa23872c2a376019399009>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:52:33.271Z

Authors: Yu.M. Sinyukov, S.V. Akkelin, Iu.A. Karpenko, Y. Hama

Published: 2009-01-12T14:07:06.000Z

## Abstract

The problem of spectra formation in hydrodynamic approach to A+A collisions is considered within the Boltzmann equations. It is shown analytically and illustrated by numerical calculations that the particle momentum spectra can be presented in the Cooper-Frye form despite freeze-out is not sharp and has the finite temporal width. The latter is equal to the inverse of the particle collision rate at points $(t\_{\\sigma}({\\bf r},p),{\\bf r})$ of the maximal emission at a fixed momentum $p$. The set of these points forms the hypersurfaces $t\_\\sigma({\\bf r},p)$ which strongly depend on the values of $p$ and typically do not enclose completely the initially dense matter. This is an important difference from the standard Cooper-Frye prescription (CFp), with a common freeze-out hypersurface for all $p$, that affects significantly the predicted spectra. Also, the well known problem of CFp as for negative contributions to the spectra from non-space-like parts of the freeze-out hypersurface is naturally eliminated in this improved prescription.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0901.1576>)

[PDF](<https://arxiv.org/pdf/0901.1576.pdf>)