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Fully integrated transport approach to heavy ion reactions with an intermediate hydrodynamic stage (0806.1695v3)

Published 10 Jun 2008 in nucl-th, hep-ph, and nucl-ex

Abstract: We present a coupled Boltzmann and hydrodynamics approach to relativistic heavy ion reactions. This hybrid approach is based on the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. Event-by-event fluctuations are directly taken into account via the non-equilibrium initial conditions generated by the initial collisions and string fragmentations in the microscopic UrQMD model. After a (3+1)-dimensional ideal hydrodynamic evolution, the hydrodynamical fields are mapped to hadrons via the Cooper-Frye equation and the subsequent hadronic cascade calculation within UrQMD proceeds to incorporate the important final state effects for a realistic freeze-out. This implementation allows to compare pure microscopic transport calculations with hydrodynamic calculations using exactly the same initial conditions and freeze-out procedure. The effects of the change in the underlying dynamics - ideal fluid dynamics vs. non-equilibrium transport theory - will be explored. The freeze-out and initial state parameter dependences are investigated for different observables. Furthermore, the time evolution of the baryon density and particle yields are discussed. We find that the final pion and proton multiplicities are lower in the hybrid model calculation due to the isentropic hydrodynamic expansion while the yields for strange particles are enhanced due to the local equilibrium in the hydrodynamic evolution. The results of the different calculations for the mean transverse mass excitation function, rapidity and transverse mass spectra for different particle species at three different beam energies are discussed in the context of the available data.

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Summary

  • The paper introduces a novel hybrid model that integrates UrQMD and ideal hydrodynamics to capture both microscopic fluctuations and macroscopic equilibrium in heavy ion collisions.
  • It details a robust coupling methodology that preserves conservation laws and employs the Cooper-Frye freeze-out prescription for realistic particle evolution.
  • Numerical results reveal modified particle yields, enhanced strangeness production, and potential QGP phase transition signatures, steering future high-energy nuclear research.

An Integrated Transport and Hydrodynamics Model in Heavy Ion Collisions

The investigation of heavy ion collisions is crucial for understanding the properties and behavior of hot and dense QCD matter. The paper "A Fully Integrated Transport Approach to Heavy Ion Reactions with an Intermediate Hydrodynamic Stage" introduces a novel hybrid model combining aspects of both the microscopic Ultra-relativistic Quantum Molecular Dynamics (UrQMD) framework and macroscopic hydrodynamics. This hybrid approach enables a more comprehensive analysis of relativistic heavy ion collisions while explicitly incorporating local event fluctuations and equilibrations encountered in such processes.

The hybrid model leverages the strengths of each constituent method: the microscopic UrQMD effectively models the initial non-equilibrium stages of the reaction, accounting for the event-by-event fluctuations and complex inter-particle interactions, while the intermediate hydrodynamic phase assumes local thermal equilibrium to describe the evolution of the hot and dense matter formed in heavy ion collisions. The paper explicitly discusses the coupling methodology between the transport model and the hydrodynamic phase, ensuring conservation laws and realistic freeze-out conditions are adhered to throughout the transition between these frameworks.

The authors meticulously detail each step in constructing this hybrid approach, detailing initial conditions, the hydrodynamic evolution criteria, the choice of the equation of state (EoS), and transition back to transport dynamics via a freeze-out prescription using the Cooper-Frye equation. Particular emphasis is placed on the importance of the initial conditions in determining particle densities and pressure gradients, which fundamentally affect the subsequent flow characteristics and particle yields observed experimentally.

The paper presents strong numerical results across various energy regimes, highlighting the differences between a purely microscopic hadronic model and one where an ideal hydrodynamic stage is introduced. Particularly insightful are findings on particle yields and momentum spectra: the hybrid model predicts lower pion and proton yields when compared to UrQMD due to the isentropic characteristics of hydrodynamic evolution, while showing enhanced production of strange particles—a consequence of achieving thermal equilibrium.

The research also provides valuable insights into the phase structure of nuclear matter. By exploring different equations of state within the hydrodynamic phase (e.g., a free hadron gas model), it paves the way for identifying signatures associated with potential phase transitions from hadronic matter to quark-gluon plasma (QGP). The framework's capacity to accommodate alternate EoS models signals future research avenues aimed at probing the existence and nature of phase transitions in nuclear matter.

The paper's significance is further evidenced by its implications on understanding phenomena such as elliptic flow and strangeness yields, suggesting that delicate interplay between thermal and chemical equilibrations significantly influences final state observables. Consequently, findings presented in this paper serve to refine the theoretical underpinnings required for interpreting experimental data from particle accelerators like CERN-SPS, BNL-RHIC, and FAIR.

In conclusion, this hybrid transport-hydrodynamics model represents a meaningful advancement in modeling heavy ion collisions. By synthesizing microscopic and macroscopic approaches, the framework unveils deeper insights into the complex dynamics inherent in high-energy nuclear reactions and positions itself as a pivotal tool for future explorations of the QGP and associated phase transitions. The paper invites future enhancements including investigating different EoS and extending simulations to higher energies, all vital for capturing the full scope of heavy ion collisions.

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