Non-equilibrium Equation and Density Functional

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311.

**Chapter 6**

**Abstract**

nucleon.

**93**

**1. Introduction**

of Heavy Ions

*A.T. D'yachenko and I.A. Mitropolsky*

Non-equilibrium Equation of State

in the Approximation of the Local

High-Energy Particles in Collisions

The non-equilibrium equation of state is found in the approximation of the functional on the local density, and its application to the description of the emission of protons and pions in heavy ion collisions is considered. The non-equilibrium equation of state is studied in the context of the hydrodynamic approach. The compression stage, the expansion stage, and the freeze-out stage of the hot spot formed during the collisions of heavy ions are considered. The energy spectra of protons and subthreshold pions produced in collisions of heavy ions are calculated with inclusion of the nuclear viscosity effects and compared with experimental data for various combinations of colliding nuclei with energies of several tens of MeV per

**Keywords:** local density functional, hydrodynamics, non-equilibrium equation of

The main object of studying heavy ion collisions is to study the equation of state (EOS) of nuclear matter. Along with molecular dynamics and the Vlasov dynamic equation, nuclear hydrodynamics is an effective method for describing the interaction of heavy ions with medium and intermediate energies (see, e.g., [1]). Typically, the equilibrium EOS is used [1]; it involves the local thermodynamic equilibrium in the system. A hybrid model was proposed for use at high energies in [2, 3]. It includes a fast non-equilibrium stage and the subsequent description of the dynamics of a nucleus-nucleus collision based on equilibrium relativistic hydrodynamics of an ideal fluid. We showed in our works [4–11] that local thermodynamic equilibrium is not immediately established in the process of collisions of heavy ions, since the non-equilibrium component of the distribution function, which leads to the formation of a collisionless shock wave, is important at the compression stage.

state, heavy ions, hot spot, nuclear viscosity, protons, subthreshold pions

Density Functional and Its

Application to the Emission of
