Production of Subthreshold Pions in Heavy-Ion Collisions Using a Hydrodynamic Approach with a Nonequilibrium Equation of
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uction of Subthreshold Pions in Heavy-Ion Collisions Using a Hydrodynamic Approach with a Nonequilibrium Equation of State A. T. D’yachenkoa, b, * and I. A. Mitropolskyb aEmperor bKonstantinov
Alexander I State Transport University, St. Petersburg, 190031 Russia Institute of Nuclear Physics, National Research Center “Kurchatov Institute,” Gatchina, Leningrad oblast, 188300 Russia *e-mail: [email protected]
Received October 30, 2019; revised November 25, 2019; accepted December 27, 2019
Abstract—A hydrodynamic approach with a nonequilibrium equation of state is used to describe collisions between heavy ions with medium energies. The double differential cross sections for the production of subthreshold π0 mesons and π + mesons during collisions between various nuclei are calculated to develop this approach with the inclusion of nuclear viscosity effects. They are in good agreement with the available experimental data. DOI: 10.3103/S1062873820040061
INTRODUCTION The main aim of studying heavy ion collisions is to investigate the equation of state of nuclear matter (EOS). Along with molecular dynamics and Vlasov’s dynamic equation [1], nuclear hydrodynamics is an effective way of describing the interaction between heavy ions at medium and intermediate energies. Equilibrium EOS [1], which indicates the local thermodynamic equilibrium in a system, is normally used. The authors of [2, 3] proposed using a hybrid model at high energies that includes a fast nonequilibrium stage and the subsequent description of the dynamics of a nucleus–nucleus collision based on the equilibrium relativistic hydrodynamics of an ideal fluid. In [4–11], we showed that local thermodynamic equilibrium is not immediately established in collisions between heavy ions, since the nonequilibrium component of the distribution function that leads to the formation of a collisionless shock wave is considerable at the stage of compression. We use the kinetic equation to find the nucleon distribution function, which is solved in conjunction with hydrodynamic equations that are essentially local laws of the conservation of mass, momentum, and energy. Since the emitted secondary particles (nucleons, fragments, and pions) contain basic information about EOS, we must know the differential cross sections for the emission of these particles. In this work, we analyze the energy spectra of subthreshold pions in order to develop [11–13], which are devoted to the energy spectra of protons and fragments.
Subthreshold production refers to the formation of π -mesons at energies less than threshold ENN of pion production in free nucleon–nucleon collisions. The absolute threshold for pion production is ENN = 2mπ + mπ2 ≈ 290 MeV in nucleon–nucleon collisions, 2m ENA ≈ mπ ≈ 140 MeV in nucleon–nucleus collisions, m2 + 2( A + B )mπ m and EBA = π ≈ 20 MeV in nucleus– 2 ABm nucleus collisions with A = B = 12, where mπ is the mass of a pion and m is that of a nucleon. This expression for the absolute threshold energy is obtained by comparing relativistic invariants J = E 2
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