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We estimate the temperature dependence of the bulk viscosity in a relativistic hadron gas. Employing the Green–Kubo formalism in the SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) transport approach, we study different hadronic systems in increasing order of complexity. We analyze the (in)validity of the single exponential relaxation ansatz for the bulk-channel correlation function and the strong influence of the resonances and their lifetimes. We discuss the difference between the inclusive bulk viscosity of an equilibrated, long-lived system, and the effective bulk viscosity of a short-lived mixture like the hadronic phase of relativistic heavy-ion collisions, where the processes whose inverse relaxation rate are larger than the fireball duration are excluded from the analysis. This clarifies the differences between previous approaches which computed the bulk viscosity including/excluding the very slow processes in the hadron gas. We compare our final results with previous hadron gas calculations and confirm a decreasing trend of the inclusive bulk viscosity over entropy density as temperature increases, whereas the effective bulk viscosity to entropy ratio, while being lower than the inclusive one, shows no strong dependence to temperature.
In the past two decades, pions created in the high density regions of heavy ion collisions have been predicted to be sensitive at high densities to the symmetry energy term in the nuclear equation of state, a property that is key to our understanding of neutron stars. In a new experiment designed to study the symmetry energy, the multiplicities of negatively and positively charged pions have been measured with high accuracy for central 132Sn+124Sn, 112Sn+124Sn, and 108Sn+112Sn collisions at E/A = 270 MeV with the SπRIT Time Projection Chamber. While individual pion multiplicities are measured to 4% accuracy, those of the charged pion multiplicity ratios are measured to 2% accuracy. We compare these data to predictions from seven major transport models. The calculations reproduce qualitatively the dependence of the multiplicities and their ratios on the total neutron and proton number in the colliding systems. However, the predictions of the transport models from different codes differ too much to allow extraction of reliable constraints on the symmetry energy from the data. This finding may explain previous contradictory conclusions on symmetry energy constraints obtained from pion data in Au+Au system. These new results call for still better understanding of the differences among transport codes, and new observables that are more sensitive to the density dependence of the symmetry energy.