Constraining the density dependence of the symmetry energy using the multiplicity and average 
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 ratios of charged pions

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175

Simulations by transport codes are indispensable to extract valuable physical information from heavy-ion collisions. In order to understand the origins of discrepancies among different widely used transport codes, we compare 15 such codes under controlled conditions of a system confined to a box with periodic boundary, initialized with Fermi-Dirac distributions at saturation density and temperatures of either 0 or 5 MeV. In such calculations, one is able to check separately the different ingredients of a transport code. In this second publication of the code evaluation project, we only consider the two-body collision term; i.e., we perform cascade calculations. When the Pauli blocking is artificially suppressed, the collision rates are found to be consistent for most codes (to within 1% or better) with analytical results, or completely controlled results of a basic cascade code. PHYSICAL REVIEW C 97, 034625 (2018) to reach that goal, it was necessary to eliminate correlations within the same pair of colliding particles that can be present depending on the adopted collision prescription. In calculations with active Pauli blocking, the blocking probability was found to deviate from the expected reference values. The reason is found in substantial phase-space fluctuations and smearing tied to numerical algorithms and model assumptions in the representation of phase space. This results in the reduction of the blocking probability in most transport codes, so that the simulated system gradually evolves away from the Fermi-Dirac toward a Boltzmann distribution. Since the numerical fluctuations are weaker in the Boltzmann-Uehling-Uhlenbeck codes, the Fermi-Dirac statistics is maintained there for a longer time than in the quantum molecular dynamics codes. As a result of this investigation, we are able to make judgements about the most effective strategies in transport simulations for determining the collision probabilities and the Pauli blocking. Investigation in a similar vein of other ingredients in transport calculations, like the mean-field propagation or the production of nucleon resonances and mesons, will be discussed in the future publications.

Section: Introductionmentioning

confidence: 99%

Comparison of heavy-ion transport simulations: Collision integral in a box

Zhang¹,

Wang²,

Colonna³

et al. 2018

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175

“…To obtain meaningful physical information from measured pion data, it is an urgent and extremely important task to provide reliable predictions on the production of pions based on transport theories. It should be noted that the π − /π + ratio is expected to depend not only on the nuclear equation of state, but also on other physical ingredients such as the potentials for pions and ∆ resonances [11][12][13][14][15][16][17][18][19][20][21], the in-medium N N cross sections [18,22], and the cluster correlations [23,24]. It may also depend on the treatment of Pauli blocking [24] and the momentum dependence of the nuclear mean field.…”

Section: Introductionmentioning

confidence: 99%

Comparison of heavy-ion transport simulations: Collision integral with pions and Δ resonances in a box

Ono

Colonna

et al. 2019

Background: Simulations by transport codes are indispensable for extracting valuable physical information from heavy-ion collisions. Pion observables such as the π − /π + yield ratio are expected to be sensitive to the symmetry energy at high densities.Purpose: To evaluate, understand and reduce the uncertainties in transport-code results originating from different approximations in handling the production of ∆ resonances and pions. Methods:We compare ten transport codes under controlled conditions for a system confined in a box, with periodic boundary conditions, and initialized with nucleons at saturation density and at 60 MeV temperature. The reactions N N ↔ N∆ and ∆ ↔ N π are implemented, but the Pauli blocking and the mean-field potential are deactivated in the present comparison. Thus these are cascade calculations including pions and ∆ resonances. Results are compared to those from the two reference cases of a chemically equilibrated ideal gas mixture and of the rate equation. Results:For the numbers of ∆ and π, deviations from the reference values are observed in many codes, and they depend significantly on the size of the time step. These deviations are tied to different ways in ordering the sequence of reactions, such as collisions and decays, that take place in the same time step. Better agreements with the reference values are seen in the reaction rates and the number ratios among the isospin species of ∆ and π. Both the reaction rates and the number ratios are, however, affected by the correlations between particle positions, which are absent in the Boltzmann equation, but are induced by the way particle scatterings are treated in many of the transport calculations. The uncertainty in the transport-code predictions of the π − /π + ratio, after letting the existing ∆ resonances decay, is found to be within a few percent for the system initialized at n/p = 1.5. Conclusions:The uncertainty in the final π − /π + ratio in this simplified case of particles in a box is sufficiently small so that it does not strongly impact constraining the high-density symmetry energy from heavy-ion collisions. Most of the sources of

“…Therefore, more in-depth studies and careful modeling of pion production in heavy ion collision are important, especially because more systematic experimental measurements of the pion yield from intermediate energy heavy ion collisions are being carried out by the FRIB-RIKEN Spirit Collaboration in Japan [9]. A lot of efforts have already been made recently to study various effects on pion production in heavy ion collisions at near-threshold energies, e.g., the pion in-medium potentials [10][11][12][13], isovector potential of ∆ [14], threshold effects [15,16], neutron-skin thickness [17], and nucleon short-range correlation [18].…”

Section: Introductionmentioning

confidence: 99%

Effects of energy conservation on equilibrium properties of hot asymmetric nuclear matter

Zhang

2018

Based on the relativistic Vlasov-Uehling-Uhlenbeck transport model, which includes relativistic scalar and vector potentials on baryons, we consider a N − ∆ − π system in a box with periodic boundary conditions to study the effects of energy conservation in particle production and absorption processes on the equilibrium properties of the system. The density and temperature of the matter in the box are taken to be similar to the hot dense matter formed in heavy ion collisions at intermediate energies. We find that to maintain the equilibrium numbers of N , ∆ and π, which depend on the mean-field potentials of N and ∆, requires the inclusion of these potentials in the energy conservation condition that determines the momenta of outgoing particles after a scattering or decay process. We further find that the baryon scalar potentials mainly affect the ∆ and pion equilibrium numbers, while the baryon vector potentials have considerable effects on the effective charged pion ratio at equilibrium. Our results thus indicate that it is essential to include in the transport model the effect of potentials in the energy conservation of a scattering or decay process, which is ignored in most transport models, for studying pion production in heavy ion collisions.