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.

In this paper, we present a review of recent works on weak decay of heavy mesons and baryons with two mesons, or a meson and a baryon, interacting strongly in the final state. The aim is to learn about the interaction of hadrons and how some particular resonances are produced in the reactions. It is shown that these reactions have peculiar features and act as filters for some quantum numbers which allow to identify easily some resonances and learn about their nature. The combination of basic elements of the weak interaction with the framework of the chiral unitary approach allow for an interpretation of results of many reactions and add a novel information to different aspects of the hadron interaction and the properties of dynamically generated resonances.

In order to investigate the nuclear symmetry energy at high density, we study the pion production in central collisions of neutron-rich nuclei 132 Sn + 124 Sn at 300 MeV/nucleon using a new approach that combines antisymmetrized molecular dynamics (AMD) and a hadronic cascade model (JAM). The dynamics of neutrons and protons is solved by AMD, and then pions and resonances in the reaction process are handled by JAM. We see the mechanism by which the resonance and pions are produced, reflecting the dynamics of neutrons and protons. We also investigate the impacts of cluster correlations as well as of the high-density symmetry energy on the nucleon dynamics and consequently on the pion ratio. We find that the − / ++ production ratio agrees very well with the neutron-proton squared ratio (N/Z) 2 in the high-density and high-momentum region. We show quantitatively that the production ratio, and therefore (N/Z) 2 , are directly reflected in the π − /π + ratio, with modification in the final stage of the reaction.

The Pauli blocking for the nucleon(s) in the final state of two-particle collisions and particle decays was found to be incorrect with the blocking probability too small by a factor of 4, in the code of a hadronic cascade model (JAM) employed in our original publication. This affects, in principle, the NN ↔ N and → Nπ processes in the main calculations of the original paper which combines the antisymmetrized molecular dynamics (AMD) and JAM. The results of the usual JAM simulations, which are shown mainly as a reference case without a mean field, are also affected.We revise all the figures (Figs. 1-10) with the corrected numerical results for completeness, although most of the changes are small and do not influence the statements and conclusions in the original paper except for the following point.The approximate equalityρ,p is not as good as in the original paper because the − / ++ production ratio is now higher than (N/Z) 2 ρ,p . However, the updated results even strengthen our statement since the correlation between − / ++ and (N/Z) 2 ρ,p is stronger than in our paper as seen in Fig. 8 and in the comparison of Figs. 6 and 7(b). The final π − /π + ratio is also significantly higher than in the original paper. This problem of Pauli blocking was found during the work for the transport code comparison [1]. The JAM results shown in Ref.[1] were performed after this correction and are therefore not affected.

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