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.

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

In a recent paper [1] we proposed a model for calculating cross-sections of various reaction products which arise from disintegration of projectile like fragment resulting from heavy ion collisions at intermediate or higher energy. The model has three parts: (1) abrasion, (2) disintegration of the hot abraded projectile like fragment (PLF) into nucleons and primary composites using a model of equilibrium statistical mechanics and (3) possible evaporation of hot primary composites. It was assumed that the PLF resulting from abrasion has one temperature T . Data suggested that while just one value of T seemed adequate for most cross-sections calculations, it failed when dealing with very peripheral collisions. We have now introduced a variable T = T (b) where b is the impact parameter of the collision. We argue there are data which not only show that T must be a function of b but, in addition, also point to an approximate value of T for a given b. We propose a very simple formula:is the mass of the abraded PLF and A 0 is the mass of the projectile; D 0 and D 1 are constants. Using this model we compute cross-sections for several collisions and compare with data. PACS numbers: 25.70Mn, 25.70Pq 1 I. INTRODUCTION In a recent paper [1] we proposed a model of projectile mutifragmentation which was applied to collisions of Ni on Be and Ta at 140 MeV/nucleon and Xe on Al at 790 MeV/nucleon.The model gave reasonable answers for most of the cross-sections studied. The model requires integration over impact parameter. For a given impact parameter, the part of the projectile that does not directly overlap with the target is sheared off and defines the projectile like fragment(PLF). This is abrasion and appealing to the high enrgy of the beam, is calculated using straight line geometry. The PLF has N s neutrons,Z s protons and A s (= N s + Z s ) nucleons (the corresponding quantities for the full projectile are labelled N 0 , Z 0 and A 0 ).The abraded system N s , Z s has a temperture. In the second stage this hot PLF expands to one-third of the normal nuclear density. Assuming statistical equilibrium the break up of the PLF at a temperature T is now calculated using the canonical thermodynamic model(CTM).The composites that result from this break up have the same temperature T and can evolve further by sequential decay(evaporation). This is computed. Cross-sections can now be compared with experiment. The agreements were reasonable except for very peripheral collisions and it was conjectured in [1] that the main reason for this discrepancy was due to the assumption of constant T over all impact parameters.Full details are provided in [1]. Our aim here is to improve the model by incorporating an impact parameter dependence of T = T (b). While we were led to this by computing the cross-sections of very large PLF's (which can only result from very peripheral collisions), the effect of temperature dependence is accentuated in other experiments. In fact these experiments can be used, with some aid from reasonable models, to extrac...

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We perform transport model calculations for central collisions of mass 120 on mass 120 at laboratory beam energy in the range 20 MeV/nucleon to 200 MeV/nucleon. A simplified yet accurate method allows calculation of fluctuations in systems much larger than what was considered feasible in a well-known and already existing model. The calculations produce clusters. The distribution of clusters is remarkably similar to that obtained in equilibrium statistical model.