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

Abstract

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.

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

“…The first result of the box comparison was published in Ref. [3] where 15 transport codes were compared concentrating on the N N elastic collision term without mean-field potentials, in a system with an initial Fermi-Dirac distribution at the temperature of either T = 0 or 5 MeV. One of the important findings there was that the differences among the codes are mainly due to inaccuracy in the evaluated Pauli-blocking factor, which is tightly linked to the fluctuations in the representation of the phase space in transport codes by a finite number of elements, e.g., Monte Carlo particles or so-called test particles.…”

Effects of Pauli blocking on pion production in central collisions of neutron-rich nuclei

“…Therefore, the Pauli blocking in JAM suffers from the above-mentioned problem of too weak blocking due to large fluctuations, as observed in Ref. [18] in the same way as in other QMD models, for which any general and fundamental solution is not known. In this paper, we propose a solution in our approach (AMD+JAM), which is possible because we can know a more precise phase-space distribution function in the AMD model.…”

“…The π − and π + are mainly produced by these reaction channels. We show in this figure the integrated and normalized 17), (18), (19) and (20), for the different Pauli blocking options. The left panel shows the quantities for the channels ∆ ++ → pπ + and ∆ − → nπ − , and the right panel shows the quantities multiplied by a factor 3 for the channels ∆ 0 → pπ − and ∆ + → nπ + .…”

“…In heavy-ion collisions at several hundred MeV/nucleon, the above-mentioned problem in the Pauli blocking factor may be expected to be not so important because of the high temperature, unlike in the situation of Ref. [18] for almost degenerate fermionic systems. However, we recently found that Pauli blocking plays some important role on the pion observables [8], in the comparison of the results from the AMD+JAM approach in Ref.…”

“…In Ref. [18], different 15 transport codes were compared concentrating on the two-nucleon (N N) elastic collision term without mean-field potentials, in a system with an initial Fermi-Dirac distribution at the temperature of either T = 0 or 5 MeV. As an important result, the Pauli blocking factor is found to be affected by the differences among the code strategies to represent the phase space.…”