Understanding transport simulations of heavy-ion collisions at $100A$ and $400A$ MeV: Comparison of heavy-ion transport codes under controlled conditions

Transport simulations are very valuable for extracting physics information from heavy-ion-collision experiments. With the emergence of many different transport codes in recent years, it becomes important to estimate their robustness in extracting physics information from experiments. We report on the results of a transport-code-comparison project. Eighteen commonly used transport codes were included in this comparison: nine Boltzmann-Uehling-Uhlenbeck-type codes and nine quantum-molecular-dynamics-type codes. These codes have been asked to simulate $\mathrm{Au}+\mathrm{Au}$ collisions using the same physics input for mean fields and for in-medium nucleon-nucleon cross sections, as well as the same impact parameter, the similar initialization setup, and other calculational parameters at $100A$ and $400A$ MeV incident energy. Among the codes we compare one-body observables such as rapidity and transverse flow distributions. We also monitor nonobservables such as the initialization of the internal states of colliding nuclei and their stability, the collision rates, and the Pauli blocking. We find that not completely identical initializations may have contributed partly to different evolutions. Different strategies to determine the collision probabilities and to enforce the Pauli blocking also produce considerably different results. There is a substantial spread in the predictions for the observables, which is much smaller at the higher incident energy. We quantify the uncertainties in the collective flow resulting from the simulation alone as about 30% at $100A$ MeV and 13% at $400A$ MeV, respectively. We propose further steps within the code comparison project to test the different aspects of transport simulations in a box calculation of infinite nuclear matter. This should, in particular, improve the robustness of transport model predictions at lower incident energies, where abundant amounts of data are available.

Figure 1

Initial density profiles for BUU-type (left) and QMD-type (right) models.

Figure 2

Time evolution of the density profiles in a single Au nucleus in steps of 20 fm/$c$ (see legend for the explanation of different color lines) for BUU-type models at $b=20$ fm.

Figure 3

Same as Fig. 2, but for QMD-type models.

Figure 4

Average density contours in steps of 20 fm/$c$ in $\mathrm{Au}+\mathrm{Au}$ collisions at impact parameter $b=7$ fm and beam energy $100A$ MeV from BUU-type models. This is for the B-full mode that includes both mean-field potentials and nucleon-nucleon scatterings.

Figure 5

Same as Fig. 4, but from QMD-type models.

Figure 6

Density contours for four runs with 100 TPs per nucleon from IBUU (left) and four individual events from ImQMD-CIAE (right) out of the collisions displayed in Figs. 4 and 5 at $t=100$ fm/$c$.

Figure 7

Center-of-mass energy dependence of nucleon-nucleon attempted (left) and successful (middle) scattering numbers as well as the Pauli-blocking factors (right) for the B-full mode (top), the B-cascade mode (middle) both at $100A$ MeV, and the D-full (bottom) mode at $400A$ MeV at impact parameter $b=7$ fm from BUU-type models.

Figure 8

Same as Fig. 7, but from QMD-type models.

Figure 9

Initial rapidity distributions (top panels) at the beam energy of $100A$ MeV and final rapidity distributions for the B-Vlasov mode (next panels down), the B-cascade mode (next panels down), and the B-full model (bottom panels) at impact parameter $b=7$ fm from BUU-type (left panels) and QMD-type (right panels) models.

Figure 10

Rapidity distributions at $b=7$ fm for the B-full (top panels) and D-full (bottom panels) mode from BUU-type (left panels) and QMD-type (right panels) models.

Figure 11

Transverse flow as a function of reduced rapidity for the B-Vlasov mode (top panels), the B-cascade mode (middle panels), and the B-full mode (bottom panels) at $b=7$ fm from BUU-type (left panels) and QMD-type (right panels) models.

Figure 12

Transverse flow as a function of reduced rapidity for the B-full mode ($100A$ MeV) and D-full mode ($400A$ MeV) at $b=7$ fm from BUU-type (left) and QMD-type (right) models.

Figure 13

Slope parameters of the transverse flow of nine BUU-type (left) and nine QMD-type (right) models from the B-full mode (black squares) and D-full mode (red triangles). The error bars are the fitting uncertainties. Where they are not seen they are smaller than the symbols.