Within the Transport Model Evaluation Project (TMEP), we present a detailed study of the performance of different transport models in $\text{Sn}+\text{Sn}$ collisions at $270A\mathrm{MeV}$, which are representative reactions used to study the equation of state at suprasaturation densities. We put particular emphasis on the production of pions and $\mathrm{\Delta }$ resonances, which have been used as probes of the nuclear symmetry energy. In this paper, we aim to understand the differences in the results of different codes for a given physics model to estimate the uncertainties of transport model studies in the intermediate energy range. Thus, we prescribe a common and rather simple physics model, and follow in detail the results of four Boltzmann-Uehling-Uhlenbeck (BUU) models and six quantum molecular dynamics (QMD) models. The nucleonic evolution of the collision and the nucleonic observables in these codes do not completely converge, but the differences among the codes can be understood as being due to several reasons: the basic differences between BUU and QMD models in the representation of the phase-space distributions, computational differences in the mean-field evaluation, and differences in the adopted strategies for the Pauli blocking in the collision integrals. For pionic observables, we find that a higher maximum density leads to an enhanced pion yield and a reduced ${\pi }^{-}/{\pi }^{+}$ yield ratio, while a more effective Pauli blocking generally leads to a slightly suppressed pion yield and an enhanced ${\pi }^{-}/{\pi }^{+}$ yield ratio. We specifically investigate the effect of the Coulomb force and find that it increases the total ${\pi }^{-}/{\pi }^{+}$ yield ratio but reduces the ratio at high pion energies, although differences in its implementations do not have a dominating role in the differences among the codes. Taking into account only the results of codes that strictly follow the homework specifications, we find a convergence of the codes in the final charged-pion yield ratio to a $1\sigma$ deviation of about $5\%$. However, the uncertainty is expected to be reduced to about $1.6\%$ if the same or similar strategies and ingredients, i.e., an improved Pauli blocking and calculation of the nonlinear term in the mean-field potential, are similarly used in all codes. As a result of this work, we identify the sensitive aspects of a simulation with respect to pion observables, and suggest optimal procedures in some cases. This work provides benchmark calculations of heavy-ion collisions to be complemented in the future by simulations with more realistic physics models, which include the momentum-dependence of isoscalar and isovector mean-field potentials and pion in-medium effects.

中文翻译：

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比较受控条件下 270AMeV 重离子碰撞输运模拟中的 π 介子产生

在运输模型评估项目 (TMEP) 中，我们对不同运输模型的性能进行了详细研究$\text{锡}+\text{锡}$碰撞于$270A\mathrm{兆伏}$，它们是用于研究过饱和密度状态方程的代表性反应。我们特别重视π介子的生产$\mathrm{\Delta }$共振，已被用作核对称能的探针。在本文中，我们的目的是了解给定物理模型的不同代码结果的差异，以估计中间能量范围内输运模型研究的不确定性。因此，我们提出了一个常见且相当简单的物理模型，并详细遵循了四个 Boltzmann-Uehling-Uhlenbeck (BUU) 模型和六个量子分子动力学 (QMD) 模型的结果。这些代码中碰撞的核子演化和核子可观测量并不完全收敛，但代码之间的差异可以理解为由于以下几个原因造成的： BUU 和 QMD 模型在相空间表示上的基本差异分布、平均场评估中的计算差异以及碰撞积分中泡利块所采用策略的差异。对于 π 可观测量，我们发现较高的最大密度会导致 π 产率增加并降低${\pi }^{-}/{\pi }^{+}$产率，而更有效的泡利阻断通常会导致介子产率略微受到抑制并增强${\pi }^{-}/{\pi }^{+}$产率。我们专门研究了库仑力的影响，发现它增加了总的${\pi }^{-}/{\pi }^{+}$屈服比，但在高π介子能量下降低了该比率，尽管其实现的差异并不在代码之间的差异中起主导作用。仅考虑严格遵循作业规范的代码结果，我们发现代码的最终带电π离子产率收敛于$1\sigma$偏差约为$5\%$。然而，不确定性预计将减少至约$1.6\%$如果在所有代码中类似地使用相同或相似的策略和成分，即改进的泡利分块和平均场势中的非线性项的计算。这项工作的结果是，我们确定了与 π 介子可观测量相关的模拟的敏感方面，并在某些情况下提出了最佳程序。这项工作提供了重离子碰撞的基准计算，未来将通过更现实的物理模型的模拟来补充，其中包括等标量和等矢量平均场势的动量依赖性以及π介子介质内效应。