We present a model independent method to reconstruct the impact parameter distributions of experimental data for intermediate energy heavy ion collisions, adapted from a recently proposed approach for ultra-relativistic heavy ion collisions. The method takes into account the fluctuations which are inherent to the relationship between any experimental observable and the impact parameter in this energy range. We apply the method to the very large dataset on heavy ion collisions in the energy range 20–100 MeV/nucleon obtained with the INDRA multidetector since 1993, for two observables which are the most commonly used for the estimation of impact parameters in this energy range. The mean impact parameters deduced with this new method for “central” collisions selected using typical observable cuts are shown to be significantly larger than those found when fluctuations are neglected, and as expected the difference increases as bombarding energy decreases. In addition, we will show that this new approach may provide previously inaccessible experimental constraints for transport models, such as an estimation of the extrapolated mean value of experimental observables for $b=0$ collisions. The ability to give more realistic, model independent estimations of the impact parameters associated with different experimental datasets should improve the pertinence of comparisons with transport model calculations which are essential to better constrain the equation of state of nuclear matter.

中文翻译：

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中能重离子碰撞碰撞参数分布的独立模型重建

我们提出了一种独立于模型的方法来重建中能重离子碰撞实验数据的撞击参数分布，该方法改编自最近提出的超相对论重离子碰撞方法。该方法考虑了任何实验观测值与该能量范围内的冲击参数之间的关系所固有的波动。我们将该方法应用于自 1993 年以来使用 INDRA 多探测器获得的能量范围为 20-100 MeV/核子的非常大的重离子碰撞数据集，对于两个最常用于估计该能量范围内的碰撞参数的观测值. 使用典型的可观察切割选择的“中心”碰撞的这种新方法推导出的平均撞击参数显示出明显大于忽略波动时发现的参数，并且正如预期的那样，差异随着轰击能量的降低而增加。此外，我们将展示这种新方法可以为传输模型提供以前无法获得的实验约束，例如对实验观测值的外推平均值的估计$乙=0$碰撞。对与不同实验数据集相关的影响参数进行更现实的、模型独立估计的能力应该提高与输运模型计算比较的相关性，这对于更好地约束核物质状态方程至关重要。