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Bootstrap method for constructing covariance matrices of optical-model parameters in the study of the threshold anomaly

机译：阈值异常研究中光学模型参数协方差矩阵的Bootstrap方法

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The parameters of optical-model potentials are usually obtained by adjusting theoretical calculations to the corresponding experimental elastic-scattering data. It has been observed that the use of conventional covariance matrices for the evaluation of the uncertainties of the parameters obtained in this way, leads in general to unrealistically small values. This underestimate may be caused by either, an incorrect use of the statistical recipes, or by the lack of a systematic study of the robustness of the uncertainty values against the inclusion or exclusion of experimental data points within a given data set. In the present contribution we explore both factors. Regarding the first aspect we use a re-normalization for χ2, similar to the one proposed by R.T. Birge. In the second case we use the Bootstrap method to create synthetic sets based on all the available experimental data in order to derive an effective covariance matrix. These procedures were applied to the re-analysis of elastic-scattering data for several heavy-ion systems at energies close to the Coulomb barrier
机译：光学模型电势的参数通常是通过将理论计算调整为相应的实验弹性散射数据而获得的。已经观察到，使用常规协方差矩阵来评估以这种方式获得的参数的不确定性通常导致不切实际的小值。这种低估可能是由于统计方法的错误使用，或者是由于缺乏对不确定性值针对给定数据集中包含或排除实验数据点的鲁棒性的系统研究。在目前的贡献中，我们探讨了两个因素。关于第一个方面，我们对χ2使用了归一化，类似于R.T.伯吉在第二种情况下，我们使用Bootstrap方法根据所有可用的实验数据创建综合集，以得出有效的协方差矩阵。这些程序被用于在接近库仑势垒的能量下对几个重离子系统的弹性散射数据进行重新分析。

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