标题： 不确定度带评估光学势和微分截面。 应用于$^8$Li +$^{58}$Ni 弹性散射 显示英文标题

标题： Uncertainty band evaluation of optical potentials and differential cross-sections. Application to $^8$Li + $^{58}$Ni elastic scattering

摘要： 一种统计方法被提出以评估光学核-核势和微分截面中的不确定性带。 起始点是对弹性微分截面的一组实验值进行最小二乘拟合，变化相关的光学势参数。 这是使用标准的$\chi^2$最小化代码完成的，这些代码提供了参数的协方差矩阵。 在参数空间中对$\chi^2$表面的最大似然探索允许确定与给定$\chi^2$值的轮廓相关的参数的协方差矩阵。 贝叶斯定理允许将概率（p值）分配给由$\chi^2$轮廓表征的参数空间区域。 该方法允许使用两种方法获得与给定 p 值相关联的任意可观测量的不确定性带。 一般方法确定在与该 p 值相关的参数空间区域中计算的可观测量的极限。 这需要对参数空间进行适当的采样，并在所有采样点上显式计算可观测量。 简化方法考虑了可观测量在光学模型参数方面的不确定性传播。 这涉及由$\chi^2$最小化代码给出的最小二乘协方差矩阵，以及针对每个 p 值的解析计算增强因子。 该方法在一般方法和简化方法中应用于最近测量的$^8$Li +$^{58}$Ni 弹性微分截面。 $1\sigma$和$2\sigma$不确定性带是作为距离的函数获得的光学势，以及作为角度函数的微分截面。 在这种情况下，一般方法和简化方法非常相似。 讨论了将该过程应用于确定复散射计算的不确定性带。 显示英文摘要

摘要： A statistical method is presented to evaluate the uncertainty bands in the optical nucleus-nucleus potential and in differential cross sections. The starting point is the least square fit of a set of experimental values of elastic differential cross sections, varying the relevant optical potential parameters. This is done using standard $\chi^2$ minimization codes, that provide the covariance matrix of the parameters. A maximum likelihood exploration of the $\chi^2$ surface in parameter space allows to determine the covariance matrix of the parameters associated to a contour of a given $\chi^2$ value. Bayes theorem allows to assign probabilities (p-values) to the regions in parameter space, characterized by $\chi^2$ contours. The method allows to obtain uncertainty bands of an arbitrary observables associated to a given p-value using two approaches. The general approach determines the extremes of the observables calculated in the region of parameter space associated to that p-value. This requires an adequate sampling of parameter space, and explicit calculations of the observables on all sampling points. The simplified approach considers uncertainty propagation of the observable in terms of the optical model parameters. This involves the least-square covariance matrix, given by $\chi^2$ minimization codes, and analytically calculated enhancement factors for each p-value. The method, in the general and simplified approaches, is applied to recent measurements of the elastic differential cross sections of $^8$Li + $^{58}$Ni. $1\sigma$ and $2\sigma$ uncertainty bands are obtained for the optical potentials as a function of the distance, and the differential cross sections as a function of the angle. The general and simplified approaches are very similar in this case. The application of the procedure to determine uncertainty bands of complex scattering calculations is discussed.