唯象核平均场中单粒子能量的不确定性评估和相关分析：独立模型参数传播不确定性的研究
Uncertainty evaluation and correlation analysis of single-particle energies in phenomenological nuclear mean field: An investigation of propagating uncertainties for independent model parameters
摘要：
基于Monte Carlo方法和传统的误差分析理论，以最重的双魔核$^{208}$ Pb为例，首次计算了唯象Woods-Saxon平均场中三种典型单粒子能量的普适势参数的传播不确定度.采用不相关模型参数的Woods-Saxon模型，我们发现由蒙特卡罗模拟得到的单粒子能量的标准偏差与误差传播规律吻合较好。对于给定的参数不确定度，单粒子能级的能量不确定度在很大程度上随某些量子数有规律地变化。此外，使用统计分析的方法分析了输入参数不确定性域内的单粒子能级的相关特性，例如，借助Pearson相关系数。发现两个选定的单粒子能级之间可能出现正的、负的或无关的关系，这将非常有助于评估与单粒子能级有关的理论不确定度（例如，$K$异构体）。
英文摘要：
Based on Monte Carlo approach and conventional error analysis theory, taking the heaviest doubly magic nucleus $^{208}$Pb as an example, we firstly evaluate the propagated uncertainties of universal potential parameters for three typical types of single-particle energies in the phenomenological Woods-Saxon mean field. Accepting the Woods-Saxon modeling with uncorrelated model parameters, we find that the standard deviations of single-particle energies obtained by the Monte Carlo simulation and the error propagation rules are in good agreement with each other. It seems that the energy uncertaintis of the single-particle levels regularly evoluate with some quantum numbers to a large extent for the given parameter uncertainties. Further, the correlation properties of the single-particle levels within the domain of input parameter uncertainties are analyzed using the method of statistical analysis, e.g., with the aid of Pearson correlation coefficients. It is found that the positive, negative or unrelated relationship may appear between two selected single-particle levels, which will be very helpful for evaluating the theoretical uncertainty related to the single-particle levels (e.g., $K$ isomer) in nuclear structural calculations.
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