极端条件下的核结构实验相对变得越来越困难（如目标核产生截面越来越低），因此精确可靠的理论预言显得愈发重要。理论不确定性过大的预言对实验工作是缺乏参考价值的。近些年来，原子核理论建模不确定性及模型预言能力优化的研究已成为一个快速发展的研究领域。本项目拟基于经验Woods-Saxon平均场在宏观-微观模型的框架下，首先系统研究K同核异能态，通过交差检验提取可利用的形变单粒子能级，在球形单粒子能级数据样本基础上，扩充和建立更大的实验单粒子能级标准样本数据库。然后基于反问题求解理论得到最佳Woods-Saxon势参数组及其不确定性，优化模型预言能力并给出最终预言结果的不确定性。最后基于优化的经验平均场，对极端条件下原子核（包括奇异核及超重核）的结构（如K同核异能态、超形变、奇异形变结构等）及其随转动（含3维转动）的演化进行系统研究，希望给出更好的理论描述并为实验提供更具价值的预言指标。

Nuclear structure experiments under extreme conditions are becoming more and more difficult due to, e.g., the lower production cross section of the expected nuclei. Therefore, accurate and reliable theory predictions will correspondingly become more and more important. So far, most of nuclear theory models contain some adjustable model parameters which are usually adjusted according to the appropriately chosen experimental data with error bars. The experimental errors will generate uncertainties of model parameters and thus uncertainties of final modelling predictions. Obviously, theory predictions are worthless and meaningless once their uncertainties are too big. In recent years, the corresponding research related to the propagation of uncertainties down to the model predictions is well known in applied mathematics under the name of inverse problem theory. Application of this theory in nuclear physics is a rapidly developing research field nowadays. To study theory uncertainties and to optimize model predictive power are of great importance, especially for the new areas of experimental studies. The typical examples are the exotic and super-heavy nuclei as well as nuclear states at the limits of extreme angular momenta or shapes and/or with exotic symmetries such as recently discovered tetrahedral and octahedral symmetries. In this project, we will systematically investigate K isomers based on the phenomenological Woods-Saxon mean field within the framework of macroscopic-microscopic model and create a large benchmarking single-particle sample database (including subsample databases of various areas on the Nuclear Chart), which includes not only the single particle levels in some specific nuclei (e.g., the doubly-magic spherical ones) but, importantly, the rich data based on the so-called K isomers. These isomers exist in the nuclei with axial symmetry and are due to the particle-hole excitations, possibly providing the information of the deformed single particle levels. Then, by using the inverse problem theory, we will analyze and optimize the model parameters of the deformed Woods-Saxon mean field. The uncertainties of model parameters and final theory predictions will be investigated by using the Monte-Carlo simulation approach. Finally, we will further study the nuclear properties under extreme conditions, focusing on the new areas of experimental studies as mentioned above, and give the model uncertainties, providing valuable predictions for experiments.