核反Kohn-Sham问题的第一步：从密度到势
A first step in the nuclear inverse Kohn-Sham problem: from densities to potentials
摘要：
核密度泛函理论（DFT）在理解原子核结构中起着重要作用，是应用范围最广的方法。Hohenberg和Kohn定理证明了核能密度泛函（EDF）的存在，但它的形式是未知的。由于缺乏系统改进的战略，目前建立核能EDF的努力受到阻碍。在这种情况下，应寻求替代方法，到目前为止，一个未探索的途径是与DFT逆问题有关的途径。密度泛函理论是基于Kohn-Sham（KS）势和密度之间的一一对应关系。精确的EDF产生精确的密度，因此从实验密度或{ \it ab initio}密度的知识可以通过逆向工程推导出有用的信息。这个想法已经被证明在电子系统的情况下是有用的。一般的问题应处理的步骤，目前的工作的目的是集中在测试算法，以提取Kohn-Sham潜在的最简单的ananterior从实验中子和质子密度的知识。我们的结论是，虽然强大的算法存在，实验密度提出了一些关键方面。最后，我们对未来的工作提出了一些展望。
英文摘要：
Nuclear Density Functional Theory (DFT) plays a prominent role in the understanding of nuclear structure, being the approach with the widest range of applications. Hohenberg and Kohn theorems warrant the existence of a nuclear Energy Density Functional (EDF), yet its form is unknown. Current efforts to build a nuclear EDF are hindered by the lack of a strategy for systematic improvement. In this context, alternative approaches should be pursued and, so far, an unexplored avenue is that related to the inverse DFT problem. DFT is based on the one-to-one correspondence between Kohn-Sham (KS) potentials and densities. The exact EDF produces the exact density, so that from the knowledge of experimental or {\it ab initio} densities one may deduce useful information through reverse engineering. The idea has already been proven to be useful in the case of electronic systems. The general problem should be dealt with in steps, and the objective of the present work is to focus on testing algorithms to extract the Kohn-Sham potential within the simplest ansatz from the knowledge of the experimental neutron and proton densities. We conclude that while robust algorithms exist, the experimental densities present some critical aspects. Finally, we provide some perspectives for future works.
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