连续谱格林函数协变密度泛函理论对奇特原子核的研究

The discovery of the neutron/proton-rich exotic nuclei promotes the construction of the new-generation radioactive ion beam facilities all over the world, and challenges the theoretical understandings from the present nuclear models. Based on the density functional theory, in order to describe the exotic nuclei, one should properly treat the pair correlation between nucleons and the continuum effect. The continuum Skyrme Hartree-Fock-Bogoliubov theory with the Green’s function method is one of the promising tools for this aim in the non-relativistic density functional framework. Based on the previous expertise in this theory, the applicant will extend the Green’s function method to the relativistic Hartree-Bogoliubov theory in this project, to achieve the microscopic and self-consistent covariant description of the exotic nuclei including the continuum states. The aim of the present project is to take the advantage of the Green’s function method in describing the diffusive density distribution and the continuum contribution to the density functional, further include the relativistic effect, thus achieve more reliable description of the ground state properties such as binding energy and radii. This project will be the corner stone for the next step to include the covariant continuum random phase approximation for the description of the collective excitation in the exotic nuclei.

远离稳定线的丰中子/质子奇特原子核的发现促进了新一代放射性核束装置的兴建，同时对现有的理论模型提出了新的挑战。对奇特原子核的密度泛函描述需要恰当处理核子之间的对关联以及连续谱效应。而连续谱格林函数Skyrme Hartree-Fock-Bogoliubov 理论正是非相对论密度泛函理论中描述奇特原子核的有力工具之一。本项目将结合申请人在该理论中的工作经验将格林函数方法拓展到相对论Hartree-Bogoliubov理论中，对远离稳定线的奇特原子核给出包含连续谱效应的微观自洽的协变描述。通过本项目的研究，在继承格林函数方法描述奇特原子核弥散的密度分布以及连续谱共振态对能量密度泛函贡献等方面优势的同时，进一步考虑更为广泛的相对论协变效应，从而得到更可靠的原子核结合能及半径等基态信息，为发展协变的连续谱无规相位近似理论，描述奇特原子核的激发态奠定理论基础。

远离稳定线的丰中子奇特原子核的发现对现有的理论模型提出了新的挑战。对奇特原子核的密度泛函描述需要恰当处理核子之间的对关联以及连续谱效应。而连续谱格林函数Skyrme Hartree-Fock-Bogoliubov 理论正是非相对论密度泛函理论中描述奇特原子核的有力工具之一。本项目利用该理论方法研究了丰中子原子核结构的性质。发现了原子核对密度渐近行为的一个普适规则，为核子对密度的实验测量提供了重要的理论依据；系统地计算了丰中子原子核的中子皮厚度，为原子核对称能的研究以及中子皮厚度实验测定提供了理论预言；澄清了所谓的“反晕效应”，解决了对关联在决定晕核半径中所起作用的争议。此外，将格林函数方法引入了相对论理论，实现了对丰中子原子核基态性质微观自洽的协变描述，并利用该方法对连续谱中的共振态给出了可靠的描述，为将来引入对关联效应打下了坚实的理论基础。