Green's Functions and the Nuclear Many-Body Problem

在密歇根州立大学正在建设的稀有同位素束设施(FRIB)等设施中，具有大或小中子质子比的原子核的性质正在进行实验审查。大多数研究这些奇异核的实验探测器都涉及自身相互作用强烈的粒子，这使得提取这些奇异系统中单个质子或中子的性质变得困难。这个项目旨在克服这一困难，通过使用量子力学传播方法的框架，提供正能量核子(弹性散射域)和束缚核子(核结构域)的同时描述。这种方法将提供对非常丰富的中子核的性质的关键洞察，因此通过澄清关于质子分布的中子在哪里被发现，与中子星的物理有关。PI将指导这项研究中的研究生，并与将进行相关实验的实验同事合作。传播子方法将利用受实验数据约束的非定域势，允许通过色散关系方法准确描述原子核的基态性质。同时，这种实现将能够描述或预测包括弹性散射截面在内的连续统中的所有相关实验数据。因此，有可能用这种方法的成分来研究各种核反应，类似于成功地分析电子诱导的质子敲除反应，从而澄清奇异原子核中质子和中子的性质，并提出相关的新实验。特别是，对含有过剩中子的原子核的中子分布的预测将对杰斐逊实验室的实验和未来的FRIB实验至关重要。传播子方法也将被用来计算核的性质，从核子之间的基本相互作用开始，受夸克和胶子基本理论的对称性、量子色动力学和关于两个核子性质的现有数据的约束。这样的计算将与一个新的方案一起应用，该方案允许从头计算到目前为止还没有以这种方式研究的较重原子核的性质。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The properties of nuclei with large or small neutron to proton ratios are becoming available for experimental scrutiny at facilities like the Facility for Rare Isotope Beams (FRIB) under construction on the campus of Michigan State University. Most of the experimental probes to study these exotic nuclei involve particles that interact strongly themselves, making it difficult to extract the properties of individual protons or neutrons in these exotic systems. This project aims at overcoming this difficulty by providing a simultaneous description of positive energy nucleons, the domain of elastic scattering, and bound nucleons, the domain of nuclear structure, using the framework of the propagator method of quantum mechanics. This approach will provide critical insight into the properties of very neutron-rich nuclei, and is therefore relevant for the physics of neutron stars by clarifying where neutrons are found with respect to the distribution of protons. The PI will mentor graduate students in this research and collaborate with experimental colleagues who will perform related experiments.The propagator method will be utilized with non-local potentials constrained by experimental data that allow for the accurate description of ground-state properties of nuclei by the method of dispersion relations. Simultaneously, this implementation will be able to describe or predict all relevant experimental data in the continuum including elastic scattering cross sections. It will therefore be possible to study various nuclear reactions using the ingredients of this method in analogy to the successful analysis of electron-induced proton knockout reactions, thereby clarifying the properties of protons and neutrons in exotic nuclei as well as suggesting relevant new experiments. In particular, the prediction of the neutron distribution for nuclei with excess neutrons will be of critical importance for experiments at Jefferson Lab and future experiments at FRIB. The propagator method will also be employed to calculate the properties of nuclei by starting from the underlying interactions between nucleons as constrained by the symmetries of the fundamental theory of quarks and gluons, Quantum Chromo Dynamics, and the available data for the properties of two nucleons. Such calculations will be applied with a new scheme that allows the ab initio calculation of properties of heavier nuclei that have not been studied in this way to date.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.