Green's Functions and the Nuclear Many-Body Problem

在密歇根州立大学校园内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变得可用于实验检查。大多数研究这些奇异原子核的实验探测器都涉及相互作用强烈的粒子，这使得很难提取这些奇异系统中单个质子或中子的特性。该项目旨在克服这一困难，利用量子力学传播子方法的框架，同时描述正能量核子（弹性散射领域）和束缚核子（核结构领域）。这种方法将提供关键的洞察非常丰富的中子核的属性，因此是相关的中子星的物理学澄清中子被发现相对于质子的分布。本研究将由PI指导研究生的研究，并与进行相关实验的实验同事合作。传播子方法将用于受实验数据约束的非定域势，从而通过色散关系方法精确描述原子核的基态性质。同时，该实现将能够描述或预测连续体中的所有相关实验数据，包括弹性散射截面。因此，将有可能使用这种方法的成分来研究各种核反应，类似于对电子诱导质子敲除反应的成功分析，从而澄清奇异核中质子和中子的性质，并提出相关的新实验。特别是，过剩中子的核的中子分布的预测将是至关重要的实验在杰斐逊实验室和未来的实验在FRIB。传播子方法也将被用来计算核子的性质，从核子之间的基本相互作用开始，受到夸克和胶子基本理论、量子染色体动力学和两个核子性质的可用数据的对称性的约束。这种计算将应用于一个新的计划，允许从头计算的性质较重的核还没有被这样研究的日期。这个奖项反映了NSF的法定使命，并已被认为是值得的支持，通过评估使用基金会的智力价值和更广泛的影响审查标准。

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.