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，中子质子比或大或小的原子核的性质可以用于实验审查。大多数用于研究这些奇异核的实验探针都涉及到自身强烈相互作用的粒子，这使得在这些奇异系统中提取单个质子或中子的特性变得困难。本课题旨在利用量子力学的传播子方法框架，同时描述弹性散射域的正能量核子和核结构域的束缚核子，从而克服这一困难。这种方法将对中子非常丰富的原子核的性质提供关键的见解，因此，通过澄清中子在质子分布中的位置，与中子星的物理学有关。PI将指导研究生进行这项研究，并与实验同事合作进行相关实验。传播子方法将用于受实验数据约束的非局域势，允许用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包括弹性散射截面在内的连续体中的所有相关实验数据。因此，用这种方法的成分来研究各种核反应将有可能类比于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。特别地，对于具有多余中子的原子核的中子分布的预测对于杰斐逊实验室的实验和未来在FRIB的实验将是至关重要的。传播子方法也将被用于计算原子核的性质，从基本理论夸克和胶子的对称性约束下的核子之间的基本相互作用开始，量子色动力学，以及两个核子性质的可用数据。这种计算将应用于一种新的方案，该方案允许从头计算迄今尚未以这种方式研究过的较重原子核的性质。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.