Greens Functions and the Nuclear Many-Body Problem

在密歇根州立大学即将启动的稀有同位素束设施（FRIB）等设施中，具有极端中子质子比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涉及的粒子本身相互作用强烈，这使得很难提取这些奇异系统中单个质子或中子的性质。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。这种方法将为非常富含中子的原子核的特性提供关键的见解，因此通过澄清中子在质子分布中的位置以及中子如何被富含中子的原子核捕获，与中子星的物理学相关。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，将有可能利用这种方法的成分来研究各种核反应，就像成功地分析电子诱导的质子敲除反应一样，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。特别是涉及氘核的反应，将采用非局部的服从色散关系的势来研究。对具有多余中子的核的中子分布的预测将继续保持兴趣。将开发一种方法的扩展，以允许同时描述响应函数。在夸克和胶子的基本理论、量子色动力学和两个核子的性质的可用数据的对称性约束下，从核子之间的基本相互作用开始，传播子方法也将被用于计算原子核的性质。这种计算将与一种新的策略一起应用，这种策略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散射特性。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 extreme neutron to proton ratios are becoming available for experimental scrutiny at facilities like the Facility for Rare Isotope Beams (FRIB) starting shortly 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. The 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 insights 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 and how neutrons are captured by neutron-rich nuclei. 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 reactions involving deuterons will be studied employing potentials that are nonlocal and obey dispersion relations. Continued interest in the prediction of the neutron distribution for nuclei with excess neutrons will be maintained. An extension of the method will be developed to allow a simultaneous description of response functions. 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 strategy that allows the ab initio calculation of scattering 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.