Green's functions and the nuclear many-body problem

化学元素的起源是核物理学和天体物理学的基本问题之一，对原子核结构和动力学特性的详细了解是理解核合成过程的关键因素，核合成过程允许由组成核子（质子和核子）形成原子核。这个问题带来的挑战之一是研究质子和中子数量之间存在很大不平衡的原子核。这些核通常不稳定，导致放射性，对工业、医学和国防应用具有重要的社会意义。在更广泛的背景下，该项目将为领先实验设施的科学项目提供理论支持，例如密歇根州立大学校园内正在建设的未来稀有同位素光束设施（FRIB）。特别是，PI和他的学生将继续发展一种理论方法，旨在提供核结构和核反应的一致描述，以分析FRIB和其他核物理设施的实验数据。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。本项目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。传播子方法的应用将采用非局部实现的势的描述，允许使用色散关系的方法精确描述基态性质。伴随着传播子方法的实施来描述所有相关的实验数据，包括弹性散射截面和物质和电荷分布，将使用相同的框架来计算这些性质，但从核子之间的潜在相互作用开始，受夸克和胶子基本理论的对称性限制，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。该方法还将应用于中子星超流体性质的计算。

The origin of the chemical elements is one of the fundamental problems in nuclear physics and astrophysics, and the detailed understanding of the structural and dynamical properties of nuclei is the key ingredient for progress in understanding the nucleosynthesis process that allows for the formation of atomic nuclei from constituent nucleons (protons and nucleons). One of the challenges posed by this problem concerns the study of nuclei that feature a large imbalance between the number of protons and neutrons. These nuclei are generally unstable, leading to radioactivity, and have important societal relevance for industry, medicine and defense applications. In that broader context, this project will provide theoretical support for the science programs at leading experimental facilities, such as the future Facility for Rare Isotope Beams (FRIB) under construction on the campus of Michigan State University. In particular, the PI and his students will continue the development of a theoretical approach aimed at providing a consistent description of nuclear structure and nuclear reactions needed to analyze the experimental data at FRIB and other nuclear physics facilities. The PI will mentor graduate students in this research and collaborate with experimental colleagues who will perform related experiments.This project aims at 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. The application of the propagator method will employ the nonlocal implementation of the description of the potentials that allows for the accurate description of ground-state properties using the method of dispersion relations. Accompanying the implementation of the propagator method to describe all relevant experimental data, including elastic scattering cross sections and matter and charge distributions, will be the calculation of these properties using the same framework but 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. The method will also be applied to calculations of the superfluid properties of neutron stars.