Excellence in Research: Yakubovsky Calculations for Six-Nucleon Bound States

原子核的结构和性质，以及构成原子核的质子和中子之间的基本力，已经通过量子理论得以理解。原子核比它所在的原子小约10万倍。在量子力学中，这种信息可以通过求解描述物理系统性质的薛定谔方程来获得。这个方程式描述了质子和中子是如何被强核力限制在原子核内部的。该项目将允许在并行环境中开发复杂的计算机算法和程序，以求解氦-6和锂-6核的薛定谔方程。这些都是由六个核子组成的轻核。PI将指导中央州立大学(CSU)的本科生STEM学生，CSU是一所历史上的黑人大学。学生将获得并行编程和高性能计算的实用技能，同时获得使用计算物理研究原子核结构的信心。CSU学生将通过参加这个项目学习计算机编程和数值方法的关键技能，从而提高他们在STEM工作人员或高级学位的资格。薛定谔方程经常被求解来基准和发展核物理中的核子-核子相互作用模型。虽然六核子束缚态的研究在计算上是一个具有挑战性和昂贵的问题，但它的研究提供了对核相互作用丰富结构的洞察。这个项目的主要目标是在动量空间中数值求解Faddeev-Yakubovsky形式的薛定谔方程，以计算六核子的结合能和波函数。本项目旨在通过开发相关的并行计算机算法和代码来实现六核子雅库博夫斯基方程在分波分解中的数值解。这项研究将展示在完整的六体处理中，耦合Faddeev-Yakubovsky积分方程的全解是如何探索现代两核子和三核子相互作用的。它还提供了对He-6的晕结构和Li-6的基态性质的深入了解。该项目具有潜在的更广泛的影响，超出核物理。六体束缚系统在其他物理领域的存在，从原子物理(探索超冷量子气体中的埃菲莫夫物理)到粒子物理(由六个夸克组成的双重子共振)，带来了该项目及其成果的更广泛应用。该奖项反映了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。

Understanding the structure and properties of the atomic nucleus, which is about 100,000 times smaller than the atom it lives inside, and the fundamental forces between the protons and neutrons that constitute the nucleus, has been made possible by quantum theory. In quantum mechanics, this information can be acquired by solving the Schroedinger Equation, which describes the properties of the physical system. This equation describes how protons and neutrons are confined inside a nucleus by the Strong Nuclear Force. This project will allow the development of sophisticated computer algorithms and programs in a parallel environment to solve the Schroedinger Equation for Helium-6 and Lithium-6 nuclei. These are each light nuclei consisting of six nucleons. The PI will mentor undergraduate STEM students at the Central State University (CSU), a historically black college. The students will gain practical skills in parallel programming and high-performance computing, while gaining confidence in using computational physics to study the structure of atomic nuclei. CSU students will learn the critical skills of computer programming and numerical methods by participating in this project, thereby increasing their qualifications for the STEM workforce or advanced degrees.The Schroedinger Equation is often solved to benchmark and develop nucleon-nucleon interaction models in nuclear physics. Although the study of a six-nucleon bound state is computationally a challenging and expensive problem, its investigation provides insights into the rich structure of nuclear interactions. The main goal of this project is the numerical solution of the Schroedinger Equation in the Faddeev-Yakubovsky form in momentum space to calculate the six-nucleon binding energy and wave function. This project aims to implement the numerical solution of six-nucleon Yakubovsky equations in a partial wave decomposition by developing the relevant parallel computer algorithms and codes. This investigation will show how the full solution of coupled Faddeev-Yakubovsky integral equations in a complete six-body treatment can probe the modern two- and three-nucleon interactions. It also provides an in-depth insight into the halo structure of He-6 and also the ground state properties of Li-6. This project has potential broader impacts beyond nuclear physics. The existence of six-body bound systems in other areas of physics, ranging from atomic physics (exploration of Efimov physics in ultracold quantum gases) to particle physics (dibaryon resonance composed of six quarks), brings a broader application of the project and its outcomes.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.