Collaborative Research: Galilei and Poincare Invariant Calculations of the Three Nucleon System

该奖项支持的项目目标是创建新的计算机程序，使用自然物理定律允许的最一般形式的相互作用来计算三个核子（原子序数A=3）系统的相互作用和性质。这些新的计算机程序将公开提供，从而允许其他研究人员探索相互作用的不同参数或不同的相互作用，而无需编写探索三核子系统所需的复杂计算机程序。这项研究的主要动机是了解原子核中质子和中子之间复杂的相互作用；然而，所使用的计算技术也可以应用于存在三体相互作用的其他物理领域，例如原子物理学（研究冷原子）和粒子物理学（质子内部的夸克相互作用）。预测三个或更多相互作用物体的行为是理论物理学中一个长期存在的问题。虽然两个粒子的相互作用相当容易计算，但所谓的三体问题要难解决得多。一种归因于Faddeev的方法现在被广泛使用，但Faddeev方程的实现需要长时间和复杂的计算，这些计算最适合于功能强大的计算机。计算Faddeev方程的传统方法使用一种称为部分波展开的数学技术。然而，随着三体系统中能量的增加，这种数学方法变得低效。目前的项目采用了一种新的自旋轨迹的数学方法，这使得三体问题可以在更高的能量下解决，并且通常增加了实现更广泛的粒子间力的灵活性。因此，这个项目将为三体问题的研究提供一个比目前可行的更好的理论框架。

The goal of the project supported by this award is to create new computer programs to calculate the interactions and properties of systems of three nucleons (atomic number A=3) using the most general form of interactions allowed by the physical laws of nature. These new computer programs will be made publicly available, thereby allowing other researchers to explore different parameters of the interaction or different interactions without the need to write the intricate computer programs needed to explore a three-nucleon system. A main motivation for this study is to understand the complex interactions between protons and neutrons in the nucleus; however the computational techniques used can also be applied to other areas of physics where three-body interactions are present, such as atomic physics (research with cold atoms) and particle physics (quark interactions inside the proton).The method of predicting the behavior of three or more interacting bodies is a long-standing problem in theoretical physics. While the interactions of two particles are fairly easy to calculate, the so-called three-body problem is much more difficult to solve. A method attributed to Faddeev is now widely used, but the implementation of the Faddeev equations requires long and involved calculations that are best suited for powerful computers. The traditional approach to calculating the Faddeev equations uses a mathematical technique called partial-wave expansion. However, as the energy increases in the three-body system, this mathematical technique becomes inefficient. The current project utilizes a novel mathematical approach of taking spin traces, which allows the three-body problem to be solved at much higher energies, and generally increases the flexibility of implementing a wider class of inter-particle forces. Hence, this project will provide a better theoretical framework for the investigation of the three-body problem than is presently feasible.