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

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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.