Extending the Ab-initio Nuclear Many-Body Frontier with the Renormalization Group

该奖项支持使用现代重整化群（RG）和有效场论（EFT）方法研究核结构中的各种少体和多体问题。 福尔斯提出的工作分为三类：核子间相互作用和RG方法，有限核和无限核物质的从头计算，以及基于微观的能量密度泛函（EDF）的核。 拟议研究的中心目标是研究如何使用重整化群和有效场论方法将从头计算扩展到中等质量核及更高质量核;构建基于微观的核能密度泛函（EDF），提高预测能力远离已知数据;并发展非微扰方法，为大规模壳模型应用提供壳模型（SM）有效哈密顿量和有效算子的受控计算（例如，在一个实施例中，无中微子双β衰变）。 所有这三个领域的项目都与核理论中的基本问题密切相关，例如：核稳定性的极限是什么？ 中微子的质量是多少？原子核和核物质的性质是如何从潜在的两核子和三核子（以及更高的）相互作用中显现出来的？ 拟议的研究将发挥不可或缺的作用，在控制理论的不确定性，这将是至关重要的稀有同位素束设施和天体物理应用提供理论指导的模型无关的少体和多体计算的发展。该项目将通过促进跨学科的联系和帮助在美国建立一个强大而年轻的科学界而产生更广泛的影响。有效场论和重整化群的互补技术由于其普适性和简化能力而被广泛应用于理论物理的许多领域。因此，我们使用这些现代和通用的技术将加强与其他学科，如凝聚态，原子和高能理论的相互作用。 同样，在这项工作中使用耦合团簇和能量密度泛函方法将促进与量子化学的联系。 最后，目前的项目将为研究生和博士后提供正式（分析）和实践（数值）工作的良好平衡，这将为工业或学术界的职业生涯做好准备。

This award supports the study of a wide range of few- and many-body problems in nuclear structure using modern Renormalization Group (RG) and Effective Field Theory (EFT) methods. The proposed work falls into three categories; Inter-Nucleon Interactions and RG Methods, ab-initio Calculations of Finite Nuclei and Infinite Nuclear Matter, and Microscopically-Based Energy Density Functionals (EDFs) for Nuclei. The central goals of the proposed research are to study how renormalization group and effective field theory methods can be used to extend ab-initio calculations to medium-mass nuclei and beyond; to construct microscopically-based nuclear energy density functionals (EDFs) with improved predictive power away from known data; and to develop non-perturbative methods to provide controlled calculations of shell model (SM) effective Hamiltonians and effective operators for large-scale shell model applications (e.g., neutrinoless double beta decay). The projects in all three areas are intimately connected to fundamental questions in nuclear theory such as: What are the limits of nuclear stability? What are the masses of neutrinos?, and How do the properties of nuclei and nuclear matter emerge from underlying two- and three-nucleon (and higher) interactions? The proposed research will play an integral role in the development of model-independent few- and many-body calculations with controlled theoretical uncertainties, which will be crucial to provide theoretical guidance for rare isotope beam facilities and astrophysical applications. This project will have broader impacts by fostering inter-disciplinary connections and helping to build a strong and youthful scientific community in the United States. The complementary techniques of Effective Field Theory and the Renormalization Group are widely used in many areas of theoretical physics due to their universality and power of simplification. Therefore, our use of these modern and general techniques will enhance interactions with other disciplines such as condensed matter, atomic, and high energy theory. Similarly, the use of coupled-cluster and energy density functional methods for nuclei in this work will foster connections with quantum chemistry. Finally, the current project will provide graduate students and postdocs with a good balance of formal(analytical) and practical (numerical) work, which will serve as excellent preparation for a career in industry or academia.