Nuclear Structure and Reactions from Effective Field Theory

量子色动力学（QCD）理论描述了核物理中的基本相互作用。在低能量下，QCD是一个强相互作用的理论，不能用铅笔和纸计算的第一性原理来解决。有效场论（EFT）公式提供了一个补充框架，其中低能核性质可以系统地计算。因此，EFT计算可以为直接实验测量无法获得的元素合成天体物理模型提供准确的输入。在这个项目中，PI和他的合作者将使用在时空晶格上定义的数值方法，使用EFT计算中轻原子核（质量数高达40左右）的性质。PI将使用贝叶斯统计来定量比较相互竞争的EFT公式。后者有助于建立一个准确而系统的低能核物理理论。这项研究的更广泛影响包括培养研究生在数值和分析工作方面的学术或工业生涯，造福社会。目前的项目建立在之前由PI引入的点阵EFT针孔算法的基础上。该算法允许在蒙特卡罗模拟中计算电荷和物质分布（在质心坐标中），这是将外部弱电电流耦合到原子核所必需的。PI旨在计算轻原子核的电磁矩。同样的方法将用于计算对中子物质分布敏感的中微子核相干散射。这个横截面可以作为暗物质搜索实验的背景。PI还将使用贝叶斯统计研究涉及晕核的低能核反应。晕核具有弱束缚量子系统的特征，在大爆炸和恒星燃烧的元素合成中起着重要作用。贝叶斯分析提供了一个自然的框架，用于在参数估计中纳入EFT关于耦合大小的自然性的假设。它还允许对相互竞争的理论进行定量比较，并有助于模型选择。该项目将支持美国计划在稀有同位素束流实验方面的重大投资的科学项目。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The fundamental interactions in nuclear physics are described by the theory of Quantum Chromodynamics (QCD). At low energies, QCD is a strongly interacting theory that cannot be solved from first principles in a pencil-and-paper calculation. The effective field theory (EFT) formulation provides a complementary framework where nuclear properties at low energy can be systematically calculated. As such, EFT calculations can provide accurate input for astrophysical models of element synthesis that cannot be obtained in direct experimental measurements. In this project, the PI and his collaborators will use numerical methods defined on a space-time lattice to calculate properties of medium-light atomic nuclei (mass number up to around 40) using EFT. The PI will use Bayesian statistics to quantitatively compare competing EFT formulations. The latter is useful in constructing an accurate and systematic theory for low energy nuclear physics. Broader impacts of the research include training of graduate students in numerical and analytical work for an academic or industry career benefiting society.The current project builds on the lattice EFT pinhole algorithm that was previously introduced by the PI. This algorithm allows for the calculation of the charge and matter distribution (in the center-of-mass coordinate) in Monte Carlo simulations that is necessary to couple external electro-weak currents to atomic nuclei. The PI aims to calculate electromagnetic moments of light nuclei. The same method will be used to calculate neutrino-nucleus coherent scattering that is sensitive to the neutron matter distribution. This cross section serves as a background in dark matter search experiments. The PI will study also low energy nuclear reactions involving halo nuclei using Bayesian statistics. Halo nuclei are characterized as weakly bound quantum systems and play an important role in element synthesis in the Big Bang and stellar burning. Bayesian analysis provides a natural framework to incorporate EFT assumptions about naturalness of sizes of couplings in parameter estimation. It also allows quantitative comparison of competing theories and aids in model selection. This project will support the science programs at planned major U.S. investments in rare isotope beam experiments.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.