Nuclear Structure and Reactions from Effective Field Theory

用量子色动力学(QCD)理论描述了核物理中的基本相互作用。在低能量下，QCD是一种强相互作用理论，不能用纸笔计算的第一原理来解决。有效场论(EFT)公式提供了一个补充框架，其中可以系统地计算低能下的核性质。因此，EFT计算可以为元素合成的天体物理模型提供准确的输入，而这些模型在直接的实验测量中无法获得。在这个项目中，PI和他的合作者将使用时空格子上定义的数值方法，使用电子傅立叶变换计算中轻原子核(质量数高达40左右)的性质。PI将使用贝叶斯统计对竞争对手的EFT公式进行定量比较。后者有助于建立准确、系统的低能核物理理论。这项研究的更广泛的影响包括培训研究生从事数值和分析工作，以便在学术或行业职业生涯中造福社会。当前的项目建立在PI之前引入的格子EFT针孔算法的基础上。这种算法允许在蒙特卡罗模拟中计算电荷和物质分布(在质心坐标下)，这是将外部弱电流耦合到原子核所必需的。PI的目的是计算轻核的电磁矩。同样的方法将用于计算对中子物质分布敏感的中微子-原子核相干散射。这个横截面在暗物质搜索实验中用作背景。PI还将使用贝叶斯统计方法研究涉及晕核的低能核反应。晕核被描述为弱束缚量子系统，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，将EFT关于联轴器尺寸自然度的假设纳入到参数估计中。它还允许对相互竞争的理论进行定量比较，并在模型选择方面提供帮助。该项目将支持美国计划对稀有同位素束实验进行重大投资的科学项目。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。

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.