Many-Body Methods in Nuclear Structure and Related Fields

核结构及相关领域的多体方法

• 批准号: 0140036
• 负责人: Stuart Pittel
• 金额: $ 24.88万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-01 至 2006-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0140036&HistoricalAwards=false
• 关键词: Many; Body; Methods; Nuclear; Structure

The central theme of this proposal is the development of new methods for approximately solving the Schroedingerequation for atomic nuclei and their application to problems ofcontemporary importance in nuclear structure physics. Methods having their parentage in the nuclear shell model and in mean-field theory will be considered, with the goal of developing algorithms that significantly expand their ranges of applicability. A principal focus will be on the development of theDensity Matrix Renormalization Group (DMRG), a method first introduced in the context of quantum spin lattices. Here we will focus on a new DMRG methodology that is tailored to such finite fermi systems as the atomic nucleus. We will also consider its application to an important non-nuclear problem, the two-dimensional Hubbard model, which is of relevance to systems that undergo transitions to superconductivity at high critical temperatures. A second focus will be on the properties ofweakly-bound nuclei far from stability. A method recently proposed for reliably solving the Hartree Fock Bogolyubov mean-field equations for very weakly-bound nuclei will be developed further, so as to make it computationally more viable, and will then be applied systematically to both spherical and axially-deformed nuclei throughout the periodic table. Other methods for solving the Hartree Fock Bogolyubov equations in weakly-bound systems will also be considered, to make sure that the spatial properties of such systems are being reliably treated.

该提案的中心主题是发展近似求解原子核薛定谔方程的新方法，并将其应用于核结构物理中的当代重要问题。将考虑在核壳模型和平均场理论中有其渊源的方法，其目标是开发算法，显着扩大其适用范围。一个主要的重点将是在theDensity矩阵重整化群（DMRG），量子自旋晶格的背景下首次介绍的方法的发展。在这里，我们将集中在一个新的DMRG方法，是专为有限费米系统的原子核。我们还将考虑它的应用程序的一个重要的非核问题，二维哈伯德模型，这是相关的系统，在高临界温度下进行过渡到超导性。第二个焦点将是远离稳定的弱束缚核的性质。最近提出的一种可靠地求解极弱束缚核的Hartree Fock Bogolyubov平均场方程的方法将进一步发展，以使其在计算上更可行，然后将系统地应用于整个周期表中的球形和轴向变形核。也将考虑在弱约束系统中求解Hartree Fock Bogolyubov方程的其他方法，以确保此类系统的空间性质得到可靠的处理。