壳模型哈密顿量论文：壳模型哈密顿量中的张量力分析.doc

壳模型哈密顿量论文：壳模型哈密顿量中的张量力分析【中文摘要】壳模型是最基本的微观核结构理论模型之一。该模型很好地解释了轻核和中等质量核的各种性质,如结合能,核谱,以及各种跃迁性质等。壳模型成功的关键之一是选取合适的哈密顿量。现有的哈密顿量同时包含了原子核的饱和性和能谱性质。但是由于核力的复杂性,这些哈密顿量很难从现实核子-核子相互作用出发而得到,而往往通过其他方法,如与实验能谱拟合而得到。因此研究这些现实哈密顿量,分析它们的张量力构成,对于深入认识原子核这一复杂相互作用体系的基本特性,有重要理论意义。并且对于建立新的哈密顿量也具有一定的指导意义。壳模型哈密顿量通常包括单体项和多体项。其中两体项最重要,又可以进一步分解成单极部分Hm和多极部分HM。单极部分决定了原子核的主要性质,而多极部分可以描述谱学方面的各种性质。HM可以从正常表象变换到粒子-空穴表象,以便研究哈密顿量中的张量力构成。已经知道,对力和四极相互作用对HM起主要贡献,对于描述原子核特别是变形核的许多性质非常有效。由于这个缘故,投影壳模型采用简单的对力和四极相互作用,却可以很好地描述原子核转动谱的许多现象。其它的张量力,例如Gamow-Teller力,八极和十六极相互作用等也很重要。近年来,耦合张量力越来越被重视,而壳模型哈密顿中的耦合张量力,如和,还没有被具体分析过。因此对它们进行研究,有助于我们更全面地认识壳模型哈密顿量的结构特性。本文在现有的现实壳模型哈密顿量(USD, GXPFIA和FPD6)基础上,试图通过提取哈密顿量中的多极相互作用部分,对比各种不可约张量算符,尤其是耦合张量力算符,给出哈密顿量的张量力构成。本文的研究结果表明,有些耦合张量力对壳模型哈密顿量有比较重要的贡献。【英文摘要】The Shell Model(SM) is one of the most fundamental theories in the nuclear physics. It has been very successful in describing various properties of the low-lying states in the light and medium nuclei, such as the binding energies, the spectroscopy, the transition properties, etc. The key to the success of the SM is the excellent choice of the Hamiltonians. However, an effective Hamiltonian, which provides good saturation properties and good spectroscopy, seems very difficult to be built from a realistic nuclear force.Instead, it is usually built in other ways, such as fitting the experimental data. Those Hamiltonians may include the most important information of the complex nuclear system. Therefore, to deeply understand the interacting system of the nucleus, it is necessary to study the structure of the SM Hamiltonians via analyzing the contributions of various tensor forces. Meanwhile, this analysis also provides an important guidance when one builds a new SM Hamiltonian. A shell model Hamiltonian usually includes one body term and n-body interactions. The two-body interaction is the most often used one, and can be separated into monopole part Hm and multipole part HM. Hm is responsible for the bulk properties, such as binding energies and shell gaps, while HM provides good spectroscopy. To investigate the structure of the Hamiltonian, the HM part of some realistic Shell Model Hamiltonians, USD, KB3G and GXPF1A, have been transformed from the normal representation to the particle-hole representation by using the known formulation.It is well known that HM is dominated by the pairing and the quadrupole interactions. Therefore, the modeling with pairing plus quadrupole forces has been very successful in describing various properties of nuclei, especially, for the deformed ones. A typical example is the Projected Shell Model(PSM), which provides a good description of rotational bands. Other types of tensor forces such as the Gamow-Teller force, octupole and hexadecapole interactions are also important parts of the shell model Hamiltonian. However, the coupled tensor forces, such as rY1,(?)and (?)in the shell model Hamiltonian have not yet been analyzed. The analyses seem necessary because some coupled-tensor forces have already been found to play important roles in the study of the strength function. In this thesis, the multipole term was separated from the SM Hamiltonian and various spherical tensor forces were compared with the known realistic SM Hamiltonians (USD, GXPF1A, FPD6). It has been shown that some coupled-tensor forces, such as r2Y2(?)1, also give certain important contributions to the shell model Hamiltonian.【关键词】壳模型哈密顿量 多极相互作用 不可约张量算符 约化矩阵元【英文关键词】Shell Model Hamiltonian the multi-interaction irreducible tensor operator reduced matrix element【目录】壳模型哈密顿量中的张量力分析摘要3-4ABSTRACT4-5目录6-7第一章 引言7-201.1 原子核物理的发展过程7-81.2 原子核的基本性质8-121.2.1 原子核的组成91.2.2 原子核的自旋91.2.3 原子核的电磁矩9-101.2.4 原子核的宇称101.2.5 原子核的质量10-121.2.6 原子核的同位旋121.3 核结构的微观理论12-141.4 原子核的壳模型14-20第二章 理论框架20-242.1 算符介绍