原子核配对近似和随机相互作用
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摘要
原子核是一个由中子与质子组成的复杂体系。自从1932年Chadwick发现中子以后原子核物理已成为现代科学诸多分支的一个重要领域。随着国际上新放射性核束流装置的建立与运行原子核物理进入了新纪元。
1949年Mayer与Jensen独立发展出原子核壳模型。自那以后壳模型就成为从微观角度研究原子核结构的基本理论框架。因为重原子核壳模型空间维数非常巨大，在用壳模形研究重原子核结构时人们需要对壳模型作截断。原子核配对近似（NPA）正是这样一种有效、物理图像清晰的截断方法。我们的工作将主要围绕着配对近似展开。其中包括它的有效性以及在研究重原子核低激发态中的应用。我们也将这一技术应用于研究随机相互作用中低激发态的鲁棒特征。
在第一章中我们简要介绍一些原子核物理的基础知识、原子核壳模型以及核力的短程性。从核力短程性出发我们说明原子核配对的存在以及角动量为零和二的核子配对在重原子核低激发态中的重要性。我们也讨论为什么研究原子核低激发态性质的鲁棒性是重要的。找到复杂原子核中简单特征的来源与机制是核物理与核天文的主要挑战之一。随机相互作用是研究这些简单特征的有力工具。
第二章从多方面介绍我们在原子核配对近似方面所做的具体工作。首先我们讨论了配对近似的可靠性。在这一工作中我们不仅考虑唯象的壳模型哈密顿量也考虑到有效相互作用（GXPF1A）；不仅考虑偶偶核也考虑奇数核子系统乃至奇奇核；不仅考虑半满壳核也考虑具有两种价核子的原子核系统。我们系统性地说明尽管巨大的壳模型空间被截断为很小的核子配对子空间，原子核配对近似仍然可以近似地重现出壳模型的计算结果，包括能级、跃迁机率以及波函数。其次我们也将配对近似应用到质量数在200附近的重原子核低激发态系统性计算中。在这一工作中我们使用唯象的壳模型哈密顿量。我们的计算能很好地描述这些原子核的低激发态。特别地我们讨论这些重原子核低激发态中存在的多重态图像。它对应着奇数核子系统中偶偶核心与未配对粒子之间的弱耦合。进一步地我们还将配对近似应用在如下物理图像的描述中：Ce同位素链中从球形态到形变态的形状相变、48Cr回弯效应中的质子中子配对以及128Xe中π=8同质异能态。
在第三章中我们描述在随机相互作用下原子核低激发态鲁棒特征。我们观察到当单粒子劈裂增大时半满壳偶偶核低激发态中的核子更倾向于配对存在。在随机的sd玻色子系统中我们注意到一些新奇的由s或d玻色子凝聚造成的集体运动。这一发现是对此前随机的sd玻色子系统中振动与转动集体运动模式的补充。我们对这些新发现的集体运动从波函数与相互作用特征出发进行仔细分析。
我们可以从以下两方面对配对近似进行进一步的发展：（1）在配对基矢与壳模型哈密顿量中考虑同位旋对称性；（2）用配对近似来研究原子核β衰变。
Nuclei are complex systems consisting of nucleons, neutrons and protons. Nuclear physicshas been one of the main subjects among many branches of modern science，since Chadwickdiscovered neutron in1932. With the help of new radioactive-beam facilities internationally (e.g.,RIA and RIBF, etc), nuclear physics enter a new era.
In1949, Mayer and Jensen developed the nuclear shell model. The nuclear shell model hasbeen the most important framework to study nuclear structure from a microscopic perspective.However, the configuration space of this model is too huge to deal with. Thus one has to re-sort to various truncation schemes. The nucleon pair approximation is an efficient and convenientapproach towards that goal. In this thesis we study a number of aspects of the nucleon pair approx-imation, including validity of such truncations and applications of this approach to low-lying statesof heavy nuclei. We also study general features of nuclear structure with random interactions bythis approach.
In Chapter1, we introduce some fundamentals of atomic nuclei, the shell model, the short-range feature of nuclear force. We explain why the pairing phenomenon arises from the short-rangecorrelation in nuclear interaction, why spin-zero and spin-two pairs are dominant configurations inlow-lying states of medium-heavy nuclei. We also discuss the importance to study robustness ofgeneric features in low-lying states of atomic nuclei. The origin of simplicity exhibited in complexnuclei is one of the main challenges in nuclear and astrophysics. Random interactions provide uswith a powerful approach to study such simplicity.
In Chapter2, we study the nucleon pair approximation of the shell model in a few contexts.The first is validity of pair approximation. We consider not only a phenomenological shell-modelhamiltonian but also effective shell-model hamiltonian (GXPF1A), not only even-even but alsoodd-mass nuclei, not only semi-magic but also open-shell systems. Our systematic studies demon-strate that the nucleon pair approximation is indeed able to reproduce very well the shell modelresults, although the gigantic shell model space is substantially truncated to a very small nucleon-pair subspace. Second, we apply the pair approximation to systematic studies of low-lying statesof nuclei with mass number A～200, with a separable phenomenological shell model hamilto-nian. Our calculations describe well the low-lying states of these nuclei. We also discussed theso-called multiplets which are nothing but a weak-coupling between the even-even core and the unpaired valence nucleon for some of these states. Third, we apply the nucleon pair approximationto studies of shape transition from spherical to axially deformed nuclei in the even Ce isotopes,proton-neutron pairing on backbend in48Cr, and Iπ=8isomer in~(128)Xe.
In Chapter3, we explain our studies of nuclear structure in the presence of random interac-tions. We explain the observation that semi-magic nuclei favor low-seniority if their single-particlesplittings are artificially enlarged. For the random sd (spin zero and two) boson system, we pointout that the low-lying states of such system favors a few novel collective motions due to s or dboson condensations, in addition to the well-know vibration and rotation. We analyze our resultsin terms of both wave functions and corresponding interactions among the random ensemble.
As for future developments of the above works, we would like to mention two points as fol-lows:(1) Consideration of the isospin symmetry both in the nucleon-pair basis and the hamiltonian,(2) Application of the pair approximation to β-decay problem.
1949年Mayer与Jensen独立发展出原子核壳模型。自那以后壳模型就成为从微观角度研究原子核结构的基本理论框架。因为重原子核壳模型空间维数非常巨大，在用壳模形研究重原子核结构时人们需要对壳模型作截断。原子核配对近似（NPA）正是这样一种有效、物理图像清晰的截断方法。我们的工作将主要围绕着配对近似展开。其中包括它的有效性以及在研究重原子核低激发态中的应用。我们也将这一技术应用于研究随机相互作用中低激发态的鲁棒特征。
在第一章中我们简要介绍一些原子核物理的基础知识、原子核壳模型以及核力的短程性。从核力短程性出发我们说明原子核配对的存在以及角动量为零和二的核子配对在重原子核低激发态中的重要性。我们也讨论为什么研究原子核低激发态性质的鲁棒性是重要的。找到复杂原子核中简单特征的来源与机制是核物理与核天文的主要挑战之一。随机相互作用是研究这些简单特征的有力工具。
第二章从多方面介绍我们在原子核配对近似方面所做的具体工作。首先我们讨论了配对近似的可靠性。在这一工作中我们不仅考虑唯象的壳模型哈密顿量也考虑到有效相互作用（GXPF1A）；不仅考虑偶偶核也考虑奇数核子系统乃至奇奇核；不仅考虑半满壳核也考虑具有两种价核子的原子核系统。我们系统性地说明尽管巨大的壳模型空间被截断为很小的核子配对子空间，原子核配对近似仍然可以近似地重现出壳模型的计算结果，包括能级、跃迁机率以及波函数。其次我们也将配对近似应用到质量数在200附近的重原子核低激发态系统性计算中。在这一工作中我们使用唯象的壳模型哈密顿量。我们的计算能很好地描述这些原子核的低激发态。特别地我们讨论这些重原子核低激发态中存在的多重态图像。它对应着奇数核子系统中偶偶核心与未配对粒子之间的弱耦合。进一步地我们还将配对近似应用在如下物理图像的描述中：Ce同位素链中从球形态到形变态的形状相变、48Cr回弯效应中的质子中子配对以及128Xe中π=8同质异能态。
在第三章中我们描述在随机相互作用下原子核低激发态鲁棒特征。我们观察到当单粒子劈裂增大时半满壳偶偶核低激发态中的核子更倾向于配对存在。在随机的sd玻色子系统中我们注意到一些新奇的由s或d玻色子凝聚造成的集体运动。这一发现是对此前随机的sd玻色子系统中振动与转动集体运动模式的补充。我们对这些新发现的集体运动从波函数与相互作用特征出发进行仔细分析。
我们可以从以下两方面对配对近似进行进一步的发展：（1）在配对基矢与壳模型哈密顿量中考虑同位旋对称性；（2）用配对近似来研究原子核β衰变。
Nuclei are complex systems consisting of nucleons, neutrons and protons. Nuclear physicshas been one of the main subjects among many branches of modern science，since Chadwickdiscovered neutron in1932. With the help of new radioactive-beam facilities internationally (e.g.,RIA and RIBF, etc), nuclear physics enter a new era.
In1949, Mayer and Jensen developed the nuclear shell model. The nuclear shell model hasbeen the most important framework to study nuclear structure from a microscopic perspective.However, the configuration space of this model is too huge to deal with. Thus one has to re-sort to various truncation schemes. The nucleon pair approximation is an efficient and convenientapproach towards that goal. In this thesis we study a number of aspects of the nucleon pair approx-imation, including validity of such truncations and applications of this approach to low-lying statesof heavy nuclei. We also study general features of nuclear structure with random interactions bythis approach.
In Chapter1, we introduce some fundamentals of atomic nuclei, the shell model, the short-range feature of nuclear force. We explain why the pairing phenomenon arises from the short-rangecorrelation in nuclear interaction, why spin-zero and spin-two pairs are dominant configurations inlow-lying states of medium-heavy nuclei. We also discuss the importance to study robustness ofgeneric features in low-lying states of atomic nuclei. The origin of simplicity exhibited in complexnuclei is one of the main challenges in nuclear and astrophysics. Random interactions provide uswith a powerful approach to study such simplicity.
In Chapter2, we study the nucleon pair approximation of the shell model in a few contexts.The first is validity of pair approximation. We consider not only a phenomenological shell-modelhamiltonian but also effective shell-model hamiltonian (GXPF1A), not only even-even but alsoodd-mass nuclei, not only semi-magic but also open-shell systems. Our systematic studies demon-strate that the nucleon pair approximation is indeed able to reproduce very well the shell modelresults, although the gigantic shell model space is substantially truncated to a very small nucleon-pair subspace. Second, we apply the pair approximation to systematic studies of low-lying statesof nuclei with mass number A～200, with a separable phenomenological shell model hamilto-nian. Our calculations describe well the low-lying states of these nuclei. We also discussed theso-called multiplets which are nothing but a weak-coupling between the even-even core and the unpaired valence nucleon for some of these states. Third, we apply the nucleon pair approximationto studies of shape transition from spherical to axially deformed nuclei in the even Ce isotopes,proton-neutron pairing on backbend in48Cr, and Iπ=8isomer in~(128)Xe.
In Chapter3, we explain our studies of nuclear structure in the presence of random interac-tions. We explain the observation that semi-magic nuclei favor low-seniority if their single-particlesplittings are artificially enlarged. For the random sd (spin zero and two) boson system, we pointout that the low-lying states of such system favors a few novel collective motions due to s or dboson condensations, in addition to the well-know vibration and rotation. We analyze our resultsin terms of both wave functions and corresponding interactions among the random ensemble.
As for future developments of the above works, we would like to mention two points as fol-lows:(1) Consideration of the isospin symmetry both in the nucleon-pair basis and the hamiltonian,(2) Application of the pair approximation to β-decay problem.
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