SD对壳模型下原子核形状相变（英文）

在SD 对壳模型的理论框架下讨论了原子核形状相变模式。研究结果表明,该理论模型可以把相互作用玻色子模型中U（5）-SU（3）以及U（5）-SO（6） 形状相变模式再现出来,相互作用玻色子模型中有关临界点对称性的特征也可以很好地描述。本文同时也发现原子核从振动到转动的形状相变可以通过改变相互作用强度来实现。The nuclear shape phase transitional patterns were studied in the SD-pair shell model. The results show that the transitional patterns similar to the U(5)-SU(3) and U(5)-SO(6) transitions in the interacting boson model can be produced. The signatures of the critical point symmetry in the interacting boson model are also produced approximately. It is also found that the shape phase transitional pattern between vibration and rotation can also be produced by changing the interactional strength.     

SO（8）对关联和代数壳模型中的SU（3）四极基底（英文）

建立了SO（8） 同位旋标量、同位旋矢量及总的配对基与微观壳模型坐标空间部分的Elliott SU（3） 基之间的对应关系。从该代数间的互补关系导出了在壳模型的粒子数守恒代数U（4Ω） 中所包含的具有同位旋T 及自旋S 的Wigner 超多重态（不可约） 表示。其重要性在于,该结果能用于研究对相互作用和四极-四极相互作用在核谱中的竞争效应并揭示其配对基中的SU（3） 组份。虽然仅展示了该理论对ds 壳的计算,其方法也适用于研究多壳的情形。We establish a correspondence between the SO(8) isoscalar, isovector and total pairing bases and the Elliott's SU(3) basis in the algebraic structure of the spatial part of the microscopic shell model. It is derived from the complementarity of these algebras to the same T, S, (S,T) irreducible representations (irreps) of the Wigners supermultiplets, contained in the shell-model number-conserving algebra U(4Ω). This important result allows for the evaluation of the content of SU(3) irreps into the different types of pairing bases which leads to an investigation of the complementarity and competitive effects of pairing and the quadrupole-quadrupole interactions on the energy spectra of the nuclear systems. The theory is valid for any shell and for a number of shells as well, but we illustrate it with the results for a single ds-shell.     

原子核的形状相变

简要回顾原子核形状相变研究的现状，并将相干态理论与角动量投影方法相结合，在不区分质子玻色子和中子玻色子的相互作用玻色子模型（IBM-1）框架下，对角动量驱动的轴对称情况下的具有U（5）、SU（3）对称性以及两种对称性之间过渡区的原子核的形状相变进行了具体研究。We review the status of the research of nuclear shape phase transitions in this paper. Meanwhile, by taking the coherent state theory and angular momentum projection method, we study the shape phase transitions of axially symmetric even-even nuclei with U（5） symmetry, SU（3） symmetry and those in the transitional region of the two symmetries in the framework of Interacting Boson Model-1 （IBM-1）, which does not distinguish the proton bosons from neutron bosons.     

Q-Deformed Bosons at Quasi-classical Limit of SO（3）

When a boson interacts with another to form a composite system with SO（3） dynamic symmetry, it is shown that there exists the q-deformed 5osonic excitation satisfying the q-deformed Heisenberg commutation relation in the quasi-classical limit that the angular momentum j for SO（3） is large, but not infinite. In second quantization this quasi-excitation is associated with the boson realization of SO（3） Lie algebra. Physically, the phenomena of q-deformed excitation can happen in many models of quantum dynamics, such as super emission from a system of many identical two-level atoms, the spin wave in Heisenberg chain, the high spin precession and the coherent output of Bose-Einstein atoms in a trap. Especially, in these models, the deformation parameter q is well defined intrinsically by a conservative quantity, such as the total atomic number and the angular momentum.     

Rotation Driven Shape-Phase Transition of the Yrast Nuclear States with O（6） Symmetry in the Interacting Boson Model

In a framework of the interacting boson model (usually referred to as IBM-1) with angular momentum projection on the coherent state, we obtain the energy surface functional of nuclei in terms of angular momentum and shape parameters. Analysing the rotation driven effect on the equilibrium shape shows that the yrast states of the nuclei with 0(6) symmetry will experience a shape-phase transition from γ-soft deformed to triaxially deformed and then to spherical shape along the yrast line as the angular momentum increases.     

量子N体系统的广义径向方程

介绍一种精确的方法 ,在质心坐标系中 ,把量子 N体系统的整体转动自由度和内部运动自由度完全地分离开来 .对于确定的轨道角动量状态 ,找到了一组完备且独立的角动量本征函数基 ,它们是坐标分量的齐次多项式 ,且满足 Laplace方程 .系统中的任何角动量本征函数都可以用这组函数基展开 ,组合系数只依赖于内部变量 ,称为广义径向函数 .可以简单且明显地推导出广义径向函数所满足的广义径向方程 .函数和方程式都只依赖于 (3 N- 6 )个内部变量 ,而且个数是有限的. A method without any approximation to separate the global rotational degrees of freedom in the Schrdinger equation for an N -body system completely from the internal ones is presented. For given orbital angular momentum states, we discover a complete set of independent base-functions, which are homogeneous polynomials in the components of the coordinate vectors and satisfy the Laplace equation. Any function with the given angular momentum and the given parity in the system can be...     

稀土区奇A核晕带存在从转动到振动形状演化的直接证据(英文)

原子核的形状演化效应是核结构研究的重要基础问题之一。通常认为,A=160质量区的奇A核位于大形变核区域,它们的激发态能谱将呈现出典型的转动激发特征。然而,基于E-GOS曲线方法,发现随着角动量的增加,该质量区奇A核的晕带具有显著地从转动激发演化成为振动激发的形状演化现象。此外,为深入理解原子核形状演化的微观机制,采用Total-Routhian-Surface（TRS）方法针对稀土区的奇A核进行了理论计算,结果表明,165Yb和157Dy同位素在低激发态时具有稳定的长椭形变,当角动量大于0.50 MeV后,核芯的四极形变显著减小并开始产生三轴形变。The phase transition of nuclei with increasing angular momentum (or spin) and excitation energy is one of the most fundamental topics of nuclear structure research. The odd-N nuclei with A ≈160 are widely considered belonging to the well-deformed region, and their excitation spectra are energetically favored to exhibit the rotational characteristics. In this work, however, the evidence suggesting that the nuclei changes from rotation to vibration along the yrast lines as a function of spin was found. The simple method, named as E-Gamma Over Spin (E-GOS) curves, would be used to discern the evolution from rotational to vibrational structure in nuclei for various spin ranges. Meanwhile, in order to understand the band structure properties of nuclei, theoretical calculations have been performed for the yrast bands of the odd-A rare-earth nuclei within the framework of the total routhian surface (TRS) model. The TRS plots predict that the 165Yb and 157Dy isotopes have large quadrupole shapes at low spin states. At higher rotational frequency (hω~ >0.50 MeV), a clear reduction of the quadrupole deformation is indicated by the present results, and the isotopes become rigid in the γ deformation.     

Nucleon internal structure: a new set of quark, gluon momentum, angular momentum operators and parton distribution functions

It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relation. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy both the gauge invariance and canonical momentum and angular momentum commutation relation, are proposed. The key point to achieve such a proper decomposition is to separate the gauge field into the pure gauge and the gauge covariant parts. The same conflicts also exist in QED and quantum mechanics and have been solved in the same manner. The impacts of this new decomposition to the nucleon internal structure are discussed.     

推广的相互作用玻色子模型中基于对偶代数结构的量子相变研究(英文)

本工作将相互作用玻色子模型推广为包含f-和p-玻色子的情形。利用仿射型代数方法,通过对偶代数结构数值计算了多分量玻色型对力问题。利用对偶关系解析构建了与哈密顿量及其基底相联系的,由幺正的粒子数守恒和非粒子数守恒算符构成的准旋代数。在经该模型对106-116Cd偶偶核素实验能谱拟合的基础上,计算了基态和低激发态中各种玻色子占有率,准γ带中相邻能级摇摆等几个能特征该区域核素形状相变的序参量。从而展示了这些中重质量核从振动到γ-不稳定运动的形状相变行为。An extension of the original interacting boson model to the multi-level case including negative parity f-and p-bosons is made. An affinealgebraic approach is applied to solve the multi-level pairing problem numerically via the dual algebraic structure. The duality relation is explicitly used to construct the number-conserving unitary and number-nonconserving quasi-spin algebra, related with the Hamiltonian and the corresponding bases. After fitting to the experimental level energies of even-even 106-116Cd, several order parameters to signify the shape (phase) transition, such as occupation numbers of the bosons in the ground and a few lowest excited states, the level energy staggering in the (quasi)-γ band, are calculated to demonstrate the shape (phase) transitional behavior of these medium mass transitional nuclei.     

费米子动力学对称群的玻色子实现

将费米子动力学对称模型扩展为包含较高角动量费米子对,一般导致的动力学对称群是SO(4i+2)或者SP(4k+2),本文讨论它们精确的Dyson玻色子映像表示以及泡利原理在玻色子映像中的体现问题.     

Anomalous angular momentum in the presence of a vortex

The angular momentum of a charged boson in the presence of a vortex is calculated using collective coordinates in the two-dimensional, abelian Higgs model. In agreement with already published assertions, angular momentum is found to be half-integer when the vortex flux is quantized in half-integer units.     

Traces of products of angular momentum operators

Traces of products of angular momentum operators in a spherical or cartesian basis are common in the theory of atomic levels in fields, in the theory of nuclear orientation and of asymmetric top moments. Conventional angular momentum techniques lead to difficult and cumbersome calculations. In the present paper Schwinger's coupled boson representation is used in straightforward calculations of angular momentum and spherical tensor traces, of matrix elements and of asymmetric top moments. Only simple algebra, elementary multiplication and summation of integers are necessary. The method considerably simplifies calculations with angular momentum operators.     

The amplitudes of s and d bosons in deformed nuclei

It is shown that the ground state of deformed nuclei can be considered as a condensate of bosons that do not have a well defined angular momentum. The projection on well defined angular momentum states shows that the s and d bosons take care of nearly 90% of the boson wave function.     

Holstein-Primakoff Boson Realization for the Hydrogen Atom

We apply the Holstein-Primakoff transformation to the orbital angular momentum and the Runge-Lenz operators of a hydrogen atom to study its classical Kepler's problem. In this way the classical Kepler's frequency can be directly obtained without in troducing Schwinger's boson realization and boson coherent states.     

Feynman Transformation Matrix Element for a type of Hamiltonian of Angular Momentum system

Using the technique of integration within ordered product (IWOP) of operators and the Schwinger boson representation for the angular momentum theory as well as the coherent state's method, we evaluate the Feynman transformation matrix element for the angular momentum system whose Hamiltonian is H = AJ_x + BJ_y + CJ_x (A, B, C real). The eigenstate of H is derived and the comparison between it and the SU(2) coherent state is made.     

Deformation of nuclei as a function of angular momentum in the U(6) ⊃ SU(3) model

In the framework of a hybrid rotational model, proposed recently by Moshinsky as a consequence of a comparison between the Gneuss and Greiner extension of the Bohr and Mottelson model and the interacting boson model, we study the shape of nuclei by calculating the average of the expectation value of the square of the deformation parameter β with respect to the rotational states with the same angular momentum belonging to a given irreducible representation of SU(3). This work generalises to three dimensions the corresponding analysis carried out in two dimensions by Chacón, Moshinsky, and Vanagas. We use the canonical chain for U(3), i.e., the chain U(6) ? U(3) ? U(2) ? U(1), to obtain an analytical formula for the quantity studied. We bring out the overall stretching effect of the angular momentum on the shape of nuclei. The influence of other parameters, such as the boson number and the irreducible representation of SU(3), is also studied.     

The ground state of deformed nuclei as a boson condensate

It is shown that the ground state of deformed nuclei can be considered as a condensate of bosons that do not have a well-defined angular momentum. Values for the quadrupole moment and the particle number that are very close to the values obtained using the full boson wave function are obtained by retaining only the s- and d-parts of the boson wave function.By comparing with the many-shell (realistic) situation we found the limitations of the single-shell calculations.     

Boson expansions and quantization of time-dependent self-consistent fields (I). Particle-hole excitations

Two concrete methods are presented for quantizing the time-dependent Hartree equations in terms of boson operators. The first is the well-known infinite boson expansion analogous to the Holstein-Primakoff representation of angular momentum operators. The second, a new development, consists of finite boson quadratic forms, and is analogous to the Schwinger representation of angular momenta. In each case, a physical boson subspace can easily be constructed within which the full fermion dynamics is exactly duplicated. It therefore follows that quantization of the time-dependent Hartree equations, including all degrees of freedom, retrieves the exact many-body problem. The discussion in this paper is limited to particle-hole excitations of an N-particle system. A generalization to one-nucleon transfer processes on the N-particle system is also given in terms of ideal odd nucleons, but this brings in infinite expansions.