原子核的高自旋态

本文回顾了原子核高自旋态研究工作的进展情况。七十年代初回弯现象的发现对原子核集体运动的研究方向发生了深刻影响。目前已公认正确的回弯机制是Stephens-Simon提出的带交叉。现正广泛使用转动势场中的单粒子运动(推广的Nilsson模型)来分析高自旋态的性质。由于原子核高速旋转而产生的一系列新的问题,包括原子核超导性的破坏、粒子角动量沿核集体运动方向的顺排、形变及壳结构的改变等,正引起人们广泛注意。理论预言,极高速旋转的原子核会出现扁旋转椭球形变和所谓“晕坑”,但实验上尚未观测到。从实验分析发现了Coriolis减弱问题,其原因仍是一个未解决的难题。     

原子核的高自旋态

本文回顾了原子核高自旋态研究工作的进展情况。七十年代初回弯现象的发现对原子核集体运动的研究方向发生了深刻影响。目前已公认正确的回弯机制是Stephens-Simon提出的带交叉。现正广泛使用转动势场中的单粒子运动(推广的Nilsson模型)来分析高自旋态的性质。由于原子核高速旋转而产生的一系列新的问题,包括原子核超导性的破坏、粒子角动量沿核集体运动方向的顺排、形变及壳结构的改变等,正引起人们广泛注意。理论预言,极高速旋转的原子核会出现扁旋转椭球形变和所谓“晕坑”,但实验上尚未观测到。从实验分析发现了Coriolis减弱问题,其原因仍是一个未解决的难题。     

清华大学物理系原子核物理研究的新进展

在清华大学物理系成立80周年之际,对近年来清华大学物理系原子核物理研究的主要进展情况作一介绍,包括原子核高自旋态的实验研究,原子核结构的理论研究,高能核物理的理论研究.在高自旋态研究方面,内容包括在A～100丰中子核区核的集体振动转动带结构、新的准粒子带特性、新手征二重带等特性研究;在A～140丰中子核区核的八极形变及八级关联等特性研究;在A～130缺中子核区核的形状驱动效应,包括扁椭形变带、形状共存等特性研究.在原子核结构理论研究方面,内容包括用相互作用玻色子模型、推转壳模型、投影壳模型以及相对论平均场对原子核特性的研究;对原子核结构或其他量子系统的各种对称性和代数方法的研究,如动力学对称性、超对称性、势代数方法等;与对称性紧密联系的普通李代数和非线性李代数的表示,如普通李代数、李超代数、平方根型非线性李代数、多项式型非线性李代数等.在高能核物理研究方面,内容主要包括量子色动力学（QCD）在高温高密条件下的相变以及在相对论重离子碰撞中相变信号的研究.     

第一类PschlTeller势的非线性代数结构

在形变李代数理论的基础上 ,利用哈密顿算符和自然算符 ,构造出第一类P schl Teller势的非线性谱生成代数 .该非线性代数能够完全确定势场的能量本征态集合和本征值谱 ,在适当的非线性算符变换下可以化为谐振子代数 ,显示了该系统具有新的对称性     

第一类Poschl-Teller势的非线性代数结构

在形变李代数理论的基础上,利用哈密顿算符和自然算符,构造出第一类Poschl-Teller势的非线性谱生成代数。该非线性代数能够完全确定势场的能量本征态集合和本征值谱,在适当的非线性算符变换下可以化为谐振子代数,显示了该系统具有新的对称性。     

第一类P?schl-Teller势的非线性代数结构

在形变李代数理论的基础上,利用哈密顿算符和自然算符,构造出第一类P?schl-Teller势的非线性谱生成代数.该非线性代数能够完全确定势场的能量本征态集合和本征值谱,在适当的非线性算符变换下可以化为谐振子代数,显示了该系统具有新的对称性 关键词： P?schl-Teller势 自然算符 非线性谱生成代数     

原子核高角动量激发

用推转壳模型计算研究了原子核的高速转动运动及其结构特性.讨论了A～50区核的转动特性;A～80$区(N=Z)核的形状共存问题; A～110$区丰中子核的扁椭球形变的稳定性. 基于壳模型理论, 我们用限制组态绝热堵塞方法计算讨论了A～130, 180和超重核区的高角动量同核异能态,系统预言了高角动量多准粒子态的存在, 并指出这些核态可以有较长的寿命, 这对于不稳定核的研究是很有帮助的. 计算解释了不少典型的实验观测, 一些理论预言已经被最近的实验证实.     

原子核的赝自旋对称性近似

基于相对论平均场理论,讨论了Dirac方程中严格的赝自旋对称性,以及实际原子核中的近似赝自旋对称性.在严格的赝自旋对称性下,除赝自旋单态外,所有的态都有简并的赝自旋伙伴态,而且赝自旋双重态的径向量子数相同.以正常核²⁰⁸Pb和奇特核²⁶⁴Pb为例,分析了赝离心势和赝自旋–轨道耦合势的贡献,发现对于赝自旋单态,赝离心势恒为零;对赝自旋双重态,赝自旋–轨道耦合势的贡献很小,赝自旋对称性近似满足;但对于闯入态,相对于赝离心势,赝自旋–轨道耦合势的贡献很大,赝自旋对称性被完全破坏,也即闯入态不具有赝自旋伙伴态的可能原因.     

基于实稳定方法求解单粒子共振态的Wigner函数

利用坐标空间的实稳定方法,求解了一维势场中单粒子散射态与其中共振态的本征值问题,由得到的单粒子本征波函数进一步给出相应的Wigner函数,分析了单粒子散射态与其中共振态的相空间分布特征.发现除了本征能量与本征波函数存在差异,Wigner函数在相空间的具体分布行为也可用于区分单粒子共振态与一般的散射态,在相关的量子测量实验中可能用作确定量子态的特征判据.     

单粒子在非轴对称八极形变势场中的混沌运动

针对单粒子处在长椭球谐振子势加上Y₃₂+Y_3－2形变势场中的情况, 从经典和量子两个角度分析了粒子在非轴对称八极形变势场中的混沌运动. 通过经典的轨道稳定性分析, 指出了系统等势能面性质对粒子运动特点的重要性. 又通过对体系存在的能级免交叉现象, 三维不对称谐振子相干态在势场中的演化特征的研究, 具体地说明了八级形变势的非轴对称性使单粒子更容易出现混沌运动.     

关于空间平移不变性的一些评注

推广了量子力学中关于对称性的分析,与对称性相关的守恒量相应地推广为含时守恒量;证明了单粒子(包括相对论情况)在静态均匀磁场和含时线性势中运动具有空间平移不变性;求出了波函数的变换关系和相应的含时守恒量.     

Aharonov–Anandan quantum phases and Landau quantization associated with a magnetic quadrupole moment

The arising of geometric quantum phases in the wave function of a moving particle possessing a magnetic quadrupole moment is investigated. It is shown that an Aharonov–Anandan quantum phase (Aharonov and Anandan, 1987) can be obtained in the quantum dynamics of a moving particle with a magnetic quadrupole moment. In particular, it is obtained as an analogue of the scalar Aharonov–Bohm effect for a neutral particle (Anandan, 1989). Besides, by confining the quantum particle to a hard-wall confining potential, the dependence of the energy levels on the geometric quantum phase is discussed and, as a consequence, persistent currents can arise from this dependence. Finally, an analogue of the Landau quantization is discussed.     

伪自旋对称情形下Rosen-Morse类型势场中相对论粒子的束缚态

在伪自旋对称情形下研究了Rosen-Morse类型势场中相对论粒子的束缚态,利用Nikiforov-Uvarov方法求解了伪自旋对称情形下的Klein-Gordon和Dirac方程,得到了相对论粒子被束缚在Rosen-Morse类型势场的精确束缚态解.     

Optical Tomograms and Husimi Q-Function for a Particle Moving in the Dirac Delta Potential

We study the problem of a quantum particle moving in the Dirac delta potential with instant changes in the well depth using the formalism of the tomographic-probability representation of quantum mechanics. We calculate the Husimi function for a particle moving in the Dirac delta potential and study the relation of the Husimi function to the state tomogram. We check numerically the tomographic entropic uncertainty relation for the bound state of the particle moving in the Dirac delta potential.     

Spontaneous symmetry breaking of a Boseben Fermi mixture in a two-dimensional double-well potential

We study the spontaneous symmetry breaking of a superfluid Bose-Fermi mixture in a two-dimensional double-well potential. The mixture is described by a set of coupled Gross-Pitaevskii equations. The symmetry breaking phenomenon is demonstrated in the two-dimensional double-well potential in the mixture. The results are summarized in the phase diagrams of the mixture particle numbers, which are divided into symmetric and asymmetric regions by the asymmetry ratios. The dynamical pictures of the spontaneous symmetry breaking induced by a gradual transformation of the single-well potential into a double-well one are also illustrated. The properties of the quantum degenerate mixture are explored using the realistic parameters for a ⁴⁰K-⁸⁷Rb system.     

Aharonov-Casher effect and persistent spin currents in a Coulomb-type potential induced by Lorentz symmetry breaking effects

We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field. This neutral particle is also under the influence of a background that breaks the Lorentz symmetry. We focus on the Lorentz symmetry violation background determined by a space-like vector field. Then, we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential. Furthermore, we obtain the bound state solutions to the Schrödinger-Pauli equation and show that the spectrum of energy is a function of the Aharonov-Casher geometric quantum phase. Finally, we discuss the arising of persistent spin currents.     

Directed motion for delta-kicked atoms with broken symmetries: comparison between theory and experiment

We report an experimental investigation of momentum diffusion in the delta-function kicked rotor where time symmetry is broken by a two-period kicking cycle and spatial symmetry by an alternating linear potential. We exploit this, and a technique involving a moving optical potential, to create an asymmetry in the momentum diffusion that is due to the classical chaotic diffusion. This represents a realization of a type of Hamiltonian quantum ratchet.     

A new type of conformal dynamics

We consider the Lagrangian particle model introduced in [Ann. Phys. 260 (1997) 224] for zero mass but nonvanishing second central charge of the planar Galilei group. Extended by a magnetic vortex or a Coulomb potential the model exhibits conformal symmetry. In the former case we observe an additional SO(2,1) hidden symmetry. By either a canonical transformation with constraints or by freezing scale and special conformal transformations at t=0 we reduce the six-dimensional phase-space to the physically required four dimensions. Then we discuss bound states (bounded solutions) in quantum dynamics (classical mechanics). We show that the Schrödinger equation for the pure vortex case may be transformed into the Morse potential problem thus providing us with an explanation of the hidden SO(2,1) symmetry.     

Comparing the reliability of networks by spectral analysis

Topological effects on the confinement of a moving neutral particle with an induced electric dipole moment confined to a quantum ring and a two-dimensional quantum dot (described by a hard-wall confining potential) are investigated. It is shown in this work that the spectrum of energy depends on the geometric phase obtained by Wei et al. [H. Wei, R. Han, X. Wei, Phys. Rev. Lett. 75, 2071 (1995)] and persistent currents arise from this dependence in both the quantum ring and the quantum dot. Further, the behaviour of the analogue of the Landau system for a moving electric dipole confined to a two-dimensional quantum dot is discussed, and it is shown that persistent currents are absent in this case.     

中能重离子碰撞中的同位旋效应

利用改进的量子分子动力学模型,研究了中心和擦边重离子反应中的同位旋效应.研究结果表明,在丰中子体系的中心和擦边反应中出射核子的N/Z都对对称势敏感,但对称势的密度依赖对中心和擦边反应的影响显示不同的特征.