Effect of molecular structure nonrigidity on anisotropy of dipole absorption cross section

The influence of the nonrigidity of free complex asymmetric top molecules on the anisotropy of the absorption cross section over various rotational configurations has been studied under conditions where the total angular momentum is conserved. It is shown that the nonrigidity-induced cross section anisotropy is maximal for the optical transition with the dipole moment collinear to the axis of the molecule’s mean moment of inertia and rapidly decreases with the rise of the intramolecular flexibility. For all types of tops, disturbances from internal motions are stronger in the region where the principal axes of inertia are collinear with the total rotational angular momentum.     

Dynamic rotational characteristics of actinides on empirical approach

In the paper calculation of the moments of inertia for nuclei from the region 87 ≤ Z ≤ 100 and 130 ≤ N ≤ 156 was made in dependence on the angular momentum of their rotational states. The experimental values of the moments of inertia were calculated for rotational energy of the classic rotor in its quantum form, with the use of a simple formula. The moment of inertia term appearing in the formula was treated as a variable. The calculations were carried out on the basis of experimental data for the energies of the rotational levels for 51 bands built on ground states for even-even nuclei and for nuclei with odd mass number A. In addition, 30 rotational bands built on excited states were also analysed in the investigated region in case of even-even nuclei. For many bands and nuclei the considered dependence of the moment of inertia on angular momentum has been found in the analytical form by fitting polynomials to the experimental data. It turned out that obtained results for the moments of inertia made it possible to describe the energies of rotational levels with a relative deviation not greater or only slightly greater than 1%. In general, in the case of 12 bands of ground level the maximum relative deviation of obtained level energies is smaller than 1%.      

Tilted rotation of triaxial nuclei

The Tilted Axis Cranking theory is applied to the model of two particles coupled to a triaxial rotor. Comparing with the exact quantal solutions, the interpretation and quality of the mean field approximation is studied. Conditions are discussed when the axis of rotation lies inside or outside the principal planes of the triaxial density distribution. The planar solutions represent ΔI = 1 bands, whereas the aplanar solutions represent pairs of identical ΔI = 1 bands with the same parity. The two bands differ by the chirality of the principal axes with respect to the angular momentum vector. The transition from planar to chiral solutions is evident in both the quantal and the mean field calculations. Its physical origin is discussed.     

声子角动量与手性声子

在经典的物理学理论中,声子广泛地被认为是线极化的、不具有角动量的.最近的理论研究发现,在具有自旋声子相互作用的磁性体系(时间反演对称性破缺)中,声子可以携带非零的角动量,在零温时声子除了具有零点能以外还带有零点角动量;非零的声子角动量将会修正通过爱因斯坦-德哈斯效应测量的回磁比.在非磁性材料中,总的声子角动量为零,但是在空间反演对称性破缺的六角晶格体系中,其倒格子空间的高对称点上声子具有角动量,并具有确定的手性;三重旋转对称操作给予声子量子化的赝角动量,赝角动量的守恒将决定电子谷间散射的选择定则;此外还理论预测了谷声子霍尔效应.     

用于微型卫星姿态控制的高温超导动量轮

卫星或宇宙飞船在太空中需要精确定位,动量轮是卫星或宇宙飞船姿态控制的关键部件.每个宇宙飞船上有三个或四个动量轮,这些动量轮虽然体积小,但是其角动量占宇宙飞船总角动量的绝大部分.动量轮实质上就是电机的转子,它具有很高的转动惯量.在适当的时间,启动或停止三个电机就能够控制宇宙飞船的姿态.我们已经研制了一个小的动量轮模型,该模型重量轻、结构紧凑,而且能效高.动量轮模型的主要创新点是使用了高温超导磁悬浮轴承,因此,它具有摩擦力小,转速高,储存动量大的特点.动量轮模型的最大设计转速为15,000RPM,储存的角动量为3.5J*s-1.     

Alternating Parity Band in Octupole-Soft ~(140)Xe with Axial Vibrational-Rotational Model and Triaxial Rigid Rotor Model

Energies of the yrast positive-and negative-parity excited states in140 Xe are reproduced by two different models considering quadrupole-octupole deformations, namely the axial vibrational-rotational model and the triaxial rigid rotor model, and compared with the stable octupole-deformed222 Th. The origin of the energy difference between the opposite parity sequences is considered from two different mechanisms, the vibration in axial deformed energy minima and the rotation considering the effective triaxial deformation. The success of reproducing the data in both the models implies that these two mechanisms are equivalent on some level for the octupole-soft nuclei. By investigating the probability distributions for projection of total angular momentum in the triaxial rigid rotor model, it is found that such an energy difference is associated with the difference of orientation of the rotational axis.     

The dynamics of rapidly rotating bodies

The dynamics of rapidly rotating bodies is formulated in a rotationally invariant form in all frames rotating with constant angular velocities relative to each other. This includes the energy, angular momentum, rotational frequency, and moment of inertia. The transformation between these quantities, when expressed in different frames, is then given explicitly and expressed in terms of both the angular momentum and the rotational frequency variables. Comparison with the approximate formula for the Routhian is made, and some consequences of physical interest are drawn.     

奇A Lu同位素负宇称Yrast带的研究

利用粒子一转子模型研究了奇A Lu核负宇称Yrast态带交叉前后的能谱和跃迁几率,理论值和实验值符合得较好.研究表明,^{161,163,165,167}Lu负宇称Yrast态是三轴形变的;ab公式正确地描述了带交前后核心的转动惯量随角动量I的变化.     

Comparison between formulas of rotational band for axially symmetric deformed nuclei

The experimental rotational spectra of the deformed nuclei available in even-even and odd-A nuclei in the rare-earth and actinide regions are systematically analyzed with several rotational spectra formulas,including Bohr-Mottelson's I(I+l)-expansion,Harris'w2-expansion,ab and abc formulas.It is shown that the simple 2-parameter ab formula is much better than the widely used 2-parameter Bohr-Mottelson's AB formula and Harris'αβ formula.The available data of the rotational spectra of both ground-state band in even-even nuclei and one-quaasiparticle band in odd-A nuclei can be conveniently and rather accurately reproduced by ab formula and abc formula.The moment of inertia and the variation with rotational frequency of angular momentum can be satisfactorily reproduced by ab and abc formulas.     

Nuclear rotational anomaly and the HFB equations

We show that the S-shape of the plot of moment of inertia versus square of the angular frequency observed experimentally for the rotational spectrum of rare-earth nuclei follows naturally from the solution of the Hartree-Fock-Bogoliubov equations. We consider the case of eight particles in the $\text{1}\text{h}\text{11}\text{2}$ level outside a closed shell and use the Sussex interaction for the nucleon-nucleon potential. Some properties of the upper, middle and lower branches are looked into and it is established that the transition indeed occurs due to reduction in the strength of the pairing part of the interaction due to the Coriolis force. Methods for calculating the moment of inertia and other nuclear properties in the transitional region, i.e. the middle branch, are suggested and it is found that the properties there are intermediate between the upper and lower branch. We also suggest the importance of higher (> 0) particle-particle channel coupled angular momentum of the nucleon force for the rotational spectrum of deformed nuclei at high angular momentum. A comment is also made on misleading results that can be obtained for e.g. moment of inertia, by projecting only even integral values of angular momentum in Hartree-Fock type solutions and thereby ignoring finer details.     

Effects of quantum fluctuations on electromagnetic properties in triaxial nuclei

Effects of quantum fluctuations, like wobbling and γ-fluctuations, are examined in even- as well as in odd-particle systems by making use of a simple model based on the Bohr hamiltonian. The strong signature dependence observed in ΔI = 1 E2 transitions in odd nuclei is studied in the context of an axially asymmetric deformation. We point out the importance of the quantum fluctuations especially at low-spin values and / or for shapes with small deviations from axial symmetry. It is also demonstrated that the J⁽²⁾ moment of inertia may be larger than J⁽¹⁾ due to the wobbling motion.     

氢原子的磁矩--对自旋的讨论之一

利用氢原子的相对论性波动方程计算了氢原子的磁矩。结果表明,现行量子理论中所谓的总磁矩实际上都是由电子的轨道运动产生的,由此提出了所谓的总角动量实际上是相对论性轨道角动量的看法。     

Compliant structures with time-varying moment of inertia and non-zero averaged momentum and their application in angular rate microsensors

In this work we introduce a new class of fully compliant structures performing vibratory motion, yet characterized by non-zero averaged momentum, appearing due to time-dependency of the inertial parameters. The work is motivated by microelectromechancial systems (MEMS) applications, where an implementation of unidirectional, non-vibratory motion involving relative motion of parts is not desirable for reliability reasons. Instead of changing the mass, which is challenging on the microscale, the moment of inertia of the proof mass performing tilting vibrations is controlled in such a way that it is higher or lower depending on the sign of the velocity. This results in a non-zero angular momentum averaged over the period. The equations describing the dynamics of a generic structure with a time-varying inertia and in a rotating coordinate frame are derived by using a variational principle. Simple approximate expressions for the averaged momentum and steady tilting angle are obtained and validated numerically. Based on the model results for different operational scenarios, we demonstrate that these devices can be efficiently used in fully compliant actuators and vibratory angular rate sensors (microgyros) with a steady response in a sensing mode (“pseudospinning disk gyros”), as well as in a parametrically excited gyro. The structure can be viewed also as a first step toward the realization of dynamic materials (DM) which are substances with material properties that may change in space and time.     

Solution of the Hartree-Fock-Bogoliubov equations at high angular frequency

We consider solutions to some of the difficulties which arise when Hartree-Fock-Bogoliubov equations are solved at high angular frequency. These are mainly associated with the fact that then instead of particles always decoupling in pairs, may do so singly and hence lead to quasi-particle wavefunctions containing an odd number of particle components in the quasiparticle wave function. These solutions then also lead to a satisfactory, reliable and fast method for connecting the upper and lower branches of the moment of inertia versus square of the angular frequency curve, and usually reproduce the typical S-shape of the curve. We also show the importance of higher (> 0) particle-particle channel coupled angular momentum of the nucleon-nucleon potential for the rotational spectrum of deformed nuclei at high angular momentum. Some unsolved problems and peculiar cases which arise during the solution of Hartree-Fock-Bogoliubov equations are mentioned in the end, which may be a reflection on the unsatisfactory nature of the present method of obtaining higher angular momentum rotational bands.     

电子在均匀磁场中的状态--对自旋的讨论之二

求得了在均匀磁场中的电子沿着磁场方向的动量、角动量分量和能量的共同本征态。计算了电子产生的磁矩,由此继续论证所谓的总磁矩和总角动量其实质是相对论性的轨道磁矩和轨道角动量的看法。     

On the use of a variable moment of pairing

The concept of a variable moment of pairing is introduced in analogy to the variable moment of inertia. It is shown that deviations from the limiting cases of a rigid pairing rotor and the harmonic pairing vibrator can be systematised and interpreted very conveniently within this semi-empirical model. Its bearing on the liquid-drop mass formula is also discussed.     

Turbulent equipartition and homogenization of plasma angular momentum

A physical model of turbulent equipartition (TEP) of plasma angular momentum is developed. We show that using a simple, model insensitive ansatz of conservation of total angular momentum, a TEP pinch of angular momentum can be obtained. We note that this term corresponds to a part of the pinch velocity previously calculated using quasilinear gyrokinetic theory. We observe that the nondiffusive TEP flux is inward, and therefore may explain the peakedness of the rotation profiles observed in certain experiments. Similar expressions for linear toroidal momentum and flow are computed and it is noted that there is an additional effect due the radial profile of moment of inertia density.     

线型分子的电子能级之Λ分裂的新解释

认为电子态能级发生Λ分裂虽然是角动量引起的,但不是耦合而是运动牵连作用的结果.从这一认识出发,利用欧拉方程和拉格朗日方程分别得到了包含Λ分裂的分子转动哈密顿函数和哈密顿算符,所得结果与Van.Vleck的著名结论完全一致 关键词： Λ分裂 线型分子 欧拉方程 哈密顿算符     

The strange backbending behaviour in the Yb isotopes

The rotational energies and the backbending behaviour of ^166,168,170Yb are calculated utilizing angular momentum and particle number projected deformed BCS trial wave functions. The anomaly of the moment of inertia can be reproduced quantitatively with the moment of inertia of an inert core as the only free parameter. A possible explanation for the strange behaviour in the Yb isotopes is given.