The connection of the nuclear “Coriolis” force with classical mechanics

The relation between the socalled Coriolis couplingI · j, operating in rotating nuclei, and the classical Coriolis force is discussed. The system forces acting in the cranking model for non-uniform rotation and in the rotator-particle model are examined. Differences with the molecular Coriolis coupling are indicated.     

The connection of the nuclear “Coriolis” force with classical mechanics

The relation between the socalled Coriolis couplingI · j, operating in rotating nuclei, and the classical Coriolis force is discussed. The system forces acting in the cranking model for non-uniform rotation and in the rotator-particle model are examined. Differences with the molecular Coriolis coupling are indicated.     

Spin orientation in rotating nuclei

The orientation of the angular momentum in triaxial nuclei has been investigated in a three-dimensional cranked-HFB formalism. Some quasiparticle excitations are found to favour cranking about a non-principal axis for particular combinations of shell filling and triaxial shape. This effect also exists when the energy of the rotating core is added, at least for low spins, which is shown in a complete cranking calculation for ⁸⁴Y.     

Exact angular momentum projection of cranked Hartree-Fock-Bogoliubov wave functions

The angular momentum projection of triaxial cranking model wave functions of realistic heavy nuclei is carried out exactly. Technical details of the procedure are discussed. The method is used to test the validity of the Kamlah expansion and of the angular momentum constraint in the cranking model. It turns out that the expansion up to the second order is already a very good approximation to the exact projection.     

Quantization in the high-spin RPA

The problem of how to quantize the angular momentum of the self-consistent cranking model at high spin when small oscillations (RPA) about the steady rotation are included is reexamined, in view of a recent criticism by Reinhardt of an earlier treatment. This criticism is shown to be unfounded. On the other hand, it is shown that Reinhardt's quantization procedure leads to some serious problems, and the result that the vibrational frequencies differ in the rotating and lab frames is called into question.     

Theoretical remarks for the analysis of electron scattering experiments on rotational nuclei

A convenient parametrization of longitudinal and transverse form factors of rotational nuclei is presented. This parametrization is model independent up to the order considered. It is intended to extract information on the intrinsic structure of ground state rotational bands by expressing the form factors for elastic and inelastic scattering within the band in terms of intrinsic charge and current multipoles, weighted by angular momentum dependent coefficients. The importance of the experimental measurements of transverse form factors is stressed as providing unique information on the distribution of the rotational current and hence, a unique test of the different rotational models. A qualitative comparison of three different models—rigid rotor, cranking and projected Hartree-Fock approach—is also presented in this context.     

Theory of molecular collective excitation in the scattering of identical nuclei

The excitation of nuclear molecules, formed in the scattering of ¹²C on ¹²C, is treated by the collective two-center model (CTCM). The model is referred to a rotating coordinate system and describes the continuous transition from the collective states of the separated nuclei to the states of the compound system. The diagonalization of the interaction between the nuclei leads to a splitting of the excitation energies as function of parity and angular momentum projection. The theory is applied for the explanation of the molecular resonances observed in the ¹²C-¹²C scattering.     

Semiclassical theory of nuclear rotation

The semiclassical theory of large amplitude collective motion developed previously by the author is applied to uniform nuclear rotation. In this way a sophisticated foundation of the self-consistent cranking model is given and its quantization is accomplished. The obtained quantization condition already contains the leading order correction to the self-consistent cranking model and also reveals the relation between the total angular momentum and the total signature. In the low frequency limit it yields the I(I + 1) law of a quantum rotor.     

Microscopic calculations of fission barriers and critical angular momenta for excited heavy nuclear systems

An extended version of Strutinsky's macro-microscopic method is used to calculate effective potential energies for rotating, excited heavy compound nuclei undergoing fission. Nuclear deformation is parameterized in terms of Lawrence's family of shapes. A two-center single-particle potential corresponding to these shapes is employed, with BCS pairing added. Statistical excitation is introduced by temperature-dependent occupation of (quasi-) particle energy levels. We calculate shell corrections to the energy, the free energy and the entropy as functions of deformation and temperature. The associated average quantities are derived from a temperature-dependent liquid drop model. The resulting static deformation energy is augmented by the rotational energy to yield the isothermal effective potential energy as a function of deformation, temperature and angular momentum. Moments of inertia are obtained from the adiabatic cranking model with temperature-dependent pairing included.We have also calculated the effective potential for constant entropy rather than constant temperature. Although this isentropic process physically is more appropriate than the isothermal process, it has not been treated before. For the same amount of excitation energy in the spherical state of the compound nucleus, the isentropic barriers turn out higher than the isothermal ones. For both processes we have extracted the critical angular momentum (defined as the one for which the barrier approximately vanishes) as a function of excitation. Our model is applied to the super-heavy nuclei ²⁷⁰110, ²⁷⁸110, ²⁹⁸114, ²⁹²118 and ³²²128, which have been tried to form in krypton and argon induced heavy ion reactions.     

Two-fluid model description of isovector giant resonances in fast rotating nuclei

Isovector giant resonances of arbitrary multipolarity in fast rotating nuclei are studied by solving the inviscid two-fluid equation of relative motion in a rotating frame of reference. Both Coriolis and centrifugal forces are taken into account. The resulting expressions display in a quite simple way general features of giant multipole resonances of fast rotating nuclei, in addition to a good agreement with other calculations for the giant dipole resonance. Typical values for the resonance energies and their fragmentation due to nuclear deformation and rotation are given. In particular, enormously large resonance splitting should occur in the superdeformed states.     

An approximate projection technique for the calculation of electromagnetic properties of deformed nuclei

A three-dimensional angular momentum projection is carried out for cranking model wave functions. The projected matrix elements of electromagnetic operators are evaluated using a method originally developed by Kamlah for the case of projected energy, which is valid for large deformations and weakly triaxial nuclei. The calculated spectroscopic quadrupole moments deviate substantially from the predictions of a rigid rotor model with axial symmetry. For E2 transitions the deviations are small. Projected values of the magnetic moments are almost identical with those of a semiclassical calculation. Cranking model wave functions are decomposed into its components having good angular momentum.     

Landau theory of shape phase transitions in the cranked interacting boson model

Landau theory of phase transitions is applied to quadrupole shapes of rotating atomic nuclei within the interacting boson model (IBM) with cranking. It is shown that the coherent-state method must be generalized to allow for non-Hermitian quadrupole tensors of the coherent-state coefficients, which results in important modifications of the cranking shape-phase diagram compared to previous non-IBM studies of rotating nuclei. The parameter space has two surfaces of the first-order phase transitions and a curve of the second-order phase transition at their intersection. The phase structure of the cranked IBM closely resembles systems with competing superconducting and normal phases.     

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。     

Phase separation in La-Pr manganites and its evolution in a magnetic field

The self-consistent harmonic oscillator model including the three-dimensional cranking term is extended to describe collective excitations in the random phase approximation. It is found that quadrupole collective excitations associated with wobbling motion in rotating nuclei lead to the appearance of two-or three-dimensional rotation.     

Dynamics of rotating two-component Bose-Einstein condensates and its efficient computation

In this paper, we investigate the dynamics of rotating two-component Bose-Einstein condensates (BEC) based on the coupled Gross-Pitaevskii equations (CGPEs) with an angular momentum rotation term and an external driving field, and propose an efficient and accurate method for numerical simulations. We prove the conservation of the angular momentum expectation, derive the dynamic laws for the density of each component and condensate widths, and analyze the dynamics of a stationary state with its center shifted from the trap center. By formulating the CGPEs in either 2D (two-dimensional) polar coordinate or 3D cylindrical coordinate system, the angular momentum rotation term becomes a term with constant coefficients. This allows us to develop an efficient time-splitting method which is time reversible, time transverse invariant, unconditionally stable, efficient and accurate for the problem. Moreover, it conserves the total position density in the discretized level. The numerical method is applied to verify our analytical results and study the dynamics of quantized vortex lattices in rotating two-component BEC with/without an external driving field.     

Rotational motion of triaxial shape in unfavoured-signature states of odd-A nuclei

In the region of the angular momentum where the intrinsic energy (namely, the odd-quasiparticle energy) plays a more important role than the collective rotational energy, we point out that the way of rotation in unfavoured-signature states of odd-A nuclei, which is clearly different from that in the usual cranking approximation, can be realized for triaxial intrinsic shape and leads to a peculiar signature dependence of B(E2;I→I - 1) values.     

磁转动物理——剪刀带与手征双重带

总结和系统介绍了磁转动物理领域的新进展 .阐述了剪刀带的形成机制 ,并论证了在半经典近似和平均场近似下 ,倾斜轴推转模型与粒子转子模型等价 .讨论了原子核在有三轴形变时出现的一种全新的磁转动现象——手征双重带 .并从对称性的角度讨论了剪刀带及手征双重带的能谱特征 .给出了实验上可能存在磁转动带的核区.A new interesting field —— magnetic rotation physics is reviewed. It is proved that the tilted axis cranking (TAC) model is equivalence to the particle rotor model (PRM) under the semi classical and mean field approximations. The shears mechanism and the new discovered phenomena in triaxial deformed nuclei—— chiral doublets are discussed. The possible mass region for these magnetic rotation phenomena is presented.     

Investigation of the cranking model wave function with respect to angular momentum

Projection of angular momentum on cranking model wave functions is performed for some simple cases. An extensive analysis has been possible since an algebraic projection technique is employed and a detailed numerical example is presented. The distribution of angular momentum as a function of rotational frequency and signature is analysed, and special attention is focused on the fact that the signature does not give any strict selection of angular momenta contained in the cranking wave function.