Progress on tilted axis cranking covariant density functional theory for nuclear magnetic and antimagnetic rotation

Magnetic rotation and antimagnetic rotation are exotic rotational phenomena observed in weakly deformed or near-spherical nuclei, which are respectively interpreted in terms of the shears mechanism and two shearslike mechanism. Since their observations, magnetic rotation and antimagnetic rotation phenomena have been mainly investigated in the framework of tilted axis cranking based on the pairing plus quadrupole model. For the last decades, the covariant density functional theory and its extension have been proved to be successful in describing series of nuclear ground-states and excited states properties, including the binding energies, radii, single-particle spectra, resonance states, halo phenomena, magnetic moments, magnetic rotation, low-lying excitations, shape phase transitions, collective rotation and vibrations, etc. This review will mainly focus on the tilted axis cranking covariant density functional theory and its application for the magnetic rotation and antimagnetic rotation phenomena.     

Magnetic rotation and chiral symmetry breaking

The deformed mean field of nuclei exhibits various geometrical and dynamical symmetries which manifest themselves as various types of rotational and decay patterns. Most of the symmetry operations considered so far have been defined for a situation wherein the angular momentum coincides with one of the principal axes and the principal axis cranking may be invoked. New possibilities arise with the observation of rotational features in weakly deformed nuclei and now interpreted as magnetic rotational bands. More than 120 MR bands have now been identified by filtering the existing data. We present a brief overview of these bands. The total angular momentum vector in such bands is tilted away from the principal axes. Such a situation gives rise to several new possibilities including breaking of chiral symmetry as discussed recently by Frauendorf. We present the outcome of such symmetries and their possible experimental verification. Some possible examples of chiral bands are presented.     

Interpretation and quality of the tilted axis cranking approximation

Comparing with the exact solutions of the model system of one and two particles coupled to an axial rotor, the quality of the semi classical tilted axis cranking approximation is investigated. Extensive comparisons of the energies and M1 and E2 transition probabilities are carried out for the lowest bands. Very good agreement is found, except near band crossings. Various recipes to take into account finite K within the frame of the usual principal axis cranking are included into the comparison. A set of rules is suggested that permits to construct the excited bands from the cranking configurations, avoiding spurious states.     

Interpretation and quality of the tilted axis cranking approximation

Comparing with the exact solutions of the model system of one and two particles coupled to an axial rotor, the quality of the semi classical tilted axis cranking approximation is investigated. Extensive comparisons of the energies andM1 andE2 transition probabilities are carried out for the lowest bands. Very good agreement is found, except near band crossings. Various recipes to take into account finiteK within the frame of the usual principal axis cranking are included into the comparison. A set of rules is suggested that permits to construct the excited bands from the cranking configurations, avoiding spurious states.     

推转PNC波函数的角动量投影

研究原子核较高自旋态的特征,不仅需要考虑K混合,而且应该引入Coriolis相互作用项,亦即使用推转Hamilton量.推转项的引入破坏了时间反演对称性,单粒子角动量在内禀对称轴上的投影量子数已不再是好量子数.从表面上看,这会使得理论计算变得非常复杂,但考虑到原子核的某些固有对称性,将角动量投影技术应用于含推转成份的粒子数守恒波函数(推转PNC波函数)并不十分困难.在这一理论框架下详细推导计算原子核能谱及电磁性质的基本表达式,从而表明实施该方案的可行性.     

Coherent dynamics of magnetoexcitons in semiconductor nanorings

The coherent dynamics of magnetoexcitons in semiconductor nanorings following pulsed optical excitation is studied. The calculated temporal evolution of the excitonic dipole moment may be understood as a superposition of the relative motion of electrons and holes and a global circular motion associated with the magnetic-field splitting of these states. This dynamics of the electron-hole pairs can be generated either by local optical excitation of an ordered ring or, alternatively, by homogeneous excitation of rings with broken rotational symmetry due to disorder or band tilting. Received 27 September 2000     

Rotational states and interacting bosons

Rotational states are investigated in terms of the interacting boson model. A ground-state rotational band is built from a shell-model many-nucleon system. It is shown that the S and D collective nucleon pairs play dominant roles in low-spin states of the band and that this S-D dominance is broken in high-spin states. The intrinsic hamiltonian is constructed from the effective nucleon-nucleon interaction used in the shell model calculation and the intrinsic state of the rotational band is shown to be comprised primarily of S and D pairs. We introduce a λ boson which is a linear combination of s, d and higher angular momentum bosons, and the boson intrinsic state is given by the λ boson condensate state. The s and d bosons constitute approximately 90 % of the λ boson, and the boson intrinsic state reproduces very well the energy and the intrinsic quadrupole moment of the nucleon intrinsic state. The s-d boson hamiltonian is constructed from the S and D pairs, while effects of non S-D pairs are also included by renormalization of the boson hamiltonian. The renormalization is made by using the λ boson. The s-d boson quadrupole operator is derived similarly. The boson hamiltonian and quadrupole operator thus derived reproduce well the exactly calculated values for low-spin states of the rotational band, although the accuracy decreases in high-spin states. It is shown that the IBM possesses the same physical picture of the rotational states as the Nilsson scheme with pairing correlations. It is therefore concluded that the IBM is capable of describing low-lying rotational states.     

Chiral doublet structures in odd-odd n = 75 isotones: chiral vibrations

New sideband partners of the yrast bands built on the pi(h11/2)nu(h11/2) configuration were identified in 55Cs, 57La, and 61Pm N = 75 isotones of 134Pr. These bands form with 134Pr unique doublet-band systematics suggesting a common basis. Aplanar solutions of 3D tilted axis cranking calculations for triaxial shapes define left- and right-handed chiral systems out of the three angular momenta provided by the valence particles and the core rotation, which leads to spontaneous chiral symmetry breaking and the doublet bands. Small energy differences between the doublet bands suggest collective chiral vibrations.     

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。     

M1 and E2 band structures in the Sn-Xe-Ba region

In the present talk I will discuss some ‘rare’ aspects of the E2 band structures and the novel features concerning the dipole bands in this mass region. Reliable and accurate lifetimes have been measured using coincidence recoil distance method. The results of ^129,130Ba will be discussed. In contrast to the predictions of the tilted axis cranking model, the dipole bands in Sb-Xe-Ba nuclei can be nicely described as high-K prolate bands. New data from multi-detector arrays has established extended bands structure, their decay to low lying states have been established and the angular correlation supports the predominant, ΔI=1 character. Finally the sensitive measures, i.e. B(M1) rates of the tilted axis model are compared with the high-K formula based on 1-dim cranking model.     

Probing the paramagnetic interactions between the unpaired electronic spins of carbon atoms and the nuclear spins of hydrogen molecules with Raman spectroscopy

Carbon materials typically have a high density of unpaired electronic spins but the exact nature of the defect sites that give rise to their magnetic properties are not yet well understood. In this work, the paramagnetic interactions between the unpaired electronic spins of carbon atoms and the nuclear spins of hydrogen molecules were probed with Raman spectroscopy by monitoring the relative population of H₂ rotational states. For H₂, the symmetries of nuclear spin and rotational wave functions are correlated. Because of the weak interactions between H₂ nuclear spins, the transitions between odd and even rotational states are normally hindered. The magnetic field generated by unpaired electronic spins relaxes the selection rules and promotes transitions between H₂ rotational levels of different symmetry. This affects the rotational levels' relaxation kinetics toward equilibrium and makes H₂ molecules useful to study unpaired electrons in paramagnetic materials. It is suggested that simultaneous electron paramagnetic resonance and Raman measurements on carbon materials interacting with hydrogen molecules could result in a better understanding of the nature of paramagnetic defects in carbon materials, which could have a substantial impact on Li‐ion batteries or for understanding the graphene electronic properties. Copyright © 2011 John Wiley & Sons, Ltd.     

Se同位素的形状共存

基于形变Woods Saxon势下的推转壳模型对Se同位素进行Total Routhian Surface (TRS) 计算。 结果表明, 原子核的形状随中子数变化很明显。 对66,72, 92, 94Se 基态TRS图进行分析, 发现缺中子同位素和中子滴线附近核素均存在扁椭球和长椭球的形状共存。 分别对72Se和94Se进行推转计算,长椭球和扁椭球形状在低推转频率下共存, 由于g9/2闯入轨道的影响, 随着推转频率的增加,扁椭球形变逐渐消失,长椭球形变带成为转晕带。 Nuclear shape change and shape coexistence in the Selenium isotopes have been investigated by Total Routhian Surface(TRS) calculations. It is found that nuclear shapes vary significantly with increasing neutron number. The TRS calculations for the ground states of 66, 72, 92, 94Se isotopes show that both neutron deficient and neutron dripline Selenium isotopes have oblate and prolate shape coexistence. The cranking shell model calculations for 72, 94Se give that prolate and oblate shape coexistence in low rotational frequency. However, oblate rotational bands disappear and prolate rotational bands become yrast bands with increasing rotational frequency, which is due to the intrusion of the g9/2 orbitals.     

Stability of nuclear rotational states

The stability of rotational states described by using a procedure of the Hartree-Fock-Bogoliubov method is discussed. The stability condition is obtained in a general form and some of its properties are examined with the aid of simplifying approximations. It is pointed out in conclusion that the Coriolis force might lead to the instability of rotational states for sufficiently large angular momenta. The instability of rotational states is caused by the instability of the pairing density, and also by that of the nuclear density distribution. In the former case it is shown that below the critical angular momentum, a first-order phase transition takes place and in some cases the rotational band breaks off. In the latter case, it might be considered that the assumption of an axially symmetric deformation is broken or large change of the equilibrium deformation is brought suddenly. Then discontinuous change of the rotational level might be seen at the unstable point.     

On oblate-prolate transition in the ground state rotational band of light mercury isotopes

The transition from an oblate to a prolate shape in the ground state band of even mass Hg isotopes and in the ground states of the chain of odd mass Hg isotopes are studied. The shape is found by minimizing the deformation energy which is calculated by means of Strutinsky's shell correction method. The rotational energy corresponds to the axialsymmetric rotator. The moment of inertia is calculated with the help of the cranking model. Pairing and hexadecupole deformation are included. The results are in good agreement with the available experimental data.     

Rotational consequences of stable octupole deformation in nuclei

The characteristic features of high-spin spectra of octupole-deformed nuclei are demonstrated by means of Woods-Saxon-Bogolyubov cranking calculations. The rotational spectra of Ra and Th nuclei are studied. The experimental data suggests shape changes with increasing neutron number from N ? 130 (nearly spherical shapes) through N ? 134 (octupole-deformed shapes) to N ? 140 (well-deformed reflection-symmetric shapes). The octupole mixing between the high-j intruder states and normal-parity orbitals leads to specific patterns of quasiparticle spectra characterised by a quantum number referred to as simplex. The influence of octupole deformation on high-spin properties of nuclear spectra like spin alignment, band interaction, etc. are discussed.     

Antimagnetic rotation band in nuclei: a microscopic description

Covariant density functional theory and the tilted axis cranking method are used to investigate antimagnetic rotation (AMR) in nuclei for the first time in a fully self-consistent and microscopic way. The experimental spectrum as well as the B(E2) values of the recently observed AMR band in (105)Cd are reproduced very well. This gives a further strong hint that AMR is realized in specific bands in nuclei.     

Equilateral-triangular shape in 14C

An equilateral-triangular shape of three alpha clusters surrounded by excess neutrons is suggested for 14C, based on the molecular-orbit model. It is found that the attractive interaction between an excess neutron and an alpha particle stabilizes the K(pi)=0(+) and 3(-) rotational bands, which demonstrates an equilateral-triangular symmetry. This K(pi)=3(-) band at 3 MeV below the 10Be+alpha threshold energy corresponds to the experimentally observed band built on top of the second 3(-) state. A positive-parity rotational band (0(+), 2(+), 4(+)) arises similarly. These two bands suggest a molecular 3-alpha structure stabilized by the excess neutrons and can be viewed as a realization of the alpha crystallization in the dilute nuclear medium.     

缀饰格子中时间反演对称破缺的量子自旋霍尔效应

<正>研究了缀饰格子中的量子自旋霍尔效应,模型中同时考虑了Rashba自旋轨道耦合和交换场的作用.缀饰格子具有简立方对称性,以零能平带和单狄拉克锥结构为主要特点.在缀饰格子中,不论是实现量子自旋霍尔效应还是量子反常霍尔效应,都需要一个不为零的内禀自旋轨道耦合作用来打开一个完全的体能隙,这与石墨烯等六角格子模型有着很大的不同.在交换场破坏了时间反演对称性的情况下,以自旋陈数为标志的量子自旋霍尔效应仍然能够存在,边缘态和极化率的相关结果也证明了这一结论.结果表明自旋陈数比z2拓扑数在表征量子自旋霍尔效应方面有着更广泛的适用范围,相应的结论为利用磁场控制量子自旋霍尔效应提出了一个理论模型和依据.     

ΔI= 4 Bifurcation and the sdg Interacting Boson Model

We show that the superdeformed nuclear states can be described in the framework of the interacting boson model (IBM) with the g-bosons being taken into account in this paper.The ΔI= 4 bifurcation in superdeformed rotational bands can be reproduced in the SU(5) limit of the sdg IBM. The perturbation causing the ΔI= 4 bifurcation to emerge in the ΔI= 2 superdeformed rotational band may possess the SU(5) symmetry.     

FDTD analysis of 12-fold photonic quasi-crystal central pattern localized states

The TM bandgap features of the 2D 12-fold quasi-crystal are examined based on the width of the dielectric strip and pattern central symmetry location within the quasi-crystal. Results indicate that the bandgap properties observed for a particular fill factor is independent of the rotational symmetry center when the dielectric strip is wide, and still observable when the strip width is considerably reduced, confirming the general belief that the bandgap generating properties of the quasi-crystal are a local dielectric effect for the lower frequency band. Thin strips are shown to posses defect states in the bandgap region of the thicker equivalent strips, defect states analogous to intentionally introduced defect states of translational symmetric photonic crystals. We explore the mode profiles of the defect state when the defect is coincidental with the rotational symmetry central pivot point of the quasi-crystal pattern. In addition we show that the rotational center “defect” may be used to enhance the optical guidance of light around a 90° bend in a waveguide implanted in the quasi-crystal.