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.     

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.     

A composite chiral pair of rotational bands in the odd-A nucleus 135Nd

High-spin states in 135Nd were populated with the 110Pd(30Si,5n)135Nd reaction at a 30Si bombarding energy of 133 MeV. Two DeltaI=1 bands with close excitation energies and the same parity were observed. These bands are directly linked by DeltaI=1 and DeltaI=2 transitions. The chiral nature of these two bands is confirmed by comparison with three-dimensional tilted axis cranking calculations. This is the first observation of a three-quasiparticle chiral structure and establishes the primarily geometric nature of this phenomenon.     

Coexistence of terminating bands and more collective bands in theA ∼ 100 region of nuclei

Nilsson-Strutinsky cranking calculations onA≥100 Ru and Pd nuclei suggest that, contrary to other mass regions, it should be possible to follow the ground state rotational bands to their termination at spins just aboveI=30? and then also to observe other bands which terminate at higher spins.     

Coexistence of terminating bands and more collective bands in the A ∼ 100 region of nuclei

Nilsson-Strutinsky cranking calculations on A ≥ 100 Ru and Pd nuclei suggest that, contrary to other mass regions, it should be possible to follow the ground state rotational bands to their termination at spins just above I = 30? and then also to observe other bands which terminate at higher spins.     

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.     

Restoration of the broken D2-symmetry in the mean field description of rotating nuclei

Signature effects observed in rotational bands are a consequence of an inherent D2-symmetry. This symmetry is naturally broken by the mean field cranking approximation when a tilted (non-principal) axis orientation of the nuclear spin becomes stable. The possible tunneling forth and back between the two symmetry-related minima in the double-humped potential-energy surface appears as a typical bifurcation of the rotational band. We describe this many-body process in which all nucleons participate by diagonalizing the nuclear Hamiltonian within a selected set of tilted and non-tilted cranking quasiparticle states. This microscopic approach is able to restore the broken D2 symmetry and reproduce the quantum fluctuations between symmetry-related HFB states which emerge as splitting of the band energies and in parallel staggering in intraband M1 transitions.     

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.     

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.     

The Vibrational and Rotational Motions Model of Nucleus(Ⅲ) Study of Superdeformed Bands in A～190 Region

The rotational spectra formula for superdeformed bands is derived from the cranking Bohr-Mottelson Hamiltonian proposed by us.Level spins and transition energies of 24 superdeformed bands in the A～190 region are studied with this formula.The obtained results are satisfactory.     

Identical superdeformed bands

The phenomenon of identical bands is studied by analyzing the distributions of fractional changes in the dynamical moments of inertia of pairs of bands in superdeformed (SD) nuclei. These distributions are found to exhibit a peak with a centroid at nearly zero. Their widths increase in going from the SD bands in the massA～150, to the SD bands in the mass ～190 and to the normally-deformed bands in the rare-earth region. These differences may be attributed to the weaker pairing correlations and the stabilizing role of intruder orbitals on the structures of SD bands. Precise level lifetimes have been measured for various pairs of identical SD bands in Gd and Dy isotopes. By comparing the derived quadrupole moments with calculations performed in the framework of the cranking Skyrme-Hartree-Fock model, it is shown that, independently of the intrinsic configuration and of the proton and neutron numbers, the charge moments calculated with respect to the doubly-magic SD core of¹⁵²Dy can be expressed in terms of independent contributions from the individual hole and particle orbitals.     

Backbending in theN=96 isotones

The backbending in the even-even,N=96 isotones can be quantitatively accounted for by the rotation-alignment of the spins of neutrons in i 13/2 orbits, as shown by comparing the aligned angular momentum and relative Routhian for thes-bands in these isotones and for the i 13/2 bands in the corresponding isotopes withN=91. The influence of protons on this backbending situation is shown to be indirect, acting through a change of the nuclear deformation, which yields a change of the moment of inertia of the g.s. band and of the non-rigid character of the rotation. The experimental data on theN=96 and 97 isotones are in reasonable agreement with cranking model calculations. Possible reasons for the inhibition of backbending in the h 9/2 proton bands in the odd-Z, N=96 isotones, all related to a change of deformation, are presented.     

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.     

Collective gyromagnetic ratio from density dependent hartree-fock calculations: (II). Odd nuclei

The collective gyromagnetic ratio and moment of inertia of deformed odd-proton and oddneutron axially symmetric nuclei have been calculated in the cranking approximation using wave functions obtained with the Skyrme force SIII. Good agreement with experiment is found for g_R. Our parameter-free cranking results are better than those of Prior, Boehm and Nilsson where effective charges were used. The cranking formula leads to better results than the projection method (in which one simply takes the expectation value of the relevant operator in the deformed HF ground state, neglecting corrections of relative order 1/〈J²〉. In particular, the cranking results follow nicely the exceptionally large/small g_R for the odd-proton/neutron nuclei around mass 153–167.     

Measurement of the neutron-induced deuteron breakup reaction cross-section between 5 and 25 MeV

High-spin states in ¹⁸⁷Pt have been studied by means of ??-ray spectroscopy techniques. Known bands have been significantly extended and new bands have been found. The band structures are discussed in the framework of the cranking model and negative-parity states are compared with calculations performed with a semi-microscopic axial-rotor plus one-quasiparticle coupling model. Shape coexistence is observed from low excitation energy.     

Triaxial superdeformation in 163Lu

High-spin states in ¹⁶³Lu have been investigated using the Euroball spectrometer array. The previously known superdeformed band has been extended at low and high energies, and its connection to the normal-deformed states has been established. From its decay the mixing amplitude and interaction strength between superdeformed and normal states are derived. In addition, a new band with a similar dynamic moment of inertia has been found. The experimental results are compared to cranking calculations which suggest that the superdeformed bands in this mass region correspond to shapes with a pronounced triaxiality (γ≈±20°).     

Collective gyromagnetic ratio and moment of inertia from density-dependent Hartree-Fock calculations

The collective gyromagnetic ratio and moment of inertia of deformed even-even axially symmetric nuclei are calculated in the cranking approximation using wave functions obtained with the Skyrme force S-III. Good agreement is found for g_R, while the moment of inertia is about 20 % too small. The cranking formula leads to better agreement than the projection method.     

原子核振动与转动模型（Ⅰ）推转玻尔─莫特逊哈密顿量和偶偶核正常转动谱分析

从推转壳模型出发，导出了转动频率未量子化的集体振动－转动哈密顿量，称为推转玻尔－莫特逊哈密顿量（ＣＢＭＨ）．引入合理的集体运动位势，由ＣＢＭＨ可以得到解析形式的转动谱公式．应用这一振动－转动模型，对偶偶变形核的正常转动能谱进行了分析，取得了满意的结果．     

Vibrational and Rotational Motions Model of Nucleus(Ⅰ) Cranking Bohr-Mottelson Hamiltonian and Analyses of the Rotational Bands of Even-Even Nuclei

Starting from cranking shell model,a collective vibrational and rotational Hamiltonian(cranking Bohr-Mottelson Hamiltonian CBMH)is derived,in which the rotational frequency is not quantized.Introducing a reasonable collective potential,the formula for the rotational spectrum can be obtained.The formula is applied to analyze the rotational bands of even-even nuclei with satisfactory results.