U(5)-SU(3) nuclear shape transition within the interacting boson model applied to dysprosium isotopes

In the framework of the interacting boson model (IBM) with intrinsic coherent state, the shape Hamiltonian from spherical vibrator U(5) to axially symmetric prolate deformed rotator SU(3) are examined. The Hamiltonian used is composed of a single boson energy term and quadrupole term. The potential energy surfaces (PES’ s) corresponding to the U(5)-SU(3) transition are calculated with variation of a scaling and control parameters. The model is applied to ^150–162Dy chain of isotopes. In this chain a change from spherical to well deformed nuclei is observed when moving from the lighter to heavier isotopes. ¹⁵⁶Dy is a good candidate for the critical point symmetry X(5). The parameters of the model are determined by using a computer simulated search program in order to minimize the deviation between our calculated and some selected experimental energy levels, B(E2) transition rates and the two neutron separation energies S_2n. We have also studied the energy ratios and the B(E2) values for the yrast state of the critical nucleus. The nucleon pair transfer intensities between ground-ground and ground-beta states are examined within IBM and boson intrinsic coherent framework.     

Evolution of ground state nuclear shapes in tungsten nuclei in terms of interacting boson model

The tungsten nuclei ^180–190W are investigated within the framework of the interacting boson model using an intrinsic coherent state formalism. The Hamiltonian operator contains only multipole operators of the subalgebra associated with the dynamical symmetries SU(3) and O(6). The study includes the behavior of potential energy surfaces (BES’s) and critical points in the space of the model parameters to declare the geometric character of the tungsten isotopic chain. Some selected energy levels and reduced E2 transition probabilities B(E2) for each nucleus are calculated to adjust the model parameters by using a computer code PH INT and simulated computer fitting programme to fit the experimental data with the IBM calculation by minimizing the root mean square deviations. The ^180–190W isotopes lies in shape transition SU(3)-O(6) region of the IBM such that the lighter isotopes comes very clare to the SU(3) limit, while the behavior ones tend to be near the γ-unstable O(6) limit.     

The interacting Boson Model applied to the mercury isotopes

The even isotopes of mercury have been systematically studied using the Interacting Boson Model (IBM). In order to treat shape coexistence in the light isotopes, two separate IBM calculations were performed with different configurations, which were subsequently mixed. The four Hamiltonian parameters, which were allowed to vary freely from isotope to isotope, were found to be consistent with the corresponding IBM parameters used for platinum and osmium. Overall, the calculated energy spectra and electromagnetic properties are in reasonable agreement with experiment.     

原子核过渡区的量子相变

在相互作用玻色子模型(IBM) 基础上用O(6) 高阶项代替传统的SU(3) 四极-四极相互作用来研究原子核从振动到转动过渡区的量子相变行为。利用U(5)-SU(3) 和UQ 两种方案,在玻色子数分别为N = 8 和N = 20 不同情况下,研究了原子核的一些低激发态的能级比和电四极跃迁比。结果表明:随着玻色子数N 的增大,系统的量子相变行为得到加强;两种方案都可以用来描述从振动到转动过渡区的原子核的量子相变特征且O(6) 高阶项方案下量子相变行为更为明显。在此基础上,进一步应用这两种方案具体讨论了152Sm 核的低激发态能级和电四极跃迁性质并与实验数据进行对比分析。结果表明,用O(6) 高阶项可以更为合理地描述带内跃迁及不同带之间的带间跃迁性质。With the framework of Interacting Boson Model(IBM), transitional patterns from the spherical to the axially deformed limit of the IBM with a schematic Hamiltonian are studied by replacing the SU(3) quadrupole-quadrupole term with O(6) cubic interaction. But, we use the two schemes to investigate some energy ratios and B(E2) ratios for different bosons N = 8 and N = 20. The results show that with the increasing of the numbers of bosons, the transitional behaviors can be enhanced; the transitional behaviors are very similar in the two schemes. However, there are some distinctive differences for some quantities across the entire transitional region, such as energy levels and ratios, B(E2) values and ratios, and expectation values of the shape variables. Generally speaking, the transition is smoother and the nuclear shape is less well defined in the new scheme. Then we apply the two schemes to the critical point symmetry candidate, such as 152Sm, and find the overall fitting quality of the UQ scheme is better than that of the U(5)-SU(3) scheme, especially for the inter-band E2 transitions in 152Sm.     

奇质量核的超越平均场玻色子费米子模型描述(英文)

对近年发展起来的一个基于核密度泛函理论和粒子核心耦合方案来计算中重质量奇A核谱性质的理论方法进行了评述。该方法首先在平均场层面通过选择合适的能量密度泛函和对力结构来自洽求解偶偶核心的势能曲面、球单粒子能级和奇粒子占有率,进一步将得到的结果作为微观输入来建立相互作用玻色子费米子模型哈密顿量,其中三个与粒子核心耦合强度相关的参数需要通过拟合一些特定奇质量核低激发谱数据来最终确定。通过对轴形变奇质量Eu同位素的低激发能谱和电磁跃迁几率的系统研究来说明该模型方法的有效性。另外,还讨论了该方法在描述轴形变奇质量核形状相变以及描述丰中子奇质量Ba同位素中八极关联方面的应用。A recently developed method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is reviewed, that is based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the eveneven core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained by a self-consistent mean-field calculation with the choice of the energy density functional and pairing properties. These quantities are then used as a microscopic input to build the interacting bosonfermion Hamiltonian. Only three strength parameters for the particle-core coupling are specifically adjusted to selected data for the low-lying states of a particular odd-mass nucleus. The method is illustrated in a systematic study of low-energy excitation spectra and electromagnetic transition rates of axially-deformed odd-mass Eu isotopes. Recent applications of the method, to the calculations of the signatures of shapes phase transitions in axially-deformed odd-mass nuclei, octupole correlations in neutron-rich odd-mass Ba isotopes, are discussed.     

Mean-field derivation of the interacting boson model Hamiltonian and exotic nuclei

A novel way of determining the Hamiltonian of the interacting boson model (IBM) is proposed. Based on the fact that the potential energy surface of the mean-field model, e.g., the Skyrme model, can be simulated by that of the IBM, parameters of the IBM Hamiltonian are obtained. By this method, the multifermion dynamics of surface deformation can be mapped, in a good approximation, onto a boson system. The validity of this process is examined for Sm and Ba isotopes, and an application is presented to an unexplored territory of the nuclear chart, namely, the right lower corner of 208Pb.     

Low-lying states and isospin excitation in the Ge isotopes

The level structure of 64-70Ge isotopes has been studied within the framework of the interacting boson model-3 (IBM-3). The symmetry character in the proton and neutron degrees of freedom of the energy levels has been investigated. The isospin excitation states (T>Tz) have been assigned for the 64Ge (N=Z) nucleus. Some intruder states in these nuclei have been suggested. The calculated energy levels and transition probabilities are in good agreement with recent experimental data. The study indicates that the Ge isotopes are in transition from γ-unstable to vibrational.     

142-164Dy核的低能谱和电磁跃迁的相互作用玻色子模型

采用IBM模型研究了^142-164Dy核的低能正宇称态的能谱和电磁跃迁。应用U(5)→SU(3)的简化哈密顿量较好地描述了它们的能谱和电磁跃迁。研究结果表明，该核基本属于U(5)→SU(3)的过渡核Spectra and E2 transition rates for the even even 142-164Dy isotopes are studied in the framework of the interacting boson model. A schematic Hamiltonian capable of describing their spectra and transition is used. It is found that the even even 142-164Dy isotopes are in the transition from U(5)to SU(3) dynamical symmetry.     

Spectra and E2 Transition Rates in 116-132X in the IBM

The positive-parity collective states in the even-even ^116-132Xe isotopes are studied in the framework of the interacting boson model. It is found that the isotopes can be well described by a schematic Hamiltonian in transition from U(5) to SU(3) dynamical symmetry. As the valence neutron number changes, the structure of the isotopes shows regular patterns of change.     

Nuclear structure of <Superscript>128–140</Superscript>Nd in IBM

We determined the most appropriate Hamiltonian that is needed for calculations of nuclei in the A ≅ 130 region from the viewpoint of the interacting boson model (IBM). Using the best-fitted values of parameters in the Hamiltonian, we have calculated energy levels and B(E2) values for a number of transitions in some doubly even Nd nuclei of 128 ⩽ N ⩽ 140. The results were compared with the previous experimental and theoretical data, and it is observed that they are in good agreement. The calculations have been extended to Nd isotopes for which some B(E2) values are still not known. The text was submitted by the author in English.     

62-76Zn核的低能谱和电磁跃迁的相互作用玻色子模型(英文)

采用相互作用玻色子模型研究了62—76Zn核的低能正宇称态的能谱和电磁跃迁.应用一个简单的哈密顿量能够较好地描述它们的能谱和电四极跃迁.研究表明,62—76Zn同位素核基本上属于U(5)到O(6)的过渡核.Spectra and E2 transition rates for the even even 62-76Zn isotopes are studied in the framework of the interacting boson model. A schematic Hamiltonian capable of describing their spectra and transition is used. It is found that the even even 62-76Zn isotopes are in the transition from U(5) to O(6) dynamical symmetry.     

原子核形状演变的又一个特征指标E0跃迁及对102—110Pd偶偶核的应用

利用相互作用玻色子模型分别在U(5)—SU(3)和U(5)—O(6)描述下研究了^102—110Pd偶偶核的电单极跃迁.研究表明,这些偶偶Pd核能够用U(5)—SU(3)更好地描述.     

Low-lying spectra and E2 transition rates in 160-170Er isotopes in the interaction boson model

Spectra and E2 transition rates for the 160-170Er isotopes are studied in the framework of the interaction boson model. A schematic Hamiltonian able to describe their spectra and B(E2) transition is used.It is found that the 160-170Er isotopes are in the transition from the vibrational limit to rotational limit.     

Critical behaviour in nuclear structure from spherical to axially symmetric deformed shape in IBM

To compare with the predictions of the transitional dynamical symmetry X(5) proposed by Iachello (2001 Phys. Rev. Lett. 87 052502), the critical behaviours of U(5)--SU(3) are studied in the space of two control parameters in the interacting boson model (IBM). A simple-shaped phased diagram has been presented. It is found that X(5) predictions cannot be exactly reproduced by our calculations and that the best agreement is close to the calculations with boson numbers N = 11 and 12. By comparing with experimental data on X(5)-like nuclei, we find that X(5) predictions and IBM calculations can reproduce the energy ratios and E2 transition ones.     

Well-Known Distinctive Signatures of Quantum Phase Transition in Shape Coexistence Configuration of Nuclei

It is interesting that a change of nuclear shape may be described in terms of a phase transition. This paper studies the quantum phase transition of the U(5) to SO(6) in the interacting boson model (IBM) on the finite number N of bosons. This paper explores the well-known distinctive signatures of transition from spherical vibrational to γ-soft shape phase in the IBM with the variation of a control parameter. Quantum phase transitions occur as a result of properties of ground and excited states levels. We apply an affine \(\widehat {SU(1,1)}\) approach to numerically solve non-linear Bethe Ansatz equation and point out what observables are particularly sensitive to the transition. The main aim of this work is to describe the most prominent observables of QPT by using IBM in shape coexistence configuration. We calculate energies of excited states and signatures of QPT as energy surface, energy ratio, energy differences, quadrupole electric transition rates and expectation values of boson number operators and show their behavior in QPT. These observables are calculated and examined for ^{98 ? 102}Mo isotopes.     

Isospin and Mixed Symmetry Excitations in 60—66Zn Isotopes

The level structure of ^60—66Zn isotopes is studied within the framework of interacting boson model-3 (IBM-3). The mixed symmetry states are investigated in these nuclei by analyzing the wave functions. The isospin excitation states are identified for ⁶⁰Zn (N=Z) nucleus. The calculated energy levels and transition probabilities are compared with available experimental data. The results obtained and the values of parameters used in this calculation indicated that the Zn isotopes are in the transition from vibrational to γ-unstable nuclei.     

A theoretical description of energy spectra and two-neutron separation energies for neutron-rich zirconium isotopes

Very recently the atomic masses of neutron-rich Zr isotopes, from ⁹⁶Zr to ¹⁰⁴Zr, have been measured with high precision. Using a schematic Interacting Boson Model (IBM) Hamiltonian, the evolution from spherical to deformed shapes along the chain of Zr isotopes, describing at the same time the excitation energies as well as the two-neutron separation energies, can be rather well reproduced. The interplay between phase transitions and configuration mixing of intruder excitations in this mass region is succinctly addressed.     

A simple model of superheavy nuclei

I present a simple algebraic model of superheavy and superdeformed nuclei, produced through heavy-ion collisions, based on a microscopic evaluation of the effective boson numbers in the actinide and superheavy regions. The relevant calculations have been performed within the framework of a deformed shell model, including the pairing interaction between like-particles. As far as the actinide isotopes are concerned, the theoretical boson numbers are compared with the corresponding empirical estimates, obtaining a good agreement. The calculated boson numbers are used to predict collective spectra and electromagnetic transition intensities for actinide — including fission isomers — and superheavy nuclei, by using the interacting boson model (IBM).     

带三体势的IBM1的O(6)极限对偶偶Pt核的应用

通过在IBMI哈密顿中,引入一种简单的等效三体势,O(6)核能谱可得到不同程度的修正.本文具体计算了^192—198Pt偶偶同位素核的能谱和E2跃迁几率,理论计算值与实验数据符合较好.