Shape Transition and Triaxial Interaction Effect in the Structure of 152-166Dy Isotopes

The positive parity states in even-even ^152-166Dy are studied systematically in the framework of the interacting boson model (IBM). A cubic term, L=3, has been added to the Hamiltonian in order to produce the effect of triaxiality on the energy spectrum. The potential energy surfaces as a function of β and γ deformation parameters, for all isotopes have been produced. Energy levels and reduced electric quadrupole transition probabilities are calculated in framework of IBM with Cubic term (IBMC). All results are compared with available experimental data. It is found that these isotopes can be described by a schematic Hamiltonian in transition from U(5) (vibration) to SU(3) (rotation) dynamic symmetry.     

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.     

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.     

Study of the <Superscript>190</Superscript>Hg Nucleus: Testing the Existence of U(5) Symmetry

In this paper, we have considered the energy spectra, quadrupole transition probabilities, energy surface, charge radii, and quadrupole moment of the¹⁹⁰Hg nucleus to describe the interplay between phase transitions and configuration mixing of intruder excitations. To this aim, we have used four different formalisms: (i) interacting boson model including configuration mixing, (ii) Z(5) critical symmetry, (iii) U(6)-based transitional Hamiltonian, and (iv) a transitional interacting boson model Hamiltonian in both interacting boson model (IBM)-1 and IBM-2 versions which are based on affine \( \widehat{SU\left(1,1\right)} \) Lie algebra. Results show the advantages of configuration mixing and transitional Hamiltonians, in particular IBM-2 formalism, to reproduce the experimental counterparts when the weight of spherical symmetry increased.     

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.     

LOW-LYING SPECTRA AND E2 TRANSITION RATES IN EVEN--EVEN Pd ISOTOPES IN THE INTERACTING BOSON MODEL

The positive parity collective states in the even-even ¹⁰⁰Pd-¹¹⁶Pd 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 spectra can be well described by a U(5) plus SU(3) perturbation interaction. As the valence neutron number changes, the structure of the isotopes shows regular patterns of change. In the meantime, the behaviour of 0⁺₂ can also be partially described by the model.     

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.     

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.     

The O(6) description of the nuclear rotation

A recently developed algebraic version of the collective model has shown that a full range of Bohr model calculations can be executed in bases that range continuously from those of a spherical vibrator to a beta-vibrational Wilets-Jean limit. Thus, the establishment of close relationships between the algebraic structure of this model and the IBM is of special importance because one can learn from the complementary perspectives they afford. In this paper, we show by calculations that the familiar rotor-gamma vibrational spectra of the Bohr model can be obtained in the IBM by the addition of a scalar cubic in the quadrupole moment operators, of the type considered recently by Van Isacker, to an O(6) Hamiltonian. Simple fits of the low-lying spectra, electromagnetic transition rates and moments of inertia of the ground and gamma bands of¹⁶²Dy and¹⁶⁸Er are presented.     

Description of 160Dy nucleus by partial dynamical SU(3) symmetry

We considered the characteristic features of SU(3) partial dynamical symmetry in the interacting boson model framework to show the relevance of such intermediate symmetry structure in the nuclear spectroscopy of the ¹⁶⁰Dy nucleus. The predictions of SU(3)-PDS for the energy spectrum and the transition probabilities were compared with the most recent experimental data and an acceptable degree of agreement was achieved.     

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).     

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.     

Low-lying (K π = 0+) states of gadolinium isotopes

The sd-interacting boson approximation (sd-IBA) and the df-interacting boson approximation (df-IBA) can be related to each other and the states of the interacting boson approximation model can be identified with the fully symmetric states in the sdf interacting boson approximation model. A systematic study of the sdf-IBA model showed that the constructed Hamiltonian can successfully describe the strong octupole correlations in the deformed nuclei. We showed that the interacting boson approximation may account for many of these K ^π ?=?0⁺ states. It was found that the calculated energy spectra of the gadolinium isotopes agree quite well with the experimental data. The observed B(E2) values were also calculated and compared with the experimental data.     

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.     

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.     

First-order quantum phase transitions: Test ground for emergent chaoticity,regularity and persisting symmetries

We present a comprehensive analysis of the emerging order and chaos and enduring symmetries, accompanying a generic (high-barrier) first-order quantum phase transition (QPT). The interacting boson model Hamiltonian employed, describes a QPT between spherical and deformed shapes, associated with its U(5) and SU(3) dynamical symmetry limits. A classical analysis of the intrinsic dynamics reveals a rich but simply-divided phase space structure with a Hénon–Heiles type of chaotic dynamics ascribed to the spherical minimum and a robustly regular dynamics ascribed to the deformed minimum. The simple pattern of mixed but well-separated dynamics persists in the coexistence region and traces the crossing of the two minima in the Landau potential. A quantum analysis discloses a number of regular low-energy U(5)-like multiplets in the spherical region, and regular SU(3)-like rotational bands extending to high energies and angular momenta, in the deformed region. These two kinds of regular subsets of states retain their identity amidst a complicated environment of other states and both occur in the coexistence region. A symmetry analysis of their wave functions shows that they are associated with partial U(5) dynamical symmetry (PDS) and SU(3) quasi-dynamical symmetry (QDS), respectively. The pattern of mixed but well-separated dynamics and the PDS or QDS characterization of the remaining regularity, appear to be robust throughout the QPT. Effects of kinetic collective rotational terms, which may disrupt this simple pattern, are considered.     

Quadrupole collectivity variations in even Hafnium isotopes

The boson wave functions given by the interacting boson model have been analyzed for a chain of even Hf isotopes, along which transition from spherical to deformed nuclei, accompanied by an increase in the number of d bosons and degree of their pairing, occurs.     

Shape transitions in even Mo and Sm isotopes: Study in a new microscopic interacting boson model scheme

A simple dynamic procedure, based on the deformed Hartree-Fock solution of a nucleus, is presented to construct the IBM operators in microscopic basis. The parameters of these operators are evaluated by establishing a Marumori mapping from the truncated shell model space onto the boson space. The transitions from spherical to axial-rotor shape observed in the low-lying levels ofeven ^96–108Mo and^146–154Sm isotopes are reproduced qualitatively by applying this procedure with a fixed set of fermion input parameters to each chain. Variation of a few parameters in fermion space leads to quantitative agreement.     

Microscopic interacting boson model calculations for even-even <Superscript>128–138</Superscript>Ce nuclei

In this study, we determined the most appropriate Hamiltonian that is needed for the present calculations of energy levels and B(E2) values of ^128–138Ce nuclei which have a mass around A≅130 using the interacting boson model (IBM). Using the best-fitted values of parameters in the Hamiltonian of the IBM-2, we have calculated energy levels and B(E2) values for a number of transitions in ^{128,130,132,134,136,138}Ce. The results were compared with the previous experimental and theoretical (PTSM model) data and it was observed that they are in good agreement. Also some predictions of this model have better accuracy than those of PTSM model. It has turned out that the interacting boson approximation (IBA) is fairly reliable for calculating spectra in the entire set of ^{128,130,132,134,136,138}Ce isotopes and the quality of the fits presented in this paper is acceptable.