Phase transition studies of the odd-mass 123−135Xe isotopes based on SU(1,1) algebra in IBFM

2016 ◽  
Vol 25 (08) ◽  
pp. 1650048 ◽  
Author(s):  
M. A. Jafarizadeh ◽  
N. Fouladi ◽  
M. Ghapanvari ◽  
H. Fathi
Keyword(s):  
Experimental Data ◽  
Phase Transition ◽  
Coherent State ◽  
Critical Behavior ◽  
Energy Spectra ◽  
Transition Rates ◽  
Excitation Energies ◽  
Fermion Model ◽  
Energy Surfaces ◽  
Transition Studies

In this paper, we have investigated the positive-parity states in the odd-mass transitional [Formula: see text]Xe isotopes within the framework of the interacting boson–fermion model. Two solvable extended transitional Hamiltonians which are based on SU(1,1) algebra are employed to provide an investigation of quantum phase transition (QPT) between the spherical and deformed gamma — unstable shapes along the chain of Xe isotopes. The low-states energy spectra and B(E2) values for these nuclei have been calculated and compared with the experimental data. The predicted excitation energies and B(E2) transition rates of the odd isotopes are found to agree well with the experimental data. We have also analyzed the critical behavior of even–odd Xe isotopes via Catastrophe Theory in combination with a coherent state formalism to generate energy surfaces and special isotopes which are the best candidates for the critical point are identified.

scholarly journals Mixed Symmetry States in 92Zr and 94Mo Nuclei

2021 ◽  
Vol 66 (12) ◽  
pp. 1013
Author(s):  
S.N. Abood ◽  
A.A. Al-Rawi ◽  
L.A. Najam ◽  
F.M. Al-Jomaily
Keyword(s):  
Experimental Data ◽  
Energy Spectra ◽  
Interacting Boson Model ◽  
Transition Rates ◽  
Collective Models ◽  
Electromagnetic Transition ◽  
Mixed Symmetry ◽  
Mixed Symmetry States ◽  
Boson Model ◽  
Phonon Model

Mixed-symmetry states of 92Zr and 94Mo isotopes are investigated with the use of the collective models, Interacting Boson Model-2 (IBM-2) and Quasiparticle Phonon Model (QPM). The energy spectra and electromagnetic transition rates for these isotopes are calculated. The results of IBM-2 and QPM are compared with available experimental data. We have obtained a satisfactory agreement, and IBM-2 gives a better description. In these isotopes, we observe a few states having a mixed symmetry such as 2+2, 2+3, 3+1, and 1+s. It is found that these isotopes have a vibrational shape corresponding to the U(5) symmetry.

CRITICAL BEHAVIOR OF THE SPECIFIC HEAT IN THE VICINITY OF THE TRANSITION TEMPERATURE FOR S-TRIAZINE

2009 ◽  
Vol 23 (09) ◽  
pp. 2253-2259 ◽  
Author(s):  
M. KURT ◽  
H. YURTSEVEN
Keyword(s):  
Experimental Data ◽  
Phase Transition ◽  
Transition Temperature ◽  
Critical Exponent ◽  
Specific Heat ◽  
Power Law ◽  
Order Phase Transition ◽  
Critical Behavior ◽  
First Order ◽  
Second Order Phase Transition

The critical behavior of the specific heat is studied in s-triazine ( C 3 N 3 H 3). Using the experimental data for the CP, the temperature dependence of the specific heat is analyzed according to a power-law formula and the values of the critical exponent for CP are extracted in the vicinity of the transition temperature (TC=198.07 K ). It is indicated that s-triazine undergoes a weakly first order (quasi-continuous) or second order phase transition.

A theoretical study of energy spectra and transition probabilities of 200–204Hg isotopes in transitional region of IBM

2014 ◽  
Vol 23 (10) ◽  
pp. 1450056 ◽  
Author(s):  
H. Sabri
Keyword(s):  
Experimental Data ◽  
Theoretical Study ◽  
Transition Probabilities ◽  
Energy Spectra ◽  
Interacting Boson Model ◽  
Transitional Region ◽  
Transition Rates ◽  
Scale Factors ◽  
Boson Model ◽  
Good Agreement

In this paper, by using the SO(6) representation of eigenstates and transitional Interacting Boson Model (IBM) Hamiltonian, the evolution from prolate to oblate shapes along the chain of Hg isotopes is studied. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are found to be in good agreement with experimental data for 200–204 Hg isotopes which are supported to be located in this transitional region.

γ-rigid version of Bohr Hamiltonian with the modified Davidson potential in the position-dependent mass formalism

2017 ◽  
Vol 32 (14) ◽  
pp. 1750085 ◽  
Author(s):  
H. Hassanabadi ◽  
M. Alimohammadi ◽  
S. Zare
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Wave Function ◽  
Wave Equation ◽  
Standard Error ◽  
Energy Spectra ◽  
Transition Rates ◽  
Dependent Mass ◽  
Position Dependent Mass ◽  
Davidson Potential

In this paper, the wave equation corresponding to the [Formula: see text]-rigid version of Bohr Hamiltonian for the modified Davidson potential is investigated in the position-dependent mass formalism. By solving the related differential equation, the wave function, energy spectra and transition rates are obtained. In order to evaluate our results, they are compared with experimental data through the standard error.

scholarly journals Review of Shape Phase Transition Studies for Bose-Fermi Systems: The Effect of the Odd-Particle on the Bosonic Core

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 215
Author(s):  
M. Böyükata ◽  
C. E. Alonso ◽  
J. M. Arias ◽  
L. Fortunato ◽  
A. Vitturi
Keyword(s):  
Phase Transition ◽  
Critical Points ◽  
Potential Energy Surfaces ◽  
Energy Levels ◽  
Model Space ◽  
Fermi Systems ◽  
Energy Surfaces ◽  
Shape Phase Transition ◽  
Intrinsic Frame ◽  
Transition Studies

The quantum phase transition studies we have done during the last few years for odd-even systems are reviewed. The focus is on the quantum shape phase transition in Bose-Fermi systems. They are studied within the Interacting Boson-Fermion Model (IBFM). The geometry is included in this model by using the intrinsic frame formalism based on the concept of coherent states. First, the critical point symmetries E(5/4) and E(5/12) are summarized. E(5/4) describes the case of a single j=3/2 particle coupled to a bosonic core that undergoes a transition from spherical to γ-unstable. E(5/12) is an extension of E(5/4) that describes the multi-j case (j=1/2,3/2,5/2) along the same transitional path. Both, E(5/4) and E(5/12), are formulated in a geometrical context using the Bohr Hamiltonian. Similar situations can be studied within the IBFM considering the transitional path from UBF(5) to OBF(6). Such studies are also presented. No critical points have been proposed for other paths in odd-even systems as, for instance, the transition from spherical to axially deformed shapes. However, the study of such shape phase transition can be done easily within the IBFM considering the path from UBF(5) (spherical) to SUBF(3) (axial deformed). Thus, in a second part, this study is presented for the multi-j case. Energy levels and potential energy surfaces obtained within the intrinsic frame formalism of the IBFM Hamiltonian are discussed. Finally, our recent works within the IBFM for a single-j fermion coupled to a bosonic core that performs different shape phase transitional paths are reviewed. All significant paths in the model space are studied: from spherical to γ-unstable shape, from spherical to axially deformed (prolate and oblate) shapes, and from prolate to oblate shape passing through the γ-unstable shape. The aim of these applications is to understand the effect of the coupled fermion on the core when moving along a given transitional path and how the coupled fermion modifies the bosonic core around the critical points.

Isospin excitation and shape phase transition in odd-mass Cu isotopes

2017 ◽  
Vol 26 (06) ◽  
pp. 1750036 ◽  
Author(s):  
M. Ghapanvari ◽  
M. A. Jafarizadeh ◽  
N. Fouladi ◽  
Z. Ranjbar ◽  
N. Amiri
Keyword(s):  
Phase Transition ◽  
Transition Probabilities ◽  
Closed Shell ◽  
Energy Spectra ◽  
Control Parameters ◽  
Fermion Model ◽  
Cu Isotopes ◽  
Phase Transition Region ◽  
Shape Phase Transition ◽  
Good Agreement

In this paper, the interacting boson–fermion model generalized by considering an np-boson and the single nucleon as a vector coupled in isospin to the bosons to form the model isospin invariant. The transitional interacting boson–fermion model Hamiltonians in IBFM-1 and IBFM-3 versions based on affine SU(1,[Formula: see text]1) Lie algebra are employed to describe the evolution from the spherical to deformed gamma unstable shapes along the chain of Cu isotopes. We have studied the energy spectra of [Formula: see text] isotopes and B(E2) transition probabilities of [Formula: see text] isotopes in the shape phase transition region between the spherical and gamma unstable deformed shapes. Good agreement was achieved between the calculated results using the models and measured data. The results obtained and the values of control parameters used in this calculation indicated that the odd-mass Cu isotopes located near the closed shell provided good examples of [Formula: see text](5) symmetry without any significant deformed gamma-unstable structure. Some comparisons are made with IBFM-1.

SHAPE PHASE TRANSITIONS AND POSSIBLE E(5) SYMMETRY NUCLEI FOR Ti ISOTOPES

2008 ◽  
Vol 17 (03) ◽  
pp. 539-548 ◽  
Author(s):  
JIAN YOU GUO ◽  
XIANG ZHENG FANG ◽  
ZONG QIANG SHENG
Keyword(s):  
Field Theory ◽  
Experimental Data ◽  
Phase Transitions ◽  
Potential Energy Surfaces ◽  
Mean Field Theory ◽  
Mean Field ◽  
Dynamical Symmetry ◽  
Excitation Energies ◽  
Relativistic Mean Field ◽  
Energy Surfaces

Relativistic mean field theory is used to produce potential energy surfaces (PESs) for Ti isotopes. The relatively flat PESs suggest that 48, 52, 60 Ti , being on the way from vibrations to γ-unstable behavior, are the possible examples with the transitional dynamical symmetry E(5). Especially for 48 Ti , PES shows that it is a better candidate with E(5) symmetry. These conclusions are supported by the experimental data via the observed ratios of excitation energies.

scholarly journals Z(5): Critical Point Symmetry for the Prolate to Oblate Nuclear Shape Phase Transition

2020 ◽  
Vol 13 ◽  
pp. 73
Author(s):  
Dennis Bonatsos ◽  
D. Lenis ◽  
D. Petrellis ◽  
P. A. Terziev
Keyword(s):  
Experimental Data ◽  
Phase Transition ◽  
Critical Point ◽  
Point Symmetry ◽  
Transition Rates ◽  
Oblate Shape ◽  
Scale Factors ◽  
Shape Phase Transition ◽  
Nuclear Shape Phase Transition ◽  
Good Agreement

A critical point symmetry for the prolate to oblate shape phase transition is intro­ duced, starting from the Bohr Hamiltonian and approximately separating variables for γ=30°. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are found to be in good agreement with experimental data for 194Pt, which is supposed to be located very close to the prolate to oblate critical point, as well as for its neighbours (192Pt, 196Pt).

The X(3) model for the modified Davidson potential in a variational approach

2017 ◽  
Vol 26 (09) ◽  
pp. 1750054 ◽  
Author(s):  
M. Alimohammadi ◽  
H. Hassanabadi
Keyword(s):  
Experimental Data ◽  
Wave Function ◽  
Wave Equation ◽  
Variational Method ◽  
Collective Behavior ◽  
Variational Approach ◽  
Energy Spectra ◽  
Transition Rates ◽  
Similar Work ◽  
Davidson Potential

In this work, we investigate the [Formula: see text]-rigid version of Bohr–Hamiltonian for the modified Davidson potential. Since the corresponding wave equation cannot be solved analytically, we apply the variational method. The related wave function, energy spectra and transition rates are determined. In order to evaluate our results, we fit the formula for the energy spectra to the available experimental data for some nuclei and compare the obtained standard error with the corresponding one in other similar work. Moreover, we study the collective behavior of these nuclei through the evolution of two quantities [Formula: see text] and [Formula: see text] in terms of number of valence nucleons.

Nuclear Shape Transition Between Spherical U(5) and γ-Unstable O(6) Limits of the Interacting Boson Model

2015 ◽  
Vol 9 (1) ◽  
pp. 2330-2339
Author(s):  
Mahmoud Abokilla ◽  
A.M. Khalaf ◽  
T.M. Awwad ◽  
N. Gaballah
Keyword(s):  
Phase Transition ◽  
Potential Energy Surfaces ◽  
Dynamical Symmetry ◽  
Interacting Boson Model ◽  
Yrast Band ◽  
Excitation Energies ◽  
Energy Ratios ◽  
Boson Model ◽  
Spherical Oscillator ◽  
Energy Surfaces

The interacting boson model (IBM) with intrinsic coherent state (characterized by and ) is used to describe the nuclear second order shape phase transition (denoted E(5)) between the spherical oscillator U(5) and the -soft rotor O(6) structural limits. The potential energy surfaces (PES's) have been derived and the critical points of the phase transition have been determined . The model is examined for the spectra of even-even neutron rich xenon isotopic chain. The best adopted parameters in the IBM Hamiltonian for each nucleus have been adjusted to reproduce as closely as possible the experimental selected numbers of excitation energies of the yrast band,  by using computer simulated search program.Using the best fitted parameters , the  energy ratios for the  levels are calculated and compared to those of the O(6) and U(5) dynamical symmetry limits.122Xe and 132Xe are considered as examples for the two O(6) and U(5) dynamical symmetry limits

Sign in / Sign up

Export Citation Format

Share Document