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

Energy Levels and Electromagnetic Transition of 90-94mo Nuclei Using Ibm-1

2020 ◽  
pp. 149-152
Keyword(s):  
Experimental Data ◽  
Transition Probability ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Interacting Boson Model ◽  
Excitation Energies ◽  
Electromagnetic Transition ◽  
Boson Model ◽  
Energy States ◽  
Good Agreement

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

scholarly journals Nuclear phase transitions near the critical points: a study with the Relativistic Hartree-Bogoliubov model, the Interacting Boson Model and the Boson Coherent-State Framework

2020 ◽  
Vol 15 ◽  
pp. 136
Author(s):  
R. Fossion
Keyword(s):  
Phase Transitions ◽  
Coherent State ◽  
Analytical Solutions ◽  
Critical Points ◽  
Potential Energy Surfaces ◽  
Transfer Reactions ◽  
Interacting Boson Model ◽  
Boson Model ◽  
Nuclear Phase ◽  
Energy Surfaces

We present an analysis of the intensity of 2-particle transfer reactions in the Interacting Boson Model (IBM), and in the Boson Coherent-State framework, as a tool to study nuclear phase transitions. We study transfer reactions between two ground states, and between the ground state and the band head of the beta-vibrational band. We suggest characteristic fingerprints that should allow experimentalists to identify the critical points of the nuclear phase transition. Two analytical solutions, X(5) and E(5), have been proposed recently for two of the critical points. We present a study within the Relativistic Hartree-Bogoliubov model (RHB), using Potential-Energy Surfaces (PES), to test whether the initial approximations made in deriving the analytical solutions are valid.

Structure of the low-lying positive and negative parity states in even–even 144−154Nd isotopes

2019 ◽  
Vol 28 (12) ◽  
pp. 1950107
Author(s):  
Hussein N. Qasim ◽  
Falih H. Al-Khudair
Keyword(s):  
Potential Energy Surfaces ◽  
Transition Probability ◽  
Model Space ◽  
Negative Parity ◽  
Energy Spectra ◽  
Interacting Boson Model ◽  
Nd Isotopes ◽  
Nd Isotope ◽  
Boson Model ◽  
Energy Surfaces

The low-lying positive and negative parity states of even–even [Formula: see text]Nd isotopes are studied using the interacting boson model (IBM). The negative parity states are involved within the IBM model by adding a single angular momentum ([Formula: see text]) boson with intrinsic negative parity [Formula: see text]-boson to [Formula: see text] and [Formula: see text]-bosons model space. For these nuclei, the potential energy surfaces [Formula: see text], transition probability [Formula: see text], [Formula: see text] and [Formula: see text] are calculated. Phase transition from the [Formula: see text] limit to the [Formula: see text] limit is observed in the chain and the critical point has been determined for [Formula: see text]Nd isotope. It is found that the calculated positive and negative parity energy spectra of Nd-isotopes agree well with the experimental data.

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.

Description of the Ba–Dy(N = 92) nuclei in the interacting boson model

2017 ◽  
Vol 26 (04) ◽  
pp. 1750019 ◽  
Author(s):  
Huda H. Kassim
Keyword(s):  
Potential Energy Surfaces ◽  
Energy Levels ◽  
Interacting Boson Model ◽  
Contour Plot ◽  
Model Parameters ◽  
Transition Rates ◽  
Ground State Band ◽  
State Band ◽  
Boson Model ◽  
Energy Surfaces

Interacting Boson Model (IBM -1) has been used to study the energy levels and [Formula: see text] transition rates in Ba–Dy ([Formula: see text]) isotones. A simplified Hamiltonian is used which is written in the creation and annihilation form and for each nucleus, by fitting the selected experimental energy levels and [Formula: see text] transition rates with the calculated ones to get the best model parameters. Using the (IBM) Hamiltonian with an intrinsic state formalism, the potential energy surfaces (PES) for even–even Ba–Dy nuclei have been obtained and the contour plot of PES show that the shape phase transitions from spherical [Formula: see text] to deformed shape [Formula: see text] has been determined for the [Formula: see text], while [Formula: see text]Ce, [Formula: see text]Nd, [Formula: see text]Sm, [Formula: see text]Gd and [Formula: see text]Dy nuclei are deformed and have rotational-like characters. The behavior of energy and [Formula: see text] ratios in the ground state band are examined.

scholarly journals Study of Energy States and U(5) – O(6) Transitional Symmetry of Even–Even104 – 108Cd Isotopes by Interacting Boson Model(IBM-1).

2020 ◽  
pp. 262-267
Author(s):  
Omar Ahmed Muaffaq
Keyword(s):  
Potential Energy ◽  
Potential Energy Surfaces ◽  
Energy Levels ◽  
Interacting Boson Model ◽  
Contour Plots ◽  
Boson Model ◽  
Cd Isotopes ◽  
Energy States ◽  
Experimental Values ◽  
Energy Surfaces

In this study we calculated the energy levels of low lying structure for 104 – 108 Cd isotopes and the reduced transition B(E2) of even – even Cd nuclei for A=104,106, 108 by using" the interaction boson model IBM-1" and compared with experimental values .The ratio R(4/2) for the energy levels for 41 + and 21 + states were also calculated for those isotopes .The 104 – 108 Cd nuclei in " U(5) – O(6) transitional symmetry" were studied .The contour plots of the potential energy surfaces (P E S) was calculate for the isotopes above .

scholarly journals Study of Nuclear Structures for Nd 148,150,152 a Isotopes by Using IBM-1

2018 ◽  
Vol 28 (2) ◽  
pp. 196
Author(s):  
Sallama S. Hummadi
Keyword(s):  
Ground State ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Interacting Boson Model ◽  
Energy Ratios ◽  
Boson Model ◽  
Nuclear Structures

The nuclear structures of even-even isotopes Nd (A=148,150,152) are studied by using the first Interacting Boson Model (IBM-1). The energy levels of ground state, beta and gamma bands ,energy ratios are calculated. The results showed dynamical symmetry of these isotopes SU(3)- SU(6), SU(5)-SU(6).

scholarly journals A STUDY ON THE GROUND STATES STRUCTURE OF EVEN-EVEN 104−106Ru ISOTOPES

2020 ◽  
pp. 13-18
Author(s):  
I. Hossain ◽  
Huda H. Kassim ◽  
Fadhil I. Sharrad ◽  
Mushtaq A. Al-Jubbori ◽  
A. Salam ◽  
...  
Keyword(s):  
Experimental Data ◽  
Ground State ◽  
Potential Energy Surfaces ◽  
Energy Levels ◽  
Computer Code ◽  
Interacting Boson Model ◽  
Dynamic Symmetry ◽  
Beta Band ◽  
Boson Model ◽  
Energy Surfaces

In this paper, even-even 104−106Ru isotopes have been studied the ground state bands using Matlab computer code (IBM-1.Mat). We apply the interacting boson model-1 (IBM-1) formula for O(6) symmetry in Ru isotopes with neutron N = 60, 62. The theoretical energy levels up to spin-parity 12+ have been obtained for 104−106Ru isotopes. The yrast states, gamma band, beta band, and B(E2) values are calculated for these nuclei. The published experimental and calculated R4/2 values indicate that the even-even 104−106Ru isotopes have O(6) dynamic symmetry. The present results have been compared to the published experimental data and are found good harmony with each other. The outcome of our investigation of the potential energy surfaces (PES) of both isotopes belonging to O(6) character.

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