Interacting Boson Model Research Articles

A nuclear phenomenological study of the even–even Thorium Isotopes 228–232Th

The rotational and vibrational energies and the electric transition probability B [Formula: see text] of the even–even [Formula: see text]Th isotopes are studied empirically in framework of a nuclear phenomenological approach by using the SU(3) dynamical symmetries of the Interacting Boson Model-1 (IBM-1). Furthermore, the potential energy surfaces for these isotopes are plotted as functions of the deformation parameters [Formula: see text] and [Formula: see text]. Moreover, we introduce empirical fit formulas for rotational and vibrational energies, which used to calculate these energies for the thorium isotopes. The obtained results by applying the IBM-1 and the authors’ formulas are in good agreement with the corresponding experimental data for most of the nuclear states.

Study of the 190Hg 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.

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

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).

Low-lying states in even Gd isotopes studied with five-dimensional collective Hamiltonian based on covariant density functional theory

Five-dimensional collective Hamiltonian based on the covariant density functional theory has been applied to study the the low-lying states of even-even $^{148-162}$Gd isotopes. The shape evolution from $^{148}$Gd to $^{162}$Gd is presented. The experimental energy spectra and intraband $B(E2)$ transition probabilities for the $^{148-162}$Gd isotopes are reproduced by the present calculations. The relative $B(E2)$ ratios in present calculations are also compared with the available interacting boson model results and experimental data. It is found that the occupations of neutron $1i_{13/2}$ orbital result in the well-deformed prolate shape, and are essential for Gd isotopes.

Nuclear Structure of the (144 Ba, 146 Ce 148 Nd )by using the Interacting boson Approximation (IBA-2)

Nuclear Structure of the (144 Ba, 146 Ce 148 Nd )by using the Interacting boson Approximation (IBA-2)

γ -soft rotor with configuration mixing in the O(6) limit of the interacting boson model

To describe obvious intruder states and nonzero quadrupole moments of $\ensuremath{\gamma}$-soft nuclei such as $^{194}\mathrm{Pt}$, a rotor extension plus intruder configuration mixing with $2n$-particle and $2n$-hole configurations from $n=0$ up to $n\ensuremath{\rightarrow}\ensuremath{\infty}$ in the O(6) ($\ensuremath{\gamma}$-unstable) limit of the interacting boson model is proposed. It is shown that the configuration mixing scheme keeps the lower part of the $\ensuremath{\gamma}$-unstable spectrum unchanged and generates the intruder states due to the mixing. It is further shown that almost all low-lying levels below 2.17 MeV in $^{194}\mathrm{Pt}$ can be well described by modifying the O(6) quadrupole-quadrupole interaction into an exponential form. The third-order term needed for a rotor realization in the interacting boson model seems necessary to produce nonzero quadrupole moments with the correct sign.

Calculation of some of the nuclear properties of even-even 172-176Hf isotopes using IBM-1

A description of the even-even Hf isotopes for A = 172 ‒ 176 is carried out in the framework of the interacting boson model (IBM-1). The energy levels, B(E2) transition probabilities, electric quadrupole moment QL, and potential energy surface of those nuclei have been calculated. The calculated results are compared with the most recent experimental data. A good agreement for low lying energy states is obtained between experimental results and theoretical calculations. The contour plots of the potential energy surfaces show that the interested nuclei have rotational characters.

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 − 102Mo isotopes.

"Nuclear Structure of the (144 Ba, 146 Ce 148 Nd )by using the Interacting boson Approximation (IBA-2) "

"The Interacting Boson Hamiltonian (IBA-2) to reproduce energy spectrum of isotones is tested The calculated ratio has been suggested that these nuclei are part of O(6) group symmetry. Reduced electric quadruple transitions between states of and magnetic dipole between states of , are calculated. The mixing ratios for transitions between are evaluated as well. All the calculated results have been compared with available experimental data and satisfactory results are obtained.

Exactly solvable configuration mixing scheme in the vibrational limit of the interacting boson model

An intruder configuration mixing scheme with $2n$-particle and $2n$-hole configurations from $n=0$ up to $n\ensuremath{\rightarrow}\ensuremath{\infty}$ in the U(5) (vibrational) limit of the interacting boson model is proposed. A simple Hamiltonian suitable to describe the intruder and normal configuration mixing is found to be exactly solvable, and its eigenstates can be expressed as the SU(1,1) coherent states built on the U(5) basis vectors of the interacting boson model. It is shown that the configuration mixing scheme keeps lower part of the vibrational spectrum unchanged and generates the intruder states due to the mixing. Some low-lying level energies and experimentally known $B(E2)$ ratios of $^{108,110}\mathrm{Cd}$ are fitted and compared with the experimental results.

Isospin and symmetry structure in 22Ne

Band structure and electromagnetic transition properties of the low-lying states in the [Formula: see text]Ne nucleus were studied within the framework of interacting boson model (IBM) 3. The isospin excitation states, low-lying symmetry states, the main components of the eigen-state, isoscalar and isovector parts in the [Formula: see text] and [Formula: see text] transitions for low-lying states have been investigated. According to this study, the calculated results are in agreement with experimental data, and the nucleus [Formula: see text]Ne is in transition from [Formula: see text] to [Formula: see text].

Study of phase transition of even and odd nuclei based on q-deforme SU(1,1) algebraic model

The q-deformed Hamiltonian for the SO(6)↔U(5) transitional case in s, d interaction boson model (IBM) can be constructed by using affine SUq(1,1) Lie algebra in the both IBM-1 and 2 versions and IBFM. In this research paper, we have studied the energy spectra of Xe120−128 isotopes and Xe123−131 isotopes and B(E2) transition probabilities of Xe120−128 isotopes in the shape phase transition region between the spherical and gamma unstable deformed shapes of the theory of quantum deformation. The theoretical results agree with the experimental data fairly well. It is shown that the q-deformed SO(6)↔U(5) transitional dynamical symmetry remains after deformation.

Determine the 134–140Nd isotopes identity using IBM and NEF

The property of 134−140Neodymium nuclei have been studied in framework Interacting Boson Model (IBM) and a new method called New Empirical Formula (NEF). The energy positive parity bands of 134−140Nd have been calculated using (IBM) and (NEF) while the negative parity bands of 134−140Nd have been calculated using (NEF) only. The E-GOS curve (Eγ/I) as a function of the spin (I) has been drawn to determine the property of the positive parity yrast band. The parameters of the best fit to the measured data are determined. The reduced transition probabilities B(E2) of these nuclei was calculated. The critical point has been determined for 140Nd isotope. The potential energy surfaces (PESs) to the IBM Hamiltonian have been obtained using the intrinsic coherent state.

Nuclear matrix elements for the ββ decay of 76Ge

The nuclear matrix elements for two-neutrino double-beta (2vββ) and zeroneutrino double-beta (0vββ) decay of 76 Ge are evaluated in terms of the configuration interaction (CI), quasiparticle random phase approximation (QRPA) and interacting boson model (IBM) methods. We determine nuclear matrix elements with error bars that take into account the truncation of the model space used for CI.

Exactly solvable model in quadrupole-octupole coupled states

Exactly solvable model in quadrupole-octupole coupled (QOC) states is an interesting nuclear structure phenomenon. For example, several transitions of the electric dipole and quadrupole (E1 and E2) values are indicative of QOC states. Various collective models as three-level and four-level pairing models were employed in order to account for the observed properties of the QOC states. We suggest a simultaneous description of low-lying collective positive and negative-parity states to use the spdf and sdf interacting boson model to reproduce the general characteristics of the QOC states. Also, quantum phase transitions are investigated based on dual algebraic structures for the sd, sdf and spdf-IBM. The low lying positive and negative parity states and the QOC properties of the stable even–even Cd isotopes are calculated in solvable extended transitional Hamiltonian of the IBM-spdf and IBM-sdf models based on the affine SU(1,1)ˆ Lie algebra. Some observables such as energy levels, transition rates, expectation value of boson number operators, energy differences and staggering pattern are calculated and examined for Cd isotopes. The IBM calculations indicate a nuclear structure of the electric E1, E2 and E3 strength and energy spectra in the low-lying, thus confirming the experimental results for transition region. The calculations confirm a good agreement for the energy spectra, quantum phase transitions and fragmentation of the E1, E2 and E3 strengths.

Theoretical description of the deformation properties for 154–164Gd isotopes

The 154–164Gd isotopes in SU(3) region were investigated. For these nuclei, the positive ground-state band of 154–164Gd has been calculated using Bohr–Mottelson Model, Interacting Vector Boson Model and Interacting Boson Model, while the negative-parity band of 154–164Gd has been calculated using Bohr–Mottelson Model and Interacting Vector Boson Model only. To determine the property of the ground-state band, the ratio (r(I+2)/I) and E-GOS curve (Eγ/I) as a function of the spin (I) have been drawn. The reduced transition probabilities B(E2) of these nuclei were calculated. The results were compared with the experimental data and the previous calculations. It is shown that there is a good agreement between the results found and especially with the experimental ones. The potential energy surface (PES) has been calculated within the framework using interacting boson model (IBM-1). The contour plot of the potential energy surfaces shows that the interested nuclei are deformed and have rotational characters.

Embedded random matrix ensembles from nuclear structure and their recent applications

Embedded random matrix ensembles generated by random interactions (of low body rank and usually two-body) in the presence of a one-body mean field, introduced in nuclear structure physics, are now established to be indispensable in describing statistical properties of a large number of isolated finite quantum many-particle systems. Lie algebra symmetries of the interactions, as identified from nuclear shell model and the interacting boson model, led to the introduction of a variety of embedded ensembles (EEs). These ensembles with a mean field and chaos generating two-body interaction generate in three different stages, delocalization of wave functions in the Fock space of the mean-field basis states. The last stage corresponds to what one may call thermalization and complex nuclei, as seen from many shell model calculations, lie in this region. Besides briefly describing them, their recent applications to nuclear structure are presented and they are (i) nuclear level densities with interactions; (ii) orbit occupancies; (iii) neutrinoless double beta decay nuclear transition matrix elements as transition strengths. In addition, their applications are also presented briefly that go beyond nuclear structure and they are (i) fidelity, decoherence, entanglement and thermalization in isolated finite quantum systems with interactions; (ii) quantum transport in disordered networks connected by many-body interactions with centrosymmetry; (iii) semicircle to Gaussian transition in eigenvalue densities with [Formula: see text]-body random interactions and its relation to the Sachdev–Ye–Kitaev (SYK) model for majorana fermions.

Partial dynamical symmetry and the vibrational structure of Cd isotopes

The recently reported deviations of selected non-yrast states in 110Cd from the expected sphericalvibrator behaviour, is addressed by means of an Hamiltonian with U(5) partial dynamical symmetry. The latter preserves the U(5) symmetry in a segment of the spectrum and breaks it in other states. The effect of intruder states is treated in the framework of the interacting boson model with configuration mixing.

Isospin degree of freedom in even-even 68-76Ge and 62-70Zn isotopes

The introduction of isotopic spin is significant in light nuclei as Ge and Zn isotopes in order to take into account isospin effects on energy spectra. Dynamical symmetries in spherical, $\gamma$ -soft limits and transition in the interacting boson model IBM-3 are analyzed. Analytic expressions and exact eigenenergies, electromagnetic transitions probabilities are obtained for the transition between spherical and $\gamma$ -soft shapes by using the Bethe ansatz within an infinite-dimensional Lie algebra in light mass nuclei. The corresponding algebraic structure and reduction chain are studied in IBM-3. For examples, the nuclear structure of the 68-76Ge and 62-70Zn isotopes is calculated in IBM-3 and compared with experimental results.

Description of the 190–199Hg Nuclei Under the Frameworks of IBM-1 and IBFM-1

The energy levels and the electric quadrupole transition probabilities B(E2; Ji → Jf) for even–odd 191–199Hg have been investigated. The negative spin states of the even–odd 191–199Hg isotopes are studied within the framework of the interacting boson–fermion model (IBFM–1). The single fermion is assumed to be in one of the 2f5/2, 3p3/2, and 3p1/2 single-particle orbits. It is found that the calculated negative spin state energy spectra of the even–odd 191–199Hg isotopes agree quite well with the experimental data. The B(E2) values are also calculated and compared with the experimental data. In general, the results are in reasonably good agreement with the previous experimental values. Furthermore, the energy levels, electric quadrupole transition probabilities, and the wave function for even–even 1901–198Hg isotopes (as core for even–odd nuclei) have been calculated within the framework of the interacting boson model (IBM-1). The predicted energy levels and B(E2) transition probability results are reasonably consistent with the experimental data. These calculations have been compared with previous it and almost better than it. The study of the wave function’s structure shows that all interesting nuclei are deformed and have dynamical symmetry O(6) characters.