Interacting Boson Fermion Model Research Articles

Microscopic calculation of the β− decays of 151Sm, 171Tm, and 210Pb with implications to detection of the cosmic neutrino background

The electron spectral shapes corresponding to the low-Qβ−-decay transitions Sm151(5/2g.s.−)→Eu151(5/2g.s.+), Sm151(5/2g.s.−)→Eu151(7/21+), Tm171(1/2g.s.+)→Yb171(1/2g.s.−), Tm171(1/2g.s.+)→Yb171(3/21−), Pb210(0g.s.+)→Bi210(1g.s.−), and Pb210(0g.s.+)→Bi210(01−) have been computed using beta-decay theory with several refinements for these first-forbidden nonunique (ff-nu) β− transitions. These ff-nu β− transitions have non-trivial electron spectral shapes with transition nuclear matrix elements (NMEs) computed by using the microscopic Interacting Boson-Fermion Model (IBFM-2) for the decays of 151Sm and 171Tm, and the nuclear shell model (NSM) for the decay of 210Pb. Within the respective Q windows, the computed ff-nu electron spectral shapes deviate maximally at sub-percent level from the universal allowed shape, except for the transition Pb210(0g.s.+)→Bi210(1g.s.−), where the maximal deviation is some 2.7%. This confirms that the so-called ξ approximation is fairly good for most of these low-Qβ− transitions and thus the allowed shape is a rather good first approximation. Our computed spectral shapes could be of interest for experiments aiming to measure the cosmic neutrino background (CνB), like the PTOLEMY experiment. We have also derived CνB cross sections for the ground-state transitions of the considered nuclei at the β endpoint. Our findings indicate that more work on the atomic mismatch correction is needed in the future in order to extract reliable and precise CνB cross sections for any nuclear target.

Negative Doublet Bands with Different Shape in the 107Ag Nucleus

The existence of chirality in the negative high spin states in the 107Ag nucleus has been confirmed by the Interacting Boson-Fermion Model (IBFM). IBFM excited states and electromagnetic properties are in good agreement with the available experimental data. According to IBFM analysis, the negative parity doublet bands (3) and ( 4) in the 107Ag nucleus were interpreted as triaxial and axial shap respectively.

Investigation of Structure and Nuclear Shape Phase Transition in Odd Nuclei in a multi-j model

In this paper‎, ‎we study the nature of the dynamics in second-order Quantum Phase Transition (QPT) between vibrational ( ) and -unstable ( ) nuclear shapes‎. ‎Using a transitional Hamiltonian according to an affine SU(1,1) algebra in combination with a coherent state formalism, Shape Phase Transitions (SPT) in odd-nuclei in the framework of the Interacting Boson Fermion Model (IBFM) are investigated‎. ‎Classical analysis reveals a change in the system along with the transition in a critical point‎. ‎The role of a fermion with angular momentum j at the critical point on quantum phase transitions in bosonic systems is investigated via a semi-classical approach‎. ‎The effect of the coupling of the odd particle to an even-even boson core is discussed along with the shape transition and‎, ‎in particular‎, ‎at the critical point‎. Our study confirms the importance of the odd nuclei as necessary signatures to characterize the occurrence of the phase transition and determine the critical point's precise position‎.

Entanglement entropy as a signature of a quantum phase transition in nuclei in the framework of the interacting boson model and interacting boson-fermion model

Background: One of the fundamental problems of quantum information science is quantum entanglement. Recently, quantum phase transition in nuclear systems is studied in connection with quantum entanglement.Purpose: In this paper, the use of entanglement entropy as a suitable signal for the study of quantum phase transition in the even-even and odd-$A$ nuclei is investigated. The effect of the coupling of a single fermion to a boson core on entanglement entropy is studied.Method: By use of the affine $SU(1,1)$ Lie algebra and through the Schmidt decomposition in the framework of the interacting boson model (IBM) and interacting boson-fermion model (IBFM), entanglement entropy in the even-even and odd-$A$ are obtained. The entanglement entropy is used for tracking and studying the shape phase transition in these nuclei.Results: The entanglement entropy in the IBM and the IBFM is calculated. The entanglement entropy values of the low-lying states of $^{122--134}\mathrm{Xe}, ^{102--110}\mathrm{Pd}$, and $^{123--133}\mathrm{Xe}$ were calculated and analyzed. It is found that entanglement entropy is a suitable order parameter to detect shape phase transition in nuclear systems.Conclusions: The obtained results indicate that the entropy of entanglement is sensitive to the shape-phase transition between spherical and $\ensuremath{\gamma}$-unstable regions in nuclei. The results show that entanglement entropy is a powerful tool for identifying shape phase transitions in nuclei. It is found that the coupling of the single fermion with angular momentum $j$ to the even-even system does not change the geometry imposed by the boson core performing the transition and only the entanglement entropy values have been shifted by the addition of the odd particle with respect to the even case.

Positive parity low-spin states of even–odd 129−133Ba isotopes

The positive parity low-spin states of even-odd 129−133Ba isotopes were studied in this study using the Interacting Boson–Fermion Model (IBFM-1). The single fermion is predicted to be in one of three single-particle orbits: 2d5/2, 2d3/2, and 3s1/2. The Interacting Boson Model (IBM-1) was used to investigate the energy levels, electric quadrupole transition probabilities, and potential energy surface of even-even Barium isotopes (a core for even-odd nuclei).The measured positive parity low-state energy spectra and predicted energy levels, as well as the B(E2) transition probabilities, are reasonably consistent with the experimental data and previous research for Ba isotopes. The potential energy surface contour plot reveals that all interesting nuclei are deformed and have γ-unstable-like properties.

Magnetic moment of the 11/2− isomeric state in Mo99 and neutron spin g factor quenching in A≈100 nuclei

The gyromagnetic factor of the low-lying ${E}_{x}=684.10(19)\phantom{\rule{4pt}{0ex}}\mathrm{keV}$ isomeric state of the nucleus $^{99}\mathrm{Mo}$ was measured using the time-dependent perturbed angular distribution technique. This level is assigned a spin and parity of ${J}^{\ensuremath{\pi}}=11/{2}^{\ensuremath{-}}$, with a half-life of ${T}_{1/2}=742(13)\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$. The state of interest was populated and spin-aligned via a single-neutron transfer on a highly enriched $^{98}\mathrm{Mo}$ target. A magnetic moment ${\ensuremath{\mu}}_{\mathrm{expt}.}=\ensuremath{-}0.627(20){\ensuremath{\mu}}_{\mathrm{N}}$ was obtained. This result is far from the Schmidt value expected for a pure single-particle $\ensuremath{\nu}{h}_{11/2}$ state. A comparison of experimental spectroscopic properties of this nucleus is made with results of multishell Interacting boson-fermion Model (IBFM-1) calculations. In this approach, the ${J}^{\ensuremath{\pi}}=11/{2}^{\ensuremath{-}}$ isomeric state in $^{99}\mathrm{Mo}$ has a pure $\ensuremath{\nu}{h}_{11/2}$ configuration. Its magnetic moment, as well as that of other two excited states could be reasonably well reproduced by reducing the free neutron spin $g$ factor with a quenching factor of 0.45. This low value is not appropriate only for this case, similar values for the quenching factor being also required in order to describe magnetic moments in other nuclei from the same mass region.

Description of the negative- and positive-parity states in odd-A Radon and Francium isotopes within the framework of the interacting Boson–Fermion model

The negative- and positive-parity states and electromagnetic transitions for [Formula: see text]Rn and [Formula: see text]Fr nuclei have been studied by using the Interacting Boson–Fermion Approximation (IBFM-1). Based on our calculations, the spin assignments for some states with uncertain spin have been done. Energy spectra, electromagnetic transition probabilities and branching ratios in these isotopes are calculated and compared with available experimental data. The wave functions are analyzed to understand the nuclear structure. In addition, some predictions of levels that have no experimental data are presented such as spin and electromagnetic transitions. Good results were obtained with a decrease in the collectivity properties, especially for the most neutron-deficient isotopes.

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

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.

β -decay rates of Rh115,117 into Pd115,117 isotopes in the microscopic interacting boson-fermion model

The structure of odd-$A$ $^{(115,117)}$Rh and $^{(115,117)}$Pd isotopes is studied by means of the neutron-proton Interacting Boson-Fermion Model (IBFM-2). $J^P = \frac{1}{2}^+$ quantum number assignment for the $^{(115,117)}$Pd ground-states is critically discussed and the predicted energy levels are compared to the existing experimental data. The resulting nuclear wave functions are used to compute the $\beta$-decay $ft$ values of the transitions from $^{(115,117)}$Rh to $^{(115,117)}$Pd in the microscopic IBFM-2 and the results compared with the data.

Some Electromagnetic Transition Properties of Odd-A Palladium Isotopes

In this study, the Palladium nuclei have been studied by interacting boson fermion model for even-odd nuclei. The isotopes under study have proton number 46 and neutron numbers 63-67. The calculations involved the eigenstates and reduce electric probability. The calculations show that the energy levels are reasonable with experimental data. The B(E2) values compared with those of experimental and are in good agreements. All calculations compared with experimental and give more data for reader.

SD-pair shell model: Vibrational and rotational limits in the interacting boson–fermion model for like-nucleon system

Typical features of the Bose–Fermi symmetries associated with [Formula: see text] and [Formula: see text] limits in the interacting boson model are described in the SD-pair shell model (SDPSM) framework for like-nucleon system. It is found that the limiting spectra associated with [Formula: see text] (vibrational) and [Formula: see text] (rotational) in the interacting boson–fermion model can be well reproduced in the SDPSM framework. It is shown that coupling of collective degree of freedom with the single-particle degree of freedom in the pairing interaction almost has no effect on the spectrum of odd-A system comparing to the adjacent even–even system, while the coupling of the collective degree of freedom with the single-particle degree of freedom in the quadrupole–quadrupole interaction results in the level splitting of several excited levels.

Positive-parity states and electromagnetic transitions of odd-A Pr and Ce isotopes

Energy levels and electromagnetic transition probabilities of odd-mass [Formula: see text] and [Formula: see text] isotopes have been calculated using the interacting boson fermion model. The even–even [Formula: see text] isotopes have been used as the cores. In the model space, the bosons have angular momentum, [Formula: see text] ([Formula: see text]-boson) and [Formula: see text] ([Formula: see text]-boson) have been considered, while the nine protons for [Formula: see text] and 19–25 neutrons for [Formula: see text] are allowed to occupy the [Formula: see text] and [Formula: see text] single particle orbitals. The quasi-particle energies and occupation probabilities have been obtained by solving the BCS equation. According to the model space, the wave function for low-lying states has been investigated. The calculated results are in good agreement with the available experimental data.

β decay of odd- A nuclei with the interacting boson-fermion model based on the Gogny energy density functional

The low-energy excitations and $\beta$ decays of odd-A nuclei are studied within the interacting boson-fermion model (IBFM), based on the Gogny-D1M nuclear energy density functional (EDF). The constrained Hartree-Fock-Bogoliubov (HFB) approximation is employed to compute potential energy surfaces in terms of triaxial quadrupole degrees of freedom for even-even Xe and Ba nuclei in the mass $A\approx 130$ region. The mean field approximation also provides spherical single-particle energies and occupation probabilities for the neighboring odd-A nuclei. Those quantities represent a microscopic input for spectroscopic calculations in odd-A Xe and Ba, Cs and La isotopes. The Gamow-Teller (GT) and Fermi (F) transition matrix elements, needed to compute $\beta$-decay $\log{ft}$ values are obtained without any phenomenological fitting. It is shown that both the low-lying states and $\beta$ decays of the studied odd-A systems are described reasonably well within the employed theoretical framework.

Quantum phase transition phenomena in odd-A nuclei

Quantum phase transitions in even-even nuclei been extensively studied both in theory and experiment in the recent years. Odd-even nuclei can be considered as examples of mixed Bose-Fermi systems with a single fermion coupled to an even-even core. The eÆect of a fermion with angular momentum j on quantum phase transi- tions of a bosonic system comprised of s (L=0) and d (L=2) bosons is investigated. The analysis is based on an Interacting Boson Fermion Model (IBFM) Hamiltonian and its classical limit and it demostrates the changes in the energy level structure as well as the classical and quantum order parameters involved. Some experimental evidence is also presented and compared with theoretical calculations

Lifetimes and shape-coexisting states of Zr99

Lifetimes of intermediate-spin states in two rotational bands of 99Zr have been measured. These states were populated following the neutron-induced fission of 235U at the PF1B beamline of the Institut Laue-Langevin, Grenoble, during the EXILL-FATIMA campaign. The nucleus 99Zr59 exhibits shape coexistence and lies precisely on the border of an abrupt change in ground-state deformation when going from N=58 to N=60, making its study interesting for understanding the mechanisms involved in the rapid onset of deformation here. The B(E2) values extracted for decays in the ν3/2[541] band allow quadrupole deformations of β2=0.34(1) and 0.26(3) to be determined for the 821.6- and 1236.6-keV members, whereas β2=0.32(3) was found for the 850.5-keV member of the ν3/2[411]band. Some of the excited states known in 99Zr have been reasonably described with interacting boson-fermion model (IBFM) calculations. Type-II shell evolution is proposed to play a major role in modifying single-particle energies in 99Zr.

Two-nucleon transfer and Double Charge Exchange reactions

In this contribution we present a study of a direct and sequential two-nucleon transfer within the microscopic Interacting Boson Model (IBM-2) and Interacting Boson- Fermion Model (IBFM), respectively. We present our preliminary results for heavy-ion double-charge-exchange40Ca(18O,18Ne)40ArG.S. differential cross section too.

Description of neutron-rich odd-mass krypton isotopes within the interacting boson-fermion model based on the Gogny energy density functional

The low-lying structure of neutron-rich odd-mass Kr isotopes is studied within the interacting boson-fermion model (IBFM) based on the Gogny-D1M energy density functional (EDF). The $(\beta,\gamma)$-deformation energy surfaces, spherical single-particle energies and occupation probabilities of the odd-mass systems are obtained using the constrained Hartree-Fock-Bogoliubov (HFB) approximation. Those quantities are used as a microscopic input to determine most of the parameters of the IBFM Hamiltonian. The remaining parameters are specifically tailored to the experimental spectrum for each of the studied odd-mass nuclei. A gradual structural evolution is predicted for the odd-mass isotopes $^{87-95}$Kr as a function of the nucleon number which, agrees well with the gradual growth of collectivity observed experimentally in the neighboring even-even isotopes.

High-spin level structure and Ground-state phase transition in the odd-mass 103−109Rh isotopes in the framework of exactly solvable sdg interacting boson–fermion model

In this article, the negative-parity states in the odd-mass Rh103−109 isotopes in terms of the sd and sdg interacting-boson fermion models were studied. The transitional interacting boson–fermion model Hamiltonians in sd and sdg-IBFM versions based on affine SU(1,1) Lie Algebra were employed to describe the evolution from the spherical to deformed gamma unstable shapes along with the chain of Rh isotopes. In this method, sdg-IBFM Hamiltonian, which is a three level pairing Hamiltonian was determined easily via the exactly solvable method. Some observables of the shape phase transitions such as energy levels, the two neutron separation energies, signature splitting of the γ-vibrational band, the α-decay and double β−-decay energies were calculated and examined for these isotopes. The present calculation correctly reproduces the spherical to gamma-soft phase transition in the Rh isotopes. Some comparisons were made with sd-IBFM.

Shape transitions in odd-mass γ -soft nuclei within the interacting boson-fermion model based on the Gogny energy density functional

The interacting boson-fermion model (IBFM), with parameters determined from the microscopic Hartree-Fock-Bogoliubov (HFB) approximation, based on the parametrization D1M of the Gogny energy density functional (EDF), is employed to study the structural evolution in odd-mass $\gamma$-soft nuclei. The deformation energy surfaces of even-even nuclei, single-particle energies and occupation probabilities of the corresponding odd-mass systems have been obtained within the constrained HFB approach. Those building blocks are then used as a microscopic input to build the IBFM Hamiltonian. The coupling constants of the boson-fermion interaction terms are taken as free parameters, fitted to reproduce experimental low-lying spectra. The diagonalization of the IBFM Hamiltonian provides the spectroscopic properties for the studied odd-mass nuclei. The procedure has been applied to compute low-energy excitation spectra and electromagnetic transition rates, in the case of the $\gamma$-soft odd-mass systems $^{129-137}$Ba, $^{127-135}$Xe, $^{129-137}$La and $^{127-135}$Cs. The calculations provide a reasonable agreement with the available experimental data and agree well with previous results based on the relativistic mean-field approximation.

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.