arXiv subjects

A. Lahbas

Publications and source records attributed to A. Lahbas.

At least 19 recordsLinked to original sources

arXiv2026

Study of the shape coexistence in the 96Zr, 96Mo, 96Ru isobars

Three stable isobars, $^{96}_{40}$Zr$_{56}$, $^{96}_{42}$Mo$_{54}$ and $^{96}_{44}$Ru$_{52}$, which are in the vicinity of the harmonic oscillator proton shell closure Z=40 and the spin-orbit neutron shell closure N=50, are investigated for the presence of the shape coexistence and mixing phenomena. The ground state deformation of these isobars is extracted from the potential energy surface determined with the Covariant Density Functional Theory using a density-dependent point-coupling interaction, while the excited states are described involving the Bohr-Mottelson Hamiltonian with octic potential for both axially symmetric and $\gamma$-unstable quadrupole deformations. Within the broader view of the two approaches, the obtained results clearly highlight the significant contribution of these phenomena to the structure of the states of these nuclei.

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arXiv2026

Shape phase transition, coexistence and mixing in the $^{98-106}$Ru isotopes

The deformation properties within the $^{98-106}$Ru even-even isotopic chain, are investigated by means of the Covariant Density Functional Theory with a Density-Dependent Point-Coupling X parametrization. The considered nuclei are found to exhibit very shallow prolate and triaxial ground state deformation. This information is used to ascertain their dynamical behavior within prolate $\gamma$-stable and $\gamma$-unstable instances of a phenomenological Bohr-Mottelson Hamiltonian with an octic potential in the axial deformation variable. The comparative study of the low-lying collective states, revealed the presence of a shape phase transition from low to high deformation, as well as evidence of shape coexistence and mixing between spherical vibrator, $\gamma$-unstable or prolate configurations in ground and excited states. It is also shown that the effect of shape coexistence and mixing on the $\gamma$-band states can account to some extent for the typical $\gamma$-unstable staggering even in prolate $\gamma$-stable conditions.

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arXiv2023

Probing DDM and ML quantum concepts in shape phase transitions of $\gamma$-unstable nuclei

In a recent paper (S. Ait El Korchi et al. 2020 EPL 132 52001), we explored, inside the context of Critical Point Symmetries (CPSs) X(3) and Z(4), a correlation between two exceedingly known quantum concepts, the Minimal Length (ML) and the Deformation-Dependent Mass (DDM), that are commonly applied in various areas of physics. Such a correlation has been strongly identified in transition nuclei by calculating some physical observables of that quantum system, like as energy spectra, moments of inertia and transition probabilities. In this paper we extend that study to E(5) dynamical symmetry corresponding to the shape phase transition U(5)$\leftrightarrow$O(6). The experimental realization of the models was found to occur in some nuclei, using the existing phenomenological potentials : Infinite Square Well, Davidson and Kratzer, whose models fits provide the best agreement. Importantly the calculations performed in this work using these potentials corroborate the fact that the revealed correlation between both quantum concepts is not destructively affected by the presence of other model parameters and hence its existence is independent of the form or type of the used potential. Undoubtedly, the present work will open the way for more investigations of this correlation in the limits of other critical points symmetries in nuclear shape phase transitions which play today a major role in nuclear structure research from theoretical as well as experimental point of view.

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arXiv2022

Shape Coexistence in 74Ge, 74Se and 74Kr Investigated by Phenomenological and Microscopic Models

The deformation properties of 74Ge, 74Se and 74Kr are studied within the phenomenological Bohr-Mottelson model, having as input the experimental collective energy states, as well with Covariant Density Functional theories based on microscopic structural information. The results of these approaches are shown to be compatible in what concerns the presence of coexisting shapes in the considered nuclei, while the emergence of shape mixing is deduced from the phenomenological calculated collective states.

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arXiv2021

A $γ$-rigid solution of the Bohr Hamiltonian with deformation-dependent mass term for Kratzer potential and $γ= 30^\circ$

In this work, the Davydov-Chaban Hamiltonian, describing the collective motion of $γ$-rigid atomic nuclei, is amended by allowing the mass parameter to depend on the nuclear deformation. Further, Z(4)-DDM (Deformation-Dependent Mass) model is proposed by considering the Kratzer potential for the $β$ variable, and solving the problem by techniques of asymptotic iteration method (AIM). The results of the calculated spectra and $B(E2)$ transition rates for series of $^{192-196}$Pt isotopes are compared with the corresponding experimental data as well as with other theoretical models. Exact analytical expressions are derived for spectra and normalized wave functions of the Kratzer potential. The obtained results show an overall good agreement with the experimental data and an important improvement in respect to other models

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arXiv2020

Bohr Hamiltonian with Hulthen plus ring-shaped potential for triaxial nuclei with deformation-dependent mass term

In this work, we present a new version of the Bohr collective Hamiltonian for triaxial nuclei within Deformation-Dependent Mass formalism (DDM) using the Hulthén potential. We shall call the developed model Z(5)-HD. Analytical expressions for energy spectra are derived by means of the recent version of the Asymptotic Iteration Method. The calculated numerical results of energies and B(E2) transition rates are compared with the experimental data, and several theoretical results from Z(5) model, the model Z(5)-H using the Hulthén potential without DDM formalism as well as theoretical predictions of Z(5)-DD model with Davidson potential using DDM formalism. The obtained results show an overall agreement with experimental data and an important improvement in respect to the other models.

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arXiv2020

Excited states of odd-mass nuclei with different deformation-dependent mass coefficients

Experimental data indicate that the mass tensor of collective Bohr Hamiltonian cannot be considered as a constant but should be considered as a function of the collective coordinates. In this work our purpose is to investigate the properties of low-lying collective states of the odd nuclei $^{173}$Yb and $^{163}$Dy by using a new generalized version of the collective quadrupole Bohr Hamiltonian with deformation-dependent mass coefficients. The proposed new version of the Bohr Hamiltonian is solved for Davidson potential in $β$ shape variable, while the $γ$ potential is taken to be equal to the harmonic oscillator. The obtained results of the excitation energies and B(E2) reduced transition probabilities show an overall agreement with the experimental data. Moreover, we investigate the effect of the deformation dependent mass parameter on energy spectra and transition rates in both cases, namely: when the mass coefficients are different and when they are equal. Besides, we will show the positive effect of the present formalism on the moment of inertia.

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arXiv2019

Bohr Hamiltonian with Pöschl Teller potential in γ unstable and γ stable pictures

In this paper, we present an analytical solution for the Bohr Hamiltonian with the trigonometric Pöschl Teller (P.T) potential in the cases of γ unstable nuclei and γ stable axially symmetric prolate deformed ones with γ = 0. The energy spectra and corresponding wave functions are derived by means of the asymptotic iteration method. In addition, B(E2) transition rates are calculated and compared with experimental data. Overall good agreement is obtained for inter and intra band transitions within ground state and \b{eta} bands. Our numerical results, particularly for transition rates are much closer to experimental ones in comparison with those obtained by Davidson and Kratzer potentials which are widely used in the literature.

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arXiv2019

Comparaison between Coulomb and Hulthèn potentials within Bohr Hamiltonian for $γ$-rigid nuclei in the presence of minimal length

In this work we solve the Schrödinger equation for Bohr Hamiltonian with Coulomb and Hulthén potentials within the formalism of minimal length in order to obtain analytical expressions for the energy eigenvalues and eigenfunctions by means of asymptotic iteration method. The obtained formulas of the energy spectrum and wave functions, are used to calculate excitation energies and transition rates of $γ$-rigid nuclei and compared with the experimental data at the shape phase critical point X(3) in nuclei.

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arXiv2019

$γ$-rigid triaxial nuclei in the presence of a minimal length via a quantum perturbation method

In this work, we derive a closed solution of the Shr$ \ddot{o} $dinger equation for Bohr Hamiltonien within the minimal length formalism. This formalism is inspired by Heisenberg algebra and a generlized uncertainty principle (GUP), applied to the geometrical collective Bohr- Mottelson model (BMM) of nuclei by means of deformed canonical commutation relation and the Pauli-Podolsky prescription. The problem is solved by means conjointly of asymptotic iteration method (AIM) and a quantum perturbation method (QPM) for transitional nuclei near the critical point symmetry Z(4) corresponding to phase transition from prolate to $γ$-rigid triaxial shape. A scaled Davidson potentiel is used as a restoring potential in order to get physical minimum. The agreement between the obtained theoretical results and the experimental data is very satisfactory.

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arXiv2018

Nuclear shape phase transitions within a correlation between two quantum concepts

We present a correlation that we have revealed, for the first time, between both quantum concepts, namely: the Minimal Length (ML) and the Deformation Dependent Mass (DDM) in transitional nuclei near the critical points symmetries (CPS) X(3) and Z(4). Such a correlation could be considered as a new signature for these CPS. This new signature allowed us to predict new candidate nuclei for these critical points.

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arXiv2018

Collective motion in prolate γ-rigid nuclei within minimal length concept via a quantum perturbation method

Based on the minimal length concept, inspired by Heisenberg algebra, a closed analytical formula is derived for the energy spectrum of the prolate γ-rigid Bohr-Mottelson Hamiltonian of nuclei, within a quantum perturbation method (QPM), by considering a scaled Davidson potential in \b{eta} shape variable. In the resulting solution, called X(3)-D-ML, the ground state and the first \b{eta}-band are all studied as a function of the free parameters. The fact of introducing the minimal length concept with a QPM makes the model very flexible and a powerful approach to describe nuclear collective excitations of a variety of vibrational-like nuclei. The introduction of scaling parameters in the Davidson potential enables us to get a physical minimum of this latter in comparison with previous works. The analysis of the corrected wave function, as well as the probability density distribution, shows that the minimal length parameter has a physical upper bound limit.

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arXiv2018

Collective motion in triaxial nuclei within minimal length concept

The concept of minimal length, inspired by Heisenberg algebra, is applied to the geometrical collective Bohr- Mottelson model (BMM) of nuclei. With the deformed canonical commutation relation and the Pauli-Podolsky prescription, we have derived the quantized Hamiltonian operator for triaxial nuclei as we have previously done for axial prolate $γ$-rigid ones (M. Chabab et al., Phys. Lett. B 758 (2016) 212-218). By considering an infinite square well like potential in $β$ collective shape variable, the eigenvalues of the Hamiltonian are obtained in terms of zeros of Bessel functions of irrational order with an explicit dependence on the minimal length parameter. Moreover, the associated symmetry with the model that we have constructed here can be considered as a new quasi-dynamical critical point symmetries (CPSs) in nuclear structure. The theoretical results indicate a dramatic contribution (Low effect) of the minimal length to energy levels for lower values of the angular momentum and regular (significant effect) for higher values. In fact, these features show that the minimal length scenario which is useful in recognizing the properties of real deformed nuclei having high spins or strong rotations. Finally, numerical calculations are performed for some nuclei such as ${}^{124,128,130}$Xe and ${}^{114}$Pd revealing a qualitative agreement with the experimental data.

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arXiv2018

Davydov-Chaban Hamiltonian within the formalism of deformation-dependent effective mass for Davidson potential

In this work, we modify the Davydov-Chaban Hamiltonian describing the collective motion of a $γ$-rigid atomic nucleus by allowing the mass to depend on nuclear deformation. Exact analytical expressions are derived for energy spectra as well as normalized wave functions for Davidson potential. The model, called Z(4)-DDMD (Deformation Dependent Mass with Davidson potential), is achieved by using the Asymptotic Iteration Method (AIM). The numerical calculations for energy spectra and B(E2) transition probabilities are compared to the experimental data of $^{192-196}$Pt isotopes. The obtained results show an overall agreement with the experiment and an important improvement in respect to other models.

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arXiv2017

Davydov-Chaban Hamiltonian with deformation-dependent mass term for γ = 30°

Motivation : Several theoretical comparisons with experimental data have recently pointed out that the mass tensor of the collective Bohr Hamiltonian cannot be considered as a constant and should be taken as a function of the collective coordinates. Method : The Davydov-Chaban Hamiltonian, describing the collective motion of γ-rigid atomic nuclei, is modified by allowing the mass to depend on the nuclear deformation. Moreover, the eigenvalue problem for this Hamiltonian is solved for Davidson potential and γ = 30° involving an Asymptotic Iteration Method (AIM). The present model is conventionally called Z(4)-DDM-D (Deformation Dependent Mass with Davidson potential), in respect to the so called Z(4) model. Results : Exact analytical expressions are derived for energy spectra and normalized wave functions, for the present model. The obtained results show an overall agreement with the experimental data for 108-116Pd, 128-132Xe, 136;138Ce and 190-198Pt and an important improvement in respect to other models. Prediction of a new candidate nucleus for triaxial symmetry is made. Conclusion : The dependence of the mass on the deformation reduces the increase rate of the moment of inertia with deformation, removing a main drawback of the model and leading to an improved agreement with the corresponding experimental data.

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arXiv2016

Excited collective states of nuclei within Bohr Hamiltonian with Tietz-Hua potential

In this paper, we present new analytical solutions of the Bohr Hamiltonian problem that we derived with the Tietz-Hua potential, here used for describing the β-part of the nuclear collective potential plus harmonic oscillator one for the γ-part. Also, we proceed to a systematic comparison of the numerical results obtained with this kind of β-potential with others which are widely used in such a framework as well as with the experiment. The calculations are carried out for energy spectra and electromagnetic transition probabilities for γ-unstable and axially symmetric deformed nuclei. In the same frame, we show the effect of the shape flatness of the β-potential beyond its minimum on transition rates calculations.

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arXiv2016

Nuclear shape phase transition within a conjonction of γ-rigid and γ-stable collective behaviours in deformation dependent mass formalism

In this paper, we present a theoretical study of a conjonction of $γ$-rigid and $γ$-stable collective motions in critical point symmetries of the phase transitions from spherical to deformed shapes of nuclei using exactly separable version of the Bohr Hamiltonian with deformation-dependent mass term. The deformation-dependent mass is applied simultaneously to $γ$-rigid and $γ$-stable parts of this famous collective Hamiltonian. Moreover, the $β$ part of the problem is described by means of Davidson potential, while the $γ$-angular part corresponding to axially symmetric shapes is treated by a Harmonic Osillator potential. The energy eigenvalues and normalized eigenfunctions of the problem are obtained in compact forms by making use of the asymptotic iteration method. The combined effect of the deformation-dependent mass and rigidity as well as harmonic oscillator stiffness parameters on the energy spectrum and wave functions is duly investigated. Also, the electric quadrupole transition ratios and energy sprectrum of some $γ$-stable and prolate nuclei are calculated and compared with the experimental data as well as with other theoretical models.

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arXiv2016

Electric quadrupole transitions of the Bohr Hamiltonian with Manning-Rosen potential

Analytical expressions of the wave functions are derived for a Bohr Hamiltonian with the Manning{Rosen potential in the cases of γ-unstable nuclei and axially symmetric prolate deformed ones with γ=0. By exploiting the results we have obtained in a recent work on the same theme Ref. [1], we have calculated the B(E2) transition rates for 34 γ-unstable and 38 rotational nuclei and compared to experimental data, revealing a qualitative agreement with the experiment and phase transitions within the ground state band and showing also that the Manning-Rosen potential is more appropriate for such calculations than other potentials.

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