arXiv subjects

A. El Batoul

Publications and source records attributed to A. El Batoul.

24 records · Page 2Linked to original sources

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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arXiv2016

On γ-rigid regime of the Bohr-Mottelson Hamiltonian in the presence of a minimal length

A prolate γ-rigid regime of the Bohr-Mottelson Hamiltonian within the minimal length formalism, involving an infinite square well like potential in β collective shape variable, is developed and used to describe the spectra of a variety of vibrational-like nuclei. The effect of the minimal length on the energy spectrum and the wave function is duly investigated. Numerical calculations are performed for some nuclei revealing a qualitative agreement with the available experimental data.

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arXiv2015

Closed analytical solutions of the d-dimensional Schrödinger equation with deformed Woods-Saxon potential plus double ring-shaped potential

By employing the Pekeris approximation, the D-dimensional Schrödinger equation is solved for the nuclear deformed Woods-Saxon potential plus double ring-shaped potential within the framework of the Asymptotic Iteration Method (AIM). The energy eingenvalues are given in a closed form and the corresponding normalized eigenfunctions are obtained in terms of hypergeometric functions. Our general results reproduce many predictions obtained in the literature, using the Nikiforov-Uvarov method (NU) and the Improved Quantization Rule approach, particulary those derived by considering Woods-Saxon potential without deformation and/or without ring shape interaction.

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arXiv2015

Exact solutions of Deformed Schrodinger Equation with a class of non central physical potentials

In this paper we present exact solutions of Schrodinger equation (SE) for a class of non central physical potentials within the formalism of position-dependent effective mass. The energy eigenvalues and eigenfunctions of the bound-states for the Schrodinger equation are obtained analytically by means of asymptotic iteration method (AIM) and easily calculated through a new generalized decomposition of the effective potential allowing easy separation of the coordinates. Our results are in excellent agreement with other works in the literature.

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