Bohr Hamiltonian with Hulthén plus ring-shaped potential for triaxial nuclei with Deformation-Dependent Mass term

Abstract

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.

Collective motion in γ-unstable nuclei within energy-dependent Davidson potential and deformation dependent mass formalisms

“…Closed analytical expressions of the model for the spectra and the corresponding wave functions are obtained by solving the relevant differential equation by means of asymptotic iteration method (AIM) [26]. This method had proved to be a useful tool when dealing with physical problems involving Schrödinger-type equation [27][28][29][30]. We will proceed to a systematic comparison of the obtained results, by the presently elaborated model, for energy spectra and electromagnetic transition probabilities of several even-even nuclei in the nucleic chart region from 98 Ru to 200 Pt, with the available experimental data and some theoretical models.…”

A γ-Rigid Solution of the Bohr Hamiltonian with Deformation-Dependent Mass Term for Kratzer Potential and γ = 30°

“…Such symmetries, for example, E(5) [3] and X (5) [4] correspond to the shape phase transitions U( 5)↔O (6) and U(5)↔ SU (3), respectively. In this context, considerable attempts have been done for several potentials to achieve analytical solutions of the Bohr Hamiltonian, either in the usual case where the mass parameter is assumed to be a constant [5][6][7][8][9], or by introducing the Deformation-Dependent Mass Formalism (DDMF) [10][11][12][13][14]. In addition, another direction of research was to investigate such phenomena by imposing a γ-rigidity as in the case of Z(4) [15] or X(3) [16].…”