No abstract

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.

In this paper, we solve the eigenvalues and eigenvectors problem with Bohr collective Hamiltonian for triaxial nuclei. The β-part of the collective potential is taken to be equal to Hulthén potential while the γ-part is defined by a new generalized potential obtained from a ring shaped one. Analytical expressions for spectra and wave functions are derived by means of a recent version of the asymptotic iteration method and the usual approximations. The calculated energies and B(E2) transition rates are compared with experimental data and the available theoretical results in the literature.

In a recent work [Phys. Rev. C 84, 044321 (2011)] M. J. Ermamatov and P. R. Fraser have studied rotational and vibrational excited states of axially symmetric nuclei within the Bohr Hamiltonian with different mass parameters. However, the energy formula that the authors have used contains some inaccuracies. So the numerical results they obtained seem to be controversial. In this paper, we revisit all calculations related to this problem and determine the appropriate formula for the energy spectrum. Moreover, in order to improve such calculations, we reconsider this problem within the framework of the deformation-dependent mass formalism. Also, unlike the work of Bonatsos et al. [Phys. Rev. C 83, 044321 (2011)], in which the mass parameter has not been considered, we will show the importance of this parameter and its effect on numerical predictions.

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.

In the present work, we have obtained closed analytical expressions for eigenvalues and eigenfunctions of the Bohr Hamiltonian with the Manning-Rosen potential for γ−unstable nuclei as well as exactly separable rotational ones with γ ≈ 0. Some heavy nuclei with known β and γ bandheads have been fitted by using two parameters in the γ−unstable case and three parameters in the axially symmetric prolate deformed one. A good agreement with experimental data has been achieved.

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 β shape variable. In the resulting solution, called X(3)-D-ML, the ground state and the first β-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.

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.