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

Abstract

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.

Coriolis contribution to excited states of odd-mass nuclei with different deformation-dependent mass coefficients

“…In this present work we extend the previous one of [27] by including Coriolis interaction of the angular momentum of the external nucleon with that of the core of the odd-mass nucleus. In this case, K and Ω are nonconserved quantities.…”

“…The theory of collective quadrupole-type excitations, which takes into account the coupling of single-particle and collective motions, enables us to explain some regularities observed in the excitation spectra of deformed odd-mass nuclei. Recently, some studies are realized within the DDMF for some of such nuclei [27] but without taking into account the Coriolis interaction. They have been realized in a simple way where quantum numbers of the projections of angular momentum of a nucleus to the third principal axis K and that of the external nucleon Ω are good quantum numbers.…”

“…A similar study to that of [28] has been carried out in [29] with the aim of investigating the band structure of proton-odd nuclei 155 Eu and 153 Eu. However, the used energy formula in both [28,29] was inaccurate as proved in [17] for even-even nuclei and in [27] for the case of odd-A nuclei.…”

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

“…This approach has been firstly achieved by applying Davidson [10] and Kratzer [11] potentials to a huge number of γ-unstable and axially symmetric prolate deformed nuclei. It has also been extended to a conjunction between the prolate γ-rigid and γ-stable collective motions [12], and then tested on Davydov-Chaban Hamiltonian to describe triaxial shape nuclei around γ = π/6 [13] and recently applied to the description of odd-A nuclei by taking into account the three different mass coefficients [14].…”

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

“…Since its introduction for the first time in semi-conductor physics [1], the position dependent mass formalism has been applied in several works in many different fields of physics [2,3,4,5,6,7,8,9,10,11,12,13,14]. Such a formalism has been adopted in nuclear physics for concrete reasons, namely: from the comparison of theoretical calculations with the experimental data, it has been pointed out that the mass tensor should be taken as a function of the collective coordinates [10,15,16,17,18,19,20,21].…”