Extended study on a quasi-exact solution of the Bohr Hamiltonian

Budaca, R.; Buganu, P.; Chabab, M.; Lahbas, A.; Oulne, M.

doi:10.1016/j.aop.2016.09.011

Cited by 58 publications

(64 citation statements)

References 106 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Details of β t calculations are given in Appendix A, while m L,b is given by Eq. (25). The obtained formula given by Eq.…”

Section: Treatment Of the Case α = 0 Within Qpmmentioning

confidence: 93%

“…[4,14]. Other efforts have also been directed to special realizations in the framework of the Bohr-Mottelson model and its extensions [15,16,17,18,19,20,21,22,23,24,25] where the collective shape variables or inertial parameters are imposed by some constraints. From a structural point of view, the collective Bohr Hamiltonian induces, however, a coupling of the β, γ, and rotational degrees of freedom, thereby yielding a rich set of physical phenomena.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2018

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…Details of β t calculations are given in Appendix A, while m L,b is given by Eq. (25). The obtained formula given by Eq.…”

Section: Treatment Of the Case α = 0 Within Qpmmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

Self Cite

View full text Add to dashboard Cite

show abstract

“…Here, it is to be noted that, to achieve correctly such a comparison, the experimental data have been taken from Ref. [9] and the used number of states in formula (41) was N instead of N − 1 in order to be conform to the used calculation procedure in [8] and [9]. Thus, one can see that the present results are fairly better than those obtained by Z(4)-sextic model.…”

Section: Level Bands and Effect Of Centrifugal Potential And Deformatmentioning

confidence: 58%

“…For both Z(4) and X(3), an infinite square well potential has been used for the β variable. Also, it has been applied for treating γ-rigid nuclei by making use of different model potentials for describing β-vibrations like, for example, the harmonic oscillator [7], the sextic potential [8,9], the quartic oscillator potential [10] and the Davidson one within X(3) symmetry [11,12]. Recently, this Hamiltonian has been used as a first application of the minimal length formalism in nuclear structure [13].…”

Section: Introductionmentioning

confidence: 99%

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

Buganu¹,

Chabab

Batoul

et al. 2018

Nuclear Physics A

Self Cite

View full text Add to dashboard Cite

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 108−116 Pd, 128−132 Xe, 136, Pt 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.

show abstract

“…A unified presentation of the quasi-exact solutions of the Bohr Hamiltonian with a sextic potential has been recently given in Ref. [24], therefore here from space reasons we will discuss only an example known as X(3)-Sextic [22]. X(3)-Sextic, due to the special properties of the sextic potential, can simulate a shape phase transition from a γ-rigid prolate harmonic vibrator to an anharmonic one crossing a critical region where the potential is flat.…”

Section: Introductionmentioning

confidence: 99%

Shape phase transition in γ-rigid prolate nuclei

Buganu¹,

Budaca²

2017

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. A γ-rigid prolate version of the Bohr-Hamiltonian is quasi-exactly solved for a sextic oscillator potential. Both energies and wave functions are obtained in analytical form depending, up to a scale factor, on a single free parameter. Moreover, due to the special properties of the sextic potential, a shape evolution can be covered from a γ-rigid prolate harmonic vibrator to an anharmonic one crossing a critical region where the potential is flat.

show abstract

Extended study on a quasi-exact solution of the Bohr Hamiltonian

Cited by 58 publications

References 106 publications

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

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

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

Shape phase transition in γ-rigid prolate nuclei

Contact Info

Product

Resources

About