Bohr Hamiltonian for $\gamma = 0^{\circ}$ γ = 0 ∘ with Davidson potential

Yigitoglu, I.; Gökbulut, Melek

doi:10.1140/epjp/i2017-11609-3

Cited by 8 publications

(4 citation statements)

References 39 publications

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“…The same approach has been performed in Ref [37], in the framework of the Kratzer potential. In earlier works [19,22,39,40,41], this minimum was problematic since its obtained values were unphysical (β 0 > 1) in respect to the nuclear deformation. In the same table ( Table 2), we present the bandhead ratios R 4/2 calculated by our model compared to the experimental data.…”

Section: Modelsmentioning

confidence: 93%

“…The collective model of Bohr and Mottelson [1,2] was designed to describe the collective low energy states of the nucleus in terms of rotations and vibrations of its ground state shape, which is parameterized by β and γ variables defining the deviation from sphericity and axiallity, respectively. Recently, considerable attempts have been done for several potentials to achieve analytical solutions of Bohr Hamiltonian, either in the usual case where the mass parameter is assumed to be a constant [3][4][5][6][7][8] or in the context of deformation dependent mass formalism [9][10][11][12]. Moreover, a great interest for solutions of this model has been revived with the proposal of E(5) [13] and X(5) [14] symmetries, which describe the critical points of the shape phase transitions between spherical and γ-unstable shapes and, from spherical to axial symmetric deformed shapes, respectively.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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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.

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Section: Modelsmentioning

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

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“…The non-exact or an approximate solution, for γ 0 ≈ π/6, is referred to as Z( 5) in [9,24,25] and others. Just like the case of X(3) in [24,[26][27][28][29], the γ-variable of the Z( 4) is treated as a fixed parameter.…”

Section: Introductionmentioning

confidence: 99%

Relative variation between γ coordinate and the potential of the Bohr Hamiltonian producing X(4) from Z(4)

Ajulo,

Oyewumi,

Orosun

et al. 2024

Phys. Scr.

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In this paper, four degree of freedom γ-rigid solutions of the Bohr Hamiltonian at γ0 = π/6 areobtained. The relative variation between γ and the potential of the Hamiltonian is employed to retrieve X(4) from Z(4). γ is varied in the interval 0 ≤ γ0 ≤ π/6 while the potential minimum, β0, is varied in the interval 0 ≤ β0 ≤ ∞. Very small value of β0 yields Z(4) while a large value of β0 produces X(4) and SU(3) is realized at β0 ≈ ∞. The solutions at γ0 = 0 correspond to X(4) while the solutions at γ0 = π/6 yield Z(4): a dynamic link between Z(4) and X(4) critical point symmetries (CPSs) has been provided. The fact that γ and β0 of the potential play the same role in the dynamical link between Z(4) and X(4) shows that β0 also measures the departure from axial symmetry to other shapes as γ does. In the experimental realization of the model, the conformation of 192Pt and 194Pt isotopes to the present Z(4) model shows that the present model can be employed in the description of triaxial rotors and γ-soft isotopes. 194Pt is shown to be the best choice for triaxial rigid rotor candidacy. 130Xe, a critical point isotope, which belongs to the class of γ-soft nuclei, reproduces this present model very well in all the states. Consequently, this present model can serve as a critical point model. 40,0 - β0 distribution for Z(4) and X(4) candidate isotopes shows a significant interval between the two models where the T (4) CPS lies.

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“…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

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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.

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Bohr Hamiltonian for $\gamma = 0^{\circ}$ γ = 0 ∘ with Davidson potential

Cited by 8 publications

References 39 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

Relative variation between γ coordinate and the potential of the Bohr Hamiltonian producing X(4) from Z(4)

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

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