Analytical solution for the Davydov-Chaban Hamiltonian with a sextic potential for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>30</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math>

Buganu, P.; Budaca, R.

doi:10.1103/physrevc.91.014306

Cited by 74 publications

(67 citation statements)

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“…In the first case there exists a coexistence between the two chiral solutions. As a matter of fact the broadening of the probability density distribution attributed to coexistence phenomena have immediate repercussions on the electromagnetic properties [54][55][56].…”

Section: Comparison With Experimentsmentioning

confidence: 99%

Semiclassical description of chiral geometry in triaxial nuclei

Budaca

2018

Phys. Rev. C

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A triaxial particle-rotor Hamiltonian for three mutually perpendicular angular momentum vectors corresponding to two high-j quasiparticles and the rotation of a triaxial collective core, is treated within a time-dependent variational principle. The resulting classical energy function is used to investigate the rotational dynamics of the system. It is found that the classical energy function exhibits two minima starting from a critical angular momentum value which depends on the singleparticle configuration and the asymmetry measure γ. The emergence of the two minima is attributed to the breaking of the chiral symmetry. Quantizing the energy function for a given angular momentum, one obtains a Schrödinger equation with a coordinate dependent mass term for a symmetrical potential which changes from a single to a double well shape as the angular momentum pass the critical value. The energies of the chiral partner bands for a given angular momentum are then given by the lowest two eigenvalues. The procedure is exemplified for maximal triaxiality and two h 11/2 quasiparticles, with the results used for the description of the chiral doublet bands in 134 Pr.

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Section: Comparison With Experimentsmentioning

confidence: 99%

Semiclassical description of chiral geometry in triaxial nuclei

Budaca

2018

Phys. Rev. C

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“…This is explained by the fact that here the mass parameter depends on the β variable, while in Refs. [8,9] the mass is considered as a constant. The equation of the Davydov-Chaban Hamiltonian with sextic potential and mass parameter depending on deformation is very difficult to solve due to the quasi-exactly solvable method of the sextic potential.…”

Section: Level Bands and Effect Of Centrifugal Potential And Deformatmentioning

confidence: 99%

“…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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“…A special attention in this sense is deserved by the quartic anharmonic oscillator potential (QAOP) which not only simulates the square well but is also the lowest order anharmonic potential. The next-order anharmonic term leads to a sextic potential which allows a nonvanishing minimum, being thus suitable for the description of deformed nuclei [9,10,11,12,13,14,15,16,17].…”

Section: Harmonic Oscillator Potential With a Quartic Anharmonicity Imentioning

confidence: 99%

Harmonic oscillator potential with a quartic anharmonicity in the prolate γ-rigid collective geometrical model

Budaca¹

2015

AIP Conference Proceedings

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Abstract. An analytical expression for the energy spectrum of the ground and β bands was obtained in the axially symmetric γ-rigid regime of the Bohr-Mottelson Hamiltonian with a general quartic anharmonic oscillator potential in the β shape variable. As the Schrodinger equation for such a potential is not exactly solvable, the energy formula is derived on the basis of the JWKB approximation. Due to the scaling property of the quartic oscillator problem, the resulting energy depends on a single parameter up to an overall multiplicative constant. The upper limit of the domain of values for the free parameter is established by comparing the ground state eigenvalues with the corresponding numerically calculated results. Studying the behavior of the potential and of the whole energy spectrum as function of the free parameter, one establishes the present model's place between other γ-rigid models. The agreement with experiment is achieved through model fits for few nearvibrational nuclei.

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Analytical solution for the Davydov-Chaban Hamiltonian with a sextic potential forγ=30∘

Cited by 74 publications

References 50 publications

Semiclassical description of chiral geometry in triaxial nuclei

Semiclassical description of chiral geometry in triaxial nuclei

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

Harmonic oscillator potential with a quartic anharmonicity in the prolate γ-rigid collective geometrical model

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