Description of the isotope chain<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow /><mml:mrow><mml:mn>180</mml:mn><mml:mo>−</mml:mo><mml:mn>196</mml:mn></mml:mrow></mml:msup></mml:math>Pt within several solvable approaches

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.

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“…The Xe and P t isotopes were also analyzed in Refs. [37,47,48] using different approaches. All bands (i.e.…”

Section: Numerical Resultsmentioning

confidence: 99%

Bohr Hamiltonian with Hulthén plus ring-shaped potential for triaxial nuclei

2015

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“…Other numerical applications of these solutions were done in Refs. [26][27][28]. In the present case, the variables are exactly separated and the resulted β equation is quasi-exactly solved.…”

Section: Introductionmentioning

confidence: 99%

Sextic potential for $\gamma $-rigid prolate nuclei

Buganu

Budaca

2015

J. Phys. G: Nucl. Part. Phys.

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Abstract.The equation of the Bohr-Mottelson Hamiltonian with a sextic oscillator potential is solved for γ-rigid prolate nuclei. The associated shape phase space is reduced to three variables which are exactly separated. The angular equation has the spherical harmonic functions as solutions, while the β equation is brought to the quasi-exactly solvable case of the sextic oscillator potential with a centrifugal barrier. The energies and the corresponding wave functions are given in closed form and depend, up to a scaling factor, on a single parameter. The 0 + and 2 + states are exactly determined, having an important role in the assignment of some ambiguous states for the experimental β bands. Due to the special properties of the sextic potential, the model can simulate, by varying the free parameter, a shape phase transition from a harmonic to an anharmonic prolate β-soft rotor crossing through a critical point. Numerical applications are performed for

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“…It is interesting that although the variation of the nuclear properties with the energy is a well established fact, the energy dependent potentials are poorly employed in nuclear physics, with only few notable applications regarding quark systems [18,19]. On the other hand, some authors expended great effort to ensure the state independence of the potential [11][12][13][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Bohr Hamiltonian with an energy-dependent $\gamma$ γ -unstable Coulomb-like potential

Budaca

2016

Eur. Phys. J. A

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An exact analytical solution for the Bohr Hamiltonian with an energy dependent Coulomb-like γ-unstable potential is presented. Due to the linear energy dependence of the potential's coupling constant, the corresponding spectrum in the asymptotic limit of the slope parameter resembles the spectral structure of the spherical vibrator, however with a different state degeneracy. The parameter free energy spectrum as well as the transition rates for this case are given in closed form and duly compared with those of the harmonic U (5) dynamical symmetry. The model wave functions are found to exhibit properties that can be associated to shape coexistence. A possible experimental realization of the model is found in few medium nuclei with a very low second 0 + state known to exhibit competing prolate, oblate and spherical shapes.

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Description of the isotope chain180−196Pt within several solvable approaches

Cited by 31 publications

References 44 publications

Bohr Hamiltonian with Hulthén plus ring-shaped potential for triaxial nuclei

Bohr Hamiltonian with Hulthén plus ring-shaped potential for triaxial nuclei

Sextic potential for $\gamma $-rigid prolate nuclei

Bohr Hamiltonian with an energy-dependent $\gamma$ γ -unstable Coulomb-like potential

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