Electric quadrupole transitions of the Bohr Hamiltonian with the Morse potential

Inci, I.; Bonatsos, Dennis; Boztosun, I.

doi:10.1103/physrevc.84.024309

Cited by 47 publications

(37 citation statements)

References 44 publications

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“…The same set of experimental data for spectra and B(E2) transition rates has been used as in the cases of the Deformation Dependent Mass (DDM) Davidson model [17], the Exactly Separable Davidson (ESD) model [33], and the Morse potential [48,49], in order to facilitate comparisons of the various models among themselves and to the data. The theoretical predictions for the levels are obtained from Eq.…”

Section: A Spectra Of γ-Unstable Nucleimentioning

confidence: 99%

Bohr Hamiltonian with a deformation-dependent mass term for the Kratzer potential

et al. 2013

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The Deformation Dependent Mass (DDM) Kratzer model is constructed by considering the Kratzer potential in a Bohr Hamiltonian, in which the mass is allowed to depend on the nuclear deformation, and solving it by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. Analytical expressions for spectra and wave functions are derived for separable potentials in the cases of γ-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. Spectra and B(E2) transition rates are compared to experimental data. The dependence of the mass on the deformation, dictated by SUSYQM for the potential used, moderates the increase of the moment of inertia with deformation, removing a main drawback of the model.

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Section: A Spectra Of γ-Unstable Nucleimentioning

confidence: 99%

Bohr Hamiltonian with a deformation-dependent mass term for the Kratzer potential

et al. 2013

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“…We see that Eq . (3) has the same form as (8), obtained in the γ-unstable case, the only difference being that Λ in the first equation is replaced byΛ in the axially symmetric prolate deformed nuclei. In what follows we are going to use the symbol Λ.…”

Section: Common Form Of the Radial Partmentioning

confidence: 80%

Excited collective states of nuclei within Bohr Hamiltonian with Tietz-Hua potential

et al. 2017

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In this paper, we present new analytical solutions of the Bohr Hamiltonian problem that we derived with the Tietz-Hua potential, here used for describing the β-part of the nuclear collective potential plus harmonic oscillator one for the γ-part. Also, we proceed to a systematic comparison of the numerical results obtained with this kind of β-potential with others which are widely used in such a framework as well as with the experiment. The calculations are carried out for energy spectra and electromagnetic transition probabilities for γ-unstable and axially symmetric deformed nuclei. In the same frame, we show the effect of the shape flatness of the β-potential beyond its minimum on transition rates calculations. arXiv:1608.08674v1 [nucl-th] 30 Aug 2016In the next sections, all values of B(E2) are calculated in units of B(E2; 2+ 1 −→ 0 + 1 ).6

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“…However, it seems that changes to the Bohr Hamiltonian, e.g. by studying non-separable potentials [21] or by considering other solutions [22], do not overcome the deficiencies for the inter-band transitions. We also note that a variety of approaches addressed other shortcomings of the collective models by focusing on tri-axial deformations [23], or inclusion of isovector modes [24,25], see Ref.…”

Section: Introductionmentioning

confidence: 99%

Effective theory for the nonrigid rotor in an electromagnetic field: Toward accurate and precise calculations ofE2transitions in deformed nuclei

Pérez

Papenbrock

2015

Phys. Rev. C

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We present a model-independent approach to electric quadrupole transitions of deformed nuclei. Based on an effective theory for axially symmetric systems, the leading interactions with electromagnetic fields enter as minimal couplings to gauge potentials, while subleading corrections employ gauge-invariant non-minimal couplings. This approach yields transition operators that are consistent with the Hamiltonian, and the power counting of the effective theory provides us with theoretical uncertainty estimates. We successfully test the effective theory in homonuclear molecules that exhibit a large separation of scales. For ground-state band transitions of rotational nuclei, the effective theory describes data well within theoretical uncertainties at leading order. In order to probe the theory at subleading order, data with higher precision would be valuable. For transitional nuclei, next-to-leading order calculations and the high-precision data are consistent within the theoretical uncertainty estimates. We also study the faint inter-band transitions within the effective theory and focus on the E2 transitions from the 0 + 2 band (the "β band") to the ground-state band. Here, the predictions from the effective theory are consistent with data for several nuclei, thereby proposing a solution to a long-standing challenge.

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Electric quadrupole transitions of the Bohr Hamiltonian with the Morse potential

Cited by 47 publications

References 44 publications

Bohr Hamiltonian with a deformation-dependent mass term for the Kratzer potential

Bohr Hamiltonian with a deformation-dependent mass term for the Kratzer potential

Excited collective states of nuclei within Bohr Hamiltonian with Tietz-Hua potential

Effective theory for the nonrigid rotor in an electromagnetic field: Toward accurate and precise calculations ofE2transitions in deformed nuclei

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