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

Abstract

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

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

“…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.…”

“…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.…”

Collective motion in γ-unstable nuclei within energy-dependent Davidson potential and deformation dependent mass formalisms

“…where the energy n,τ is given by equation (16). We should notice here that, in the order to facilitate comparisons of the various models and the data, the same set of experimental data for the energy spectra and B(E2) transitions rates has been used as in the case of DDM with Davidson [10], Kratzer [11] models, the BH with Morse [46], Manning-Rosen [47] and Tietz-Hua [48] potentials. The theoretical predictions for the energy spectra of γ-unstable nuclei are realized by equation ( 16) for low-lying bands which are classified by the principal quantum number n. In this case, the g.s.…”

Triaxial nuclei and analytical solutions of the conformable fractional Bohr Hamiltonian with some exponential-type potentials

“…It is significantly more realistic than the Morse potential in explaining molecular dynamics at high rotational and vibrational quantum numbers [57]. Recently [58], in nuclear structure theory, the solutions of the BH with the Tietz-Hua potential were given, which was utilized to describe the 𝛽-part of the potential and the HOP for the 𝛾-part. The computations were performed for energy levels and 𝐵(E2) transition rates for 𝛾-unstable and axially symmetric deformed nuclei.…”