Exactly separable Bohr Hamiltonian with the Morse potential for triaxial nuclei

Abstract

In this paper, the Morse potential is used in the β-part of the collective Bohr Hamiltonian for triaxial nuclei. Energy eigenvalues and eigenfunctions are obtained in a closed form through exactly separating the Hamiltonian into its variables by using an appropriate form of the potential. The results are applied to generate the nuclear spectrum of 192 Pt , 194 Pt and 196 Pt isotopes which are known to be the best candidate exhibiting triaxiality. Electric quadrupole transition ratios are calculated and then compared with the experimental data and the Z(5) model results.

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

“…We see that the obtained results for the levels belonging to the ground state, β, and γ-band are in a quite satisfactory agreement with experimental data. Analyzing the mean deviation given in Table 2 corresponding for each nucleus, we can see that the balance is clearly in favor of our proposed model, namely, Z(5)-H, compared with the results of Z(5) [7] and esM [17].…”

“…The excited collective energies of nuclei and B(E2) transition rates are calculated and compared with the experimental data, as well as theoretical predictions of other models. Similar works already exist in the literature regarding the triaxial shapes with different potentials like Davidson [15], sextic oscillator [16] and Morse potential [17]. Also the triaxiality was studied in the framework of the algebraic collective model [18] and in the model of Davydov-Chaban [19] in which the nucleus is rigid with respect to γ-vibrations.…”

“…In order to achieve exact separation of the variables β and γ in Eq. ( 1), we choose the total wave functions in the form Ψ (β, γ, θ i ) = ξ(β)Φ(γ, θ i ), where θ i (i = 1, 2, 3) are the Euler angles, and we assume the potential in the convenient form as [17,20,21,22,23,24]…”

“…The mean deviation for the energy spectra between experimental data [53] and the theoretical value corresponding to Z(5)-H, Z(5)[7] and esM[17] of given 126−134 Xe and 192−196 Pt isotopes.…”

“…The comparison of the Z(5)-H predictions of B(E2) transition rates with the experimental data [53] and Z(5)[7] and esM[17] predictions for192,194,196 P t isotopes.Fig. 1.…”