Analytical solution for the Davydov-Chaban Hamiltonian with sextic potential for $\gamma =30^{\circ }$

Abstract

An analytical solution for the Davydov-Chaban Hamiltonian with a sextic oscillator potential for the variable $\beta$ and $\gamma$ fixed to $30^{\circ }$, is proposed. The model is conventionally called Z(4)-Sextic. For the considered potential shapes the solution is exact for the ground and $\beta$ bands, while for the $\gamma$ band an approximation is adopted. Due to the scaling property of the problem the energy and $B(E2)$ transition ratios depend on a single parameter apart from an integer number which limits the number of allowed states. For certain constraints imposed on the free parameter, which lead to simpler special potentials, the energy and $B(E2)$ transition ratios are parameter independent. The energy spectra of the ground and first $\beta$ and $\gamma$ bands as well as the corresponding $B(E2)$ transitions, determined with Z(4)-Sextic, are studied as function of the free parameter and presented in detail for the special cases. Numerical applications are done for the ${}^{128,130,132}$Xe and ${}^{192,194,196}$Pt isotopes, revealing a qualitative agreement with experiment and a phase transition in Xe isotopes.

25 pages, 10 figures, 2 tables

References in corpus (4)

• Solutions of the Bohr hamiltonian, a compendium
• Bohr Hamiltonian with Davidson potential for triaxial nuclei
• Solution of the Bohr hamiltonian for soft triaxial nuclei
• Quartic oscillator potential in the γ-rigid regime of the collective geometrical model

Cited by in corpus (4)

• Bohr Hamiltonian with an energy dependent $\gamma$-unstable Coulomb-like potential
• Conjunction of $\gamma$-rigid and $\gamma$-stable collective motion in the critical point of the phase transition from spherical to deformed nuclear shapes
• Collective states of even-even nuclei in gamma-rigid quadrupole Hamiltonian with Minimal Length under the sextic potential
• General formalism of collective motion for any deformed system