Z(5): Critical point symmetry for the prolate to oblate nuclear shape phase transition

Abstract

A critical point symmetry for the prolate to oblate shape phase transition is introduced, starting from the Bohr Hamiltonian and approximately separating variables for $\gamma =30^{\mathrm{o}}$. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are found to be in good agreement with experimental data for 194-Pt, which is supposed to be located very close to the prolate to oblate critical point, as well as for its neighbours (192-Pt, 196-Pt).

LaTeX, 14 pages

References in corpus (2)

• Ground State Bands of the E(5) and X(5) Critical Symmetries Obtained from Davidson Potentials through a Variational Procedure
• A test of X(5) for the gamma degree of freedom

Cited by in corpus (34)

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• Effects of beta-gamma coupling in transitional nuclei and the validity of the approximate separation of variables
• Gamma-rigid solution of the Bohr Hamiltonian for gamma = 30 degrees compared to the E(5) critical point symmetry
• Analytical solution for the Davydov-Chaban Hamiltonian with sextic potential for $\gamma =30^{\circ }$
• Analytical solutions of the Bohr Hamiltonian with the Morse potential
• Soft triaxial roto-vibrational motion in the vicinity of $\gamma =\pi /6$
• Sextic potential for $\gamma$-rigid prolate nuclei
• Bohr Hamiltonian with Davidson potential for triaxial nuclei
• Bohr Hamiltonian with Hulth?en plus Ring shaped potential for triaxial nuclei
• Solution of the Bohr hamiltonian for soft triaxial nuclei
• Shape coexistence in even-even nuclei: A theoretical overview
• The proxy-SU(3) symmetry in atomic nuclei
• Description of the isotope chain ${}^{180-196}$Pt within some solvable approaches
• The Low-Energy Quadrupole Mode of Nuclei
• Regularities and symmetries of subsets of collective 0+ states
• Unified description of 0+ states in a large class of nuclear collective models
• Semiclassical unified description of wobbling motion in even-even and even-odd nuclei
• Davydov-Chaban Hamiltonian with deformation-dependent mass term for γ = 30°
• New features of the triaxial nuclei described with a coherent state model
• Prolate-oblate asymmetric shape phase transition in the interacting boson model with SU (3) higher-order interactions
• Shape phase mixing in critical point nuclei
• Competing $\gamma$-rigid and $\gamma$-stable vibrations in neutron rich Gd and Dy isotopes
• Collective motion in prolate γ-rigid nuclei within minimal length concept via a quantum perturbation method
• Connecting the X(5)-${\beta }^2$, X(5)-${\beta }^4$, and X(3) models to the shape/phase transition region of the interacting boson model
• A new boson approach for the wobbling motion in even-odd nuclei
• Bohr Hamiltonian with Hulthen plus ring-shaped potential for triaxial nuclei with deformation-dependent mass term
• Triaxial nuclei and analytical solutions of the conformable fractional Bohr Hamiltonian with some exponential-type potentials
• 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
• Bohr-Mottelson Hamiltonian with octic potential applied to the ${}^{106-116}$Cd isotopes
• Probing DDM and ML quantum concepts in shape phase transitions of $\gamma$-unstable nuclei
• Study of shape coexistence in the 180-190Hg isotopes by SO(6) representation of eigenstates