Exactly separable version of X(5) and related models

Abstract

One-parameter exactly separable versions of the X(5) and X(5)-beta^2 models, labelled as ES-X(5) and ES-X(5)-beta^2 respectively, are derived by using in the Bohr Hamiltonian potentials of the form u(beta)+u(gamma)/beta^2. Unlike X(5), in these models the beta_1 and gamma_1 bands are treated on equal footing. Spacings within the gamma_1 band are well reproduced by both models, while spacings within the beta_1 band are well reproduced only by ES-X(5)-beta^2, for which several nuclei with R_{4/2}=E(4_1^+)/E(2_1^+) ratios and [normalized to E(2_1^+)] beta_1 and gamma_1 bandheads corresponding to the model predictions have been found.

12 pages, LaTeX, including three .eps figures

References in corpus (9)

• Solutions of the Bohr hamiltonian, a compendium
• A computationally tractable version of the collective model
• Effects of beta-gamma coupling in transitional nuclei and the validity of the approximate separation of variables
• Sequence of Potentials Lying Between the U(5) and X(5) Symmetries
• 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
• Soft triaxial roto-vibrational motion in the vicinity of $\gamma =\pi /6$
• Consequences of wall stiffness for a beta-soft potential
• Solution of the Bohr hamiltonian for soft triaxial nuclei

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• Exact diagonalization of the Bohr Hamiltonian for rotational nuclei: Dynamical gamma softness and triaxiality
• Closed analytical solutions of Bohr Hamiltonian with Manning-Rosen potential model
• Phonon and multi-phonon excitations in rotational nuclei by exact diagonalization of the Bohr Hamiltonian
• A solvable model which has X(5) as a limiting symmetry and removes some inherent drawbacks
• Nuclear shape phase transition within a conjonction of γ-rigid and γ-stable collective behaviours in deformation dependent mass formalism
• Conjunction of $\gamma$-rigid and $\gamma$-stable collective motion in the critical point of the phase transition from spherical to deformed nuclear shapes
• Shape phase mixing in critical point nuclei
• Competing $\gamma$-rigid and $\gamma$-stable vibrations in neutron rich Gd and Dy isotopes
• Transition probabilities in the X(5) candidate ${}^{122}$Ba
• Excited collective states of nuclei within Bohr Hamiltonian with Tietz-Hua potential
• Triaxial nuclei and analytical solutions of the conformable fractional Bohr Hamiltonian with some exponential-type potentials
• Relationship between X(5)-models and the interacting boson model
• Evidence of the Excited X(5)-like Critical-Point Symmetry Structures in 152Sm