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

Abstract

The parameter independent (up to overall scale factors) predictions of the X(5)-${\beta }^2$, X(5)-${\beta }^4$, and X(3) models, which are variants of the X(5) critical point symmetry developed within the framework of the geometric collective model, are compared to two-parameter calculations in the framework of the interacting boson approximation (IBA) model. The results show that these geometric models coincide with IBA parameters consistent with the phase/shape transition region of the IBA for boson numbers of physical interest (close to 10). Nuclei within the rare-earth region and select Os and Pt isotopes are identified as good examples of X(3), X(5)-${\beta }^2$, and X(5)-${\beta }^4$ behavior.

References in corpus (14)

• Z(5): Critical point symmetry for the prolate to oblate nuclear shape phase transition
• X(3): An Exactly Separable Gamma-Rigid Version of the X(5) Critical Point Symmetry
• 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
• Gamma-rigid solution of the Bohr Hamiltonian for gamma = 30 degrees compared to the E(5) critical point symmetry
• Sequence of Potentials Lying Between the U(5) and X(5) Symmetries
• Sequence of Potentials Interpolating between the U(5) and E(5) Symmetries
• The U(5)-O(6) transition in the Interacting Boson Model and the E(5) critical point symmetry
• Phase structure of a two-fluid bosonic system
• Phase structure of the two-fluid proton-neutron system
• Singular Character of Critical Points in Nuclei
• Consequences of wall stiffness for a beta-soft potential
• Phase Diagram of the Proton-Neutron Interacting Boson Model
• The ${\beta }^4$ potential at the U(5)-O(6) critical point of the Interacting Boson Model

Cited by in corpus (2)

• Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the Interacting Boson Approximation model
• Relationship between X(5)-models and the interacting boson model