On the relation between $E(5)-$models and the interacting boson model

Abstract

The connections between the $E(5)-$models (the original E(5) using an infinite square well, $E(5)-{\beta }^4$, $E(5)-{\beta }^6$ and $E(5)-{\beta }^8$), based on particular solutions of the geometrical Bohr Hamiltonian with $\gamma$-unstable potentials, and the interacting boson model (IBM) are explored. For that purpose, the general IBM Hamiltonian for the $U(5)-O(6)$ transition line is used and a numerical fit to the different $E(5)-$models energies is performed, later on the obtained wavefunctions are used to calculate B(E2) transition rates. It is shown that within the IBM one can reproduce very well all these $E(5)-$models. The agreement is the best for $E(5)-{\beta }^4$ and reduces when passing through $E(5)-{\beta }^6$, $E(5)-{\beta }^8$ and E(5), where the worst agreement is obtained (although still very good for a restricted set of lowest lying states). The fitted IBM Hamiltonians correspond to energy surfaces close to those expected for the critical point. A phenomenon similar to the quasidynamical symmetry is observed.

References in corpus (6)

• Quasi dynamical symmetry in an interacting boson model phase transition
• Sequence of Potentials Interpolating between the U(5) and E(5) Symmetries
• The sextic oscillator as a $\gamma$-independent potential
• The U(5)-O(6) transition in the Interacting Boson Model and the E(5) critical point symmetry
• Two-level interacting boson models beyond the mean field
• The ${\beta }^4$ potential at the U(5)-O(6) critical point of the Interacting Boson Model

Cited by in corpus (5)

• Regularities and symmetries of subsets of collective 0+ states
• The emergent dynamical symmetry at the triple point of nuclear deformations
• Spectral properties of a tractable collective Hamiltonian
• Application of the cranking method to the semimicroscopic algebraic cluster model and nuclear molecules
• Relationship between X(5)-models and the interacting boson model