The U(5)-O(6) transition in the Interacting Boson Model and the E(5) critical point symmetry

Abstract

The relation of the recently proposed E(5) critical point symmetry with the interacting boson model is investigated. The large-N limit of the interacting boson model at the critical point in the transition from U(5) to O(6) is obtained by solving the Richardson equations. It is shown explicitly that this algebraic calculation leads to the same results as the solution of the Bohr differential equation with a ${\beta }^4$ potential.

Accepted in PRC

References in corpus (1)

• A Class of Exactly Solvable Pairing Models

Cited by in corpus (31)

• Quantum phase transitions in the interacting boson model
• Solutions of the Bohr hamiltonian, a compendium
• E(5), X(5), and Prolate to Oblate Shape Phase Transitions in Relativistic Hartree Bogoliubov Theory
• Sequence of Potentials Interpolating between the U(5) and E(5) Symmetries
• The sextic oscillator as a $\gamma$-independent potential
• Analytic descriptions for transitional nuclei near the critical point
• Analytical solutions of the Bohr Hamiltonian with the Morse potential
• Bohr Hamiltonian with Davidson potential for triaxial nuclei
• An algebraic approach to problems with polynomial Hamiltonians on Euclidean spaces
• Critical point symmetries in boson-fermion systems. The case of shape transition in odd nuclei in a multi-orbit model
• E(5) and X(5) critical point symmetries obtained from Davidson potentials through a variational procedure
• Evolution of spectral properties along the O(6)-U(5) transition in the interacting boson model. I. Level dynamics
• Electric quadrupole transitions of the Bohr Hamiltonian with the Morse potential
• Two-level interacting boson models beyond the mean field
• A scalar two-level boson model to study the IBM phase diagram in the Casten triangle
• Phase transitions in the Interacting Boson Fermion Model: the gamma-unstable case
• Continuous unitary transformations in two-level boson systems
• Quartic oscillator potential in the γ-rigid regime of the collective geometrical model
• Finite-size scaling exponents in the interacting boson model
• The ${\beta }^4$ potential at the U(5)-O(6) critical point of the Interacting Boson Model
• Phase transitions in the $sdg$ interacting boson model
• Gamma-soft Analog of the Confined Beta-soft Rotor Model
• The emergent dynamical symmetry at the triple point of nuclear deformations
• Nuclear shape phase transition within a conjonction of γ-rigid and γ-stable collective behaviours in deformation dependent mass formalism
• Remarcs on the shape transition from spherical to deformed gamma unstable nuclei
• 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
• On the relation between $E(5)-$models and the interacting boson model
• Relationship between X(5)-models and the interacting boson model
• Quantum catastrophes from an algebraic perspective
• An overview of the scientific contribution of Andrea Vitturi to Nuclear Physics (being an account of the recent TNP19 meeting held in Padova)
• Evidence of the Excited X(5)-like Critical-Point Symmetry Structures in 152Sm