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)-β4, E(5)-β6, and E(5)-β8], based on particular solutions of the geometrical Bohr Hamiltonian with γ-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 wave functions 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)-β4 and reduces when passing through E(5)-β6, E(5)-β8, 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