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

Abstract

The connections between the Ε(5)-models (the original Ε(5) using an infinite square well, Ε(5) - β4 Ε(5) - β6 and Ε(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 £(5) - models energies is performed. It is shown that within the IBM one can reproduce very well all these Ε(5) - models. The agreement is the best for Ε(5) - β4 and reduces when passing through Ε(5) - β6, Ε(5) - β8 and Ε(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.