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

The connections between the E(5)−models (the original E(5) using an infinite square well, E(5)−β 4, E(5)−β 6 and E(5)−β 8), 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. 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)− β 4 and reduces when passing through E(5)− β 6, E(5)− β 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.