Relationship between X(5) models and the interacting boson model

Abstract

The connections between the X(5) models [the original X(5) using an infinite square well, X(5)-β8, X(5)-β6, X(5)-β4, and X(5)-β2], based on particular solutions of the geometrical Bohr Hamiltonian with harmonic potential in the γ degree of freedom, and the interacting boson model (IBM) are explored. This work is the natural extension of the work presented in García-Ramos and Arias, Phys. Rev. CPRVCAN0556-281310.1103/ PhysRevC.77.054307 77, 054307 (2008) for the E(5) models. For that purpose, a quite general one- and two-body IBM Hamiltonian is used and a numerical fit to the different X(5) model energies is performed; then the obtained wave functions are used to calculate B(E2) transition rates. It is shown that within the IBM one can reproduce well the results for energies and B(E2) transition rates obtained with all these X(5) models, although the agreement is not so impressive as for the E(5) models. From the fitted IBM parameters the corresponding energy surface can be extracted and, surprisingly, only the X(5) case corresponds in the moderately large N limit to an energy surface very close to the one expected for a critical point, whereas the rest of models are situated a little further away.