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

TL;DR

This paper explores the relationship between various E(5) models and the interacting boson model (IBM), demonstrating that IBM can accurately reproduce E(5) model energies and transition rates, especially near the critical point.

Contribution

It establishes a detailed connection between E(5)-models and the IBM by fitting IBM Hamiltonians to E(5) energies and wavefunctions, revealing their close correspondence.

Findings

IBM reproduces E(5)-model energies well, especially for E(5)-β^4.

Agreement decreases for higher β^n models but remains good for low-lying states.

Fitted IBM Hamiltonians correspond to critical point energy surfaces.

Abstract

The connections between the $E(5)-$models (the original E(5) using an infinite square well, $E(5)-\beta^4$, $E(5)-\beta^6$ and $E(5)-\beta^8$), based on particular solutions of the geometrical Bohr Hamiltonian with $\gamma$-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 wavefunctions 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 $E(5)-\beta^4$ and reduces when passing through $E(5)-\beta^6$, $E(5)-\beta^8$ 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. A phenomenon similar to the quasidynamical symmetry is observed.