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

TL;DR

This paper investigates the relationship between E(5)-models, which are based on solutions of the geometrical Bohr Hamiltonian, and the interacting boson model (IBM), demonstrating that IBM can accurately reproduce various E(5)-model energies.

Contribution

The study establishes a detailed connection between E(5)-models and the IBM by fitting IBM Hamiltonians to E(5)-model energies, showing strong agreement especially for certain potentials.

Findings

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

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

Fitted IBM Hamiltonians correspond to energy surfaces near the critical point.

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. 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.