Physics – Nuclear Physics – Nuclear Theory
Scientific paper
2008-12-26
AIP Conf.Proc.1090:278-282,2009
Physics
Nuclear Physics
Nuclear Theory
5 pages. Proc. 13th Int. Conf. on "Capture Gamma-Ray Spectroscopy and Related Topics", August 25-29, 2008, Cologne, Germany
Scientific paper
10.1063/1.3087027
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.
Arias José M.
Garcia-Ramos José-Enrique
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