Sequence of Potentials Interpolating between the U(5) and E(5) Symmetries

Details Sequence of Potentials Interpolating between the U(5) and E(5) Symmetries Sequence of Potentials Interpolating between the U(5) and E(5) Symmetries

2003-12-29

arxiv.org/abs/nucl-th/0312120v1

Phys.Rev. C69 (2004) 044316

Physics

Nuclear Physics

Nuclear Theory

LaTeX, 17 pages, 9 postscript figures

Scientific paper

10.1103/PhysRevC.69.044316

It is proved that the potentials of the form $\beta^{2n}$ (with $n$ being integer) provide a ``bridge'' between the U(5) symmetry of the Bohr Hamiltonian with a harmonic oscillator potential (occuring for $n=1$) and the E(5) model of Iachello (Bohr Hamiltonian with an infinite well potential, materialized for infinite $n$). Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are given for the potentials $\beta^4$, $\beta^6$, $\beta^8$, corresponding to $R_4=E(4)/E(2)$ ratios of 2.093, 2.135, 2.157 respectively, compared to the $R_4$ ratios 2.000 of U(5) and 2.199 of E(5). Hints about nuclei showing this behaviour, as well as about potentials ``bridging'' the E(5) symmetry with O(6) are briefly discussed. A note about the appearance of Bessel functions in the framework of E(n) symmetries is given as a by-product.

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