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

Dennis Bonatsos·D. Lenis·N. Minkov·P. P. Raychev·P. A. Terziev
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Abstract

It is proved that the potentials of the form $β^{2n}$ (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 $β^4$, $β^6$, $β^8$, 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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Dennis Bonatsos, D. Lenis, N. Minkov, P. P. Raychev, P. A. Terziev. 2003-12-29. Sequence of Potentials Interpolating between the U(5) and E(5) Symmetries. https://doi.org/10.1103/physrevc.69.044316

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