Bohr Hamiltonian with a potential having spherical and deformed minima at the same depth

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Abstract

A solution for the Bohr-Mottelson Hamiltonian with an anharmonic oscillator potential of sixth order, obtained through a diagonalization in a basis of Bessel functions, is presented. The potential is consid- ered to have simultaneously spherical and deformed minima of the same depth separated by a barrier (a local maximum). This particular choice is appropriate to describe the critical point of the nuclear phase transition from a spherical vibrator to an axial rotor. Up to a scale factor, which can be cancelled by a corresponding normalization, the energy spectra and the electromagnetic E2 transition probabilities depend only on a single free parameter related to the height of the barrier. Investigations of the numerical data revealed that the model represents a good tool to describe this critical point.

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Buganu, P., Budaca, R., & Budaca, A. I. (2018). Bohr Hamiltonian with a potential having spherical and deformed minima at the same depth. In EPJ Web of Conferences (Vol. 194). EDP Sciences. https://doi.org/10.1051/epjconf/201819401007

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