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

¹ Department of Theoretical Physics, Horia Hulubei – National Institute for Physics and Nuclear Engineering, Reactorului 30, Magurele, Romania, RO-077125, POB-MG6
² Academy of Romanian Scientists, Splaiul Independenei 54, RO-050094, Bucharest, Romania

^* e-mail: buganu@theory.nipne.ro

Published online: 14 November 2018

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.