Abstract

LEVAI, G. Exact analytic description of nuclear shape phase transitions. Rev. mex. fis. [online]. 2006, vol.52, suppl.1, pp.75-81. ISSN 0035-001X.

We apply the sextic oscillator as a 7-independent potential in the Bohr Hamiltonian and present exact analytic results for the energy eigenvalues and wavefunctions of the lowest few levels. Further properties, such as the flexible shape of the potential are also discussed. As illustration a potential reproducing the spectroscopic properties of the ¹³⁴Ba nucleus, the first candidate for the E(5) symmetry is constructed. Fits to the energy spectrum of the ¹⁰²Ru, ¹⁰⁴Ru and ¹⁰⁶Ru isotopes are also presented, and it is shown that in this region the potential undergoes changes characteristic for a transition from the spherical vibrator to the deformed 7-unstable domain. Possible generalizations of the model are also pointed out.

Keywords : Nuclear shape; Quadrupole collectivity; Quasi-exactly solvable potentials.