Abstract : We analyze the quadrupole-octupole collective states based on the microscopic energy density functional
framework. By mapping the deformation constrained self-consistent axially symmetric mean-field energy
surfaces onto the equivalent Hamiltonian of the sd f interacting boson model (IBM), that is, onto the energy
expectation value in the boson coherent state, the Hamiltonian parameters are determined. The resulting IBM
Hamiltonian is used to calculate excitation spectra and transition rates for the positive- and negative-parity collective
states in large sets of nuclei characteristic for octupole deformation and collectivity. Consistently with
the empirical trend, the microscopic calculation based on the systematics of β2 − β3 energy maps, the resulting
low-lying negative-parity bands and transition rates show evidence of a shape transition between stable octupole
deformation and octupole vibrations characteristic for β3-soft potentials.
