  The evolution of quadrupole and octupole collectivity and their coupling is
investigated in a series of even-even isotopes of the actinide Ra, Th, U, Pu,
Cm, and Cf with neutron number in the interval $130\leqslant N\leqslant 150$.
The Hartree-Fock-Bogoliubov approximation, based on the parametrization D1M of
the Gogny energy density functional, is employed to generate potential energy
surfaces depending upon the axially-symmetric quadrupole and octupole shape
degrees of freedom. The mean-field energy surface is then mapped onto the
expectation value of the $sdf$ interacting-boson-model Hamiltonian in the boson
condensate state as to determine the strength parameters of the boson
Hamiltonian. Spectroscopic properties related to the octupole degree of freedom
are produced by diagonalizing the mapped Hamiltonian. Calculated low-energy
negative-parity spectra, $B(E3;3^{-}_{1}\to 0^{+}_{1})$ reduced transition
rates, and effective octupole deformation suggest that the transition from
nearly spherical to stable octupole-deformed, and to octupole vibrational
states occurs systematically in the actinide region.
