  The evolution of quadrupole and octupole collectivity in neutron-deficient
Xe, Ba, Ce, and Nd nuclei near the "octupole magic" neutron number $N=56$ is
investigated within the mapped $sdf$-IBM framework. Microscopic input is
obtained via quadrupole and octupole constrained Hartree-Fock-Bogoliubov
calculations, based on the parametrization D1M of the Gogny energy density
functional. Octupole-deformed mean-field ground states are predicted for Ba and
Ce isotopes near $N=56$. Excitation energies of positive- and negative-parity
states as well as electric transition rates are computed with wave functions
resulting from the diagonalization of the mapped IBM Hamiltonian. The
parameters of the Hamiltonian are determined via the mapping of the mean-field
potential energy surfaces onto the expectation value of the Hamiltonian in the
condensate state of the $s$, $d$, and $f$ bosons. Enhanced octupolarity is
predicted for Xe, Ba, and Ce isotopes near $N=56$. The shape/phase transition
from octupole-deformed to strongly quadrupole-deformed near $N=60$ is analyzed
in detail.
