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The evolution of quadrupole and octupole collectivity in neutron-deficientXe, Ba, Ce, and Nd nuclei near the "octupole magic" neutron number $N=56$ isinvestigated within the mapped $sdf$-IBM framework. Microscopic input isobtained via quadrupole and octupole constrained Hartree-Fock-Bogoliubovcalculations, based on the parametrization D1M of the Gogny energy densityfunctional. Octupole-deformed mean-field ground states are predicted for Ba andCe isotopes near $N=56$. Excitation energies of positive- and negative-paritystates as well as electric transition rates are computed with wave functionsresulting from the diagonalization of the mapped IBM Hamiltonian. Theparameters of the Hamiltonian are determined via the mapping of the mean-fieldpotential energy surfaces onto the expectation value of the Hamiltonian in thecondensate state of the $s$, $d$, and $f$ bosons. Enhanced octupolarity ispredicted for Xe, Ba, and Ce isotopes near $N=56$. The shape/phase transitionfrom octupole-deformed to strongly quadrupole-deformed near $N=60$ is analyzedin detail.

Quadrupole-octupole coupling and the evolution of collectivity in neutron-deficient Xe, Ba, Ce, and Nd isotopes