Microscopic description of octupole collective excitations near $N=56$ and $N=88$

Octupole deformations and related collective excitations are analyzed using the framework of nuclear density functional theory. Axially-symmetric quadrupole-octupole constrained self-consistent mean-field (SCMF) calculations with a choice of universal energy density functional and a pairing interaction are performed for Xe, Ba, and Ce isotopes from proton-rich to neutron-rich regions, and neutron-rich Se, Kr, and Sr isotopes, in which enhanced octupole correlations are expected to occur. Low-energy positive- and negative-parity spectra and transition strengths are computed by solving the quadrupole-octupole collective Hamiltonian, with the inertia parameters and collective potential determined by the constrained SCMF calculations. Octupole-deformed equilibrium states are found in the potential energy surfaces of the Ba and Ce isotopes with $N\approx 56$ and 88. The evolution of spectroscopic properties indicates enhanced octupole correlations in the regions corresponding to $N\approx Z\approx 56$, $Z\approx 88$ and $Z\approx 56$, and $N\approx 56$ and $Z\approx 34$. The average $\beta_{30}$ deformation parameter and its fluctuation exhibit signatures of octupole shape phase transition around $N=56$ and 88.