  The phenomenon of reflection-asymmetric nuclear shapes is relevant to nuclear
stability, nuclear spectroscopy, nuclear decays and fission, and the search for
new physics beyond the standard model. Global surveys of ground-state octupole
deformation, performed with a limited number of models, suggest that the number
of pear-shaped isotopes is fairly limited across the nuclear landscape. We
carry out global analysis of ground-state octupole deformations for
particle-bound even-even nuclei with $Z \leq 110$ and $N \leq 210$ using
nuclear density functional theory (DFT) with several non-relativistic and
covariant energy density functionals. In this way, we can identify the best
candidates for reflection-asymmetric shapes. The calculations are performed in
the frameworks of axial reflection-asymmetric Hartree-Fock-Bogoliubov theory
and relativistic Hartree-Bogoliubov theory using DFT solvers employing harmonic
oscillator basis expansion. We consider five Skyrme and four covariant energy
density functionals. We predict several regions of ground-state octupole
deformation. In addition to the "traditional" regions of neutron-deficient
actinide nuclei around $^{224}$Ra and neutron-rich lanthanides around
$^{146}$Ba, we identified vast regions of reflecion-asymmetric shapes in very
neutron-rich nuclei around $^{200}$Gd and $^{288}$Pu, as well as in several
nuclei around $^{112}$Ba. Our analysis suggests several promising candidates
with stable ground-state octupole deformation, primarily in the
neutron-deficient actinide region, that can be reached experimentally. Detailed
comparison between Skyrme and covariant models is performed.
