  We present a computational methodology for a theory of the lowest octupole
excitations applicable to all even-even nuclei beyond the lightest. The theory
is the well-known generator-coordinate extension (GCM) of the
Hartree-Fock-Bogoliubov self-consistent mean field theory (HFB). We use the
discrete-basis Hill-Wheel method (HW) to compute the wave functions with an
interaction from the Gogny family of Hamiltonians. Comparing to the compiled
experimental data on octupole excitations, we find that the performance of the
theory depends on the deformation characteristics of the nucleus. For
nondeformed nuclei, the theory reproduces the energies to about 20 % apart from
an overall scale factor of about 1.6. The performance is somewhat poorer for
(quadrupole) deformed nuclei, and for both together the dispersion of the
scaled energies about the experimental values is about 25 %. This compares
favorably with the performance of similar theories of the quadrupole
excitations. Nuclei having static octupole deformations in HFB form a special
category. These nuclei have the smallest measured octupole excitation energies
as well as the smallest predicted energies. However, in these cases the
energies are seriously underpredicted by the theory. We find that a simple
two-configuration approximation, the Minimization After Projection method,
(MAP) is almost as accurate as the full HW treatment, provided that the
octupole-deformed nuclei are omitted from the comparison. This article is
accompanied by a tabulation of the predicted octupole excitations for 818
nuclei extending from dripline to dripline, computed with several variants of
the Gogny interaction.
