Global systematics of octupole excitations in even-even nuclei

We present a computational methodology for a theory of the lowest axially symmetric 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 (HFB) self-consistent mean field theory. We use the discrete-basis Hill-Wheeler (HW) method 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 approximate to 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 theory 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 (MAP) method, 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 drip-line to drip-line, computed with several variants of the Gogny interaction.