Global systematics of octupole excitations in even-even nuclei

TL;DR

This paper develops a computational method based on the generator-coordinate extension of mean-field theory to systematically predict octupole excitations in all even-even nuclei, comparing well with experimental data.

Contribution

It introduces a universal theoretical framework for octupole excitations applicable to all even-even nuclei, with a simplified approximation nearly matching the full method's accuracy.

Findings

The theory reproduces nondeformed nuclei energies within 20% scale factor.

Performance is less accurate for deformed nuclei, with about 25% dispersion.

Predicted energies for nuclei with static octupole deformation are significantly underestimated.

Abstract

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.