Beyond-mean-field description of octupolarity in dysprosium isotopes with the Gogny-D1M energy density functional

The emergence and stability of (static) octupole deformation effects in Dy isotopes from drip line to drip line ($72\ensuremath{\le}N\ensuremath{\le}142$) are analyzed in this paper using mean-field and beyond-mean-field techniques often used for this purpose. We find static octupole deformations at the Hartree-Fock-Bogoliubov (HFB) level with the Gogny-D1M force for $N\ensuremath{\approx}134$ isotopes, while nuclei with $N\ensuremath{\approx}88$ exhibit reflection-symmetric ground states. It is shown that, given the softness found in the mean-field and parity-projected potential energy surfaces along the octupole direction, neither of these two levels of approximation is sufficient to extract conclusions about the (permanent and/or vibrational) nature of octupole dynamic in Dy isotopes. From the analysis of the collective wave functions as well as the excitation energies of the first negative-parity states and $B(E3)$ strengths, obtained within the framework of a two-dimensional symmetry-conserving generator coordinate method (2D-GCM), it is concluded that the increased octupole collectivity in Dy isotopes with $N\ensuremath{\approx}88$ and $N\ensuremath{\approx}134$ is a vibrational-like effect that is not directly related to permanent mean-field octupole deformation in the considered nuclei. A pronounced suppression of the $B(E1)$ strengths is predicted for isotopes with $N\ensuremath{\approx}82$ and $N\ensuremath{\approx}126$. The comparison of results obtained with other parametrizations shows the robustness of the predicted trends with respect to the underlying Gogny energy density functional.