Coupling between collective modes in the deformed $^{98}$Zr nucleus: Insights from consistent HFB+QRPA calculations with the Gogny interaction

The Zirconium isotopes exhibit structural properties that present multiple challenges to nuclear theory. Investigations of the coupling present within isoscalar modes and within isovector modes are scarce but important for advancing our understanding of the microscopic picture of nuclei. To explore some of these underlying coupling features, and to test the predictive power of a state-of-the-art nuclear structure approach, we provide a detailed analysis of the properties of $^{90,96,98}$Zr. This region includes a benchmarking case and offers insights into nuclear deformation phenomena. To investigate the coupling between collective modes in deformed nuclei, we focused our analysis on the ground and excited-state properties of these isotopes, employing a consistent approach with the axially-symmetric deformed Hartree-Fock-Bogoliubov (HFB) and the Quasiparticle Random Phase Approximation (QRPA) framework, both using the Gogny D1M force. This approach effectively describes both low-lying and giant-resonance states. We devoted special attention to the deformed $^{98}$Zr nucleus, where we confirm the existence of coupling between monopole and quadrupole excitations through the $K^{\pi} = 0^{+}$ QRPA components and demonstrate an analogous dipole-octupole coupling through the $K^{\pi} = 0^{-}$ and $K^{\pi} = 1^{-}$ components. Intrinsic transition densities and associated radial projections illustrate the coupling. Our work complements and extends earlier studies carried out using density-functional-based methods and notably, we included the complete Coulomb interaction also in the pairing fields, i.e. we treat terms exactly that are approximated in typical calculations that use the Gogny D1 and D2 interaction families.