Addressing nuclear structure challenges in the Zr isotopes with self-consistent Gogny-Force HFB and QRPA predictions

The Zirconium isotopes exhibit structural properties that present multiple challenges to nuclear theory. To shed light on the underlying causes of the observations, and to test the predictive power of a state-of-the-art nuclear structure approach, we have completed a large number of calculations of ground and excited-state properties of Zr isotopes. We performed systematic calculations of ground state properties for the $^{78-122}$Zr isotopes, using an axially-symmetric, deformed Hartree-Fock-Bogoliubov (HFB) framework. For selected spherical and deformed nuclei, we have also predicted excited state properties, utilizing the Quasiparticle Random Phase Approximation (QRPA). We use a self-consistent approach that employs the same Gogny D1M force at both the HFB and QRPA levels. Our approach complements and extends earlier studies carried out using density-functional-based methods. Notably, we included the complete Coulomb interaction also in the pairing fields, i.e. we treat terms exactly that are approximated in typical calculations with Gogny D1 and D2 interaction families. The impact of these terms on the pairing energies, the binding energy, charge radius shifts, and on the evolution of the energy surface with neutron number is discussed. We compare this with the effect of using the D1S force and discuss the resulting shape predictions for $^{80}$Zr and $^{96,98}$Zr. For $^{90,96,98}$Zr, we perform QRPA calculations, implement angular-momentum symmetry restoration, and study both low-lying and giant-resonance states. For the deformed $^{98}$Zr nucleus, 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.