Quadrupole–hexadecapole coupling in the rare earth region with beyond mean field correlations

The roles of static hexadecapole deformation and beyond-mean-field quadrupole–hexadecapole configuration mixing are studied for a selected set of Yb, Hf, W and Os isotopes within the mass range \(170 \le A \le 202\), using the Hartree–Fock–Bogoliubov (HFB) and the two-dimensional Generator Coordinate Method (2D-GCM) approaches, based on the Gogny energy density functional. The 2D-GCM ground and excited states of the lighter isotopes are associated with diamond-like shapes while, for each isotopic chain, a region where those states correspond to square-like shapes has been found below the neutron shell closure \(N=126\). It is shown, that for the studied nuclei the quadrupole and hexadecapole degrees of freedom are interwoven in the ground and excited states up to the mass number \(A=184{-}188\). This structural evolution, encoded in the 2D-GCM collective wave functions, is accompanied by an enhanced prolate-oblate shape coexistence around the neutron number \(N=116\). In agreement with previous studies, it is also shown that for the considered Yb, Hf, W and Os isotopes the inclusion of hexadecapole deformation in the ground state dynamics leads to a non trivial additional correlation energy comparable to the quadrupole correlation energy itself.