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

TL;DR

This study investigates the influence of static hexadecapole deformation and configuration mixing on nuclear shapes and energies in rare earth isotopes using advanced theoretical models, revealing complex shape coexistence and correlations.

Contribution

It introduces a detailed analysis of quadrupole-hexadecapole coupling effects in rare earth nuclei using HFB and 2D-GCM methods with Gogny functional, highlighting their impact on nuclear structure.

Findings

Quadrupole and hexadecapole degrees are interconnected up to A=184-188.

Shape coexistence is enhanced around neutron number N=116.

Hexadecapole deformation contributes significantly to correlation energy.

Abstract

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.