https://doi.org/10.1140/epja/s10050-025-01638-x
Regular Article - Theoretical Physics
Quadrupole–hexadecapole coupling in the rare earth region with beyond mean field correlations
1
Department of Physics, School of Sciencies and Humanities, Nazarbayev University, 53 Kabanbay Batyr Ave., 010000, Astana, Kazakhstan
2
Center for Computational Simulation, Universidad Politécnica de Madrid, Campus Montegancedo, Boadilla del Monte, 28660, Madrid, Spain
3
Departamento de Física Teórica and CIAFF, Universidad Autónoma de Madrid, 28049, Madrid, Spain
Received:
2
March
2025
Accepted:
4
July
2025
Published online:
17
July
2025
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 
, 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 
. 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 
. This structural evolution, encoded in the 2D-GCM collective wave functions, is accompanied by an enhanced prolate-oblate shape coexistence around the neutron number 
. 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.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
