Quadrupole-hexadecapole correlations in neutron-rich samarium and gadolinium isotopes

We present an extensive study of quadrupole-hexadecapole correlation effects in even-even Sm and Gd isotopes with neutron number $N=88\text{--}106$. The calculations are performed in the framework of the Gogny energy density functional (EDF) with the D1S parametrization and the $sdg$ interacting boson model (IBM). The quadrupole-hexadecapole constrained self-consistent mean-field potential energy surface is mapped onto the expectation value of the $sdg$-boson Hamiltonian. This procedure determines the parameters of the $sdg$-IBM Hamiltonian microscopically. Calculated excitation energies and transition strengths are compared to the ones obtained with a simpler $sd$-IBM, as well as with the experimental data. The Gogny-EDF mapped $sdg$-IBM reproduces spectroscopic properties of the studied nuclei as reasonably as in the case of the previous $sdg$-boson mapping calculations that were based on the relativistic EDF, indicating that the axial quadrupole-hexadecapole method is sound regardless of whether relativistic or nonrelativistic EDF is employed. The mapped $sdg$-IBM improves some of the results in lighter Sm and Gd isotopes compared to the mapped $sd$-IBM, implying the existence of significant hexadecapole correlations in those nuclei. For those nuclei with $N\ensuremath{\ge}94$, hexadecapole effects are minor, and the only significant difference between the two boson models can be found in the description of $E0$ monopole transitions.