Spectroscopy of quadrupole and octupole states in rare-earth nuclei from a Gogny force

Abstract

Collective quadrupole and octupole states are described in a series of Sm and Gd isotopes within the framework of the interacting boson model (IBM), whose Hamiltonian parameters are deduced from mean-field calculations with the Gogny energy density functional. The link between both frameworks is the (β 2 β 3 ) potential energy surface computed within the Hartree-Fock-Bogoliubov framework in the case of the Gogny force. The diagonalization of the IBM Hamiltonian provides excitation energies and transition strengths of an assorted set of states including both positive-and negative-parity states. The resultant spectroscopic properties are compared with the available experimental data and also with the results of the configuration mixing calculations with the Gogny force within the generator coordinate method (GCM). The structure of excited 0 + states and its connection with double-octupole phonons is also addressed. The model is shown to describe the empirical trend of the low-energy quadrupole and octupole collective structure fairly well and turns out to be consistent with GCM results obtained with the Gogny force.

Spectroscopy of reflection-asymmetric nuclei with relativistic energy density functionals

“…13) but the energy surfaces are very shallow with respect to the octupole degree of freedom. Similar shape transitions in the fourteen isotopic chains have also been obtained in studies based on different relativistic energy density functionals [33,38], nonrelativistic functionals [25,34], and macroscopic+microscopic (MM) models [19,71]. Some differences between these calculations are found in the exact location of non-zero equilibrium octupole deformation and the corresponding octupole deformation energies.…”

“…Using this method, however, it is rather difficult to perform a systematic study of low-lying quadrupole and octupole states in different mass regions, because implementations of GCM are very time-consuming for heavy systems. Possible alternative approaches are the EDF-based interacting boson model [32][33][34], or the quadrupole-octupole collective Hamiltonian [43,44]. In particular, the EDF-based collective Hamiltonian can be derived from the GCM in the Gaussian overlap approximation [56], and the validity of this approximate method was recently demonstrated in a comparison with a full GCM calculation for the shape coexisting nucleus 76 Kr [57].…”

Structural evolution inA≈100nuclei within the mapped interacting boson model based on the Gogny energy density functional

“…The method allows a computationally feasible as well as quantitative description of the low-energy collective excitations. It has already been applied to study the quadrupole [29,[31][32][33] and octupole [34] modes in atomic nuclei as well as to describe shape coexistence phenomena [35][36][37]. In the present study we extend the method of Ref.…”

Lifetime measurements of low-spin negative-parity levels in Gd160

“…An in-depth discussion of this method can be found in Ref. [44][45][46]. The computed PES reveals a reflection symmetric (i.e., with zero octupole deformation) for the ground state but the PES along the octupole direction is rather soft indicating the need of a beyond-mean-field calculation using the GCM.…”