Shape transitions in odd-mass $\gamma$-soft nuclei within the interacting boson-fermion model based on the Gogny energy density functional

The interacting boson-fermion model (IBFM), with parameters determined from the microscopic Hartree-Fock-Bogoliubov (HFB) approximation, based on the parametrization D1M of the Gogny energy density functional (EDF), is employed to study the structural evolution in odd-mass $\gamma$-soft nuclei. The deformation energy surfaces of even-even nuclei, single-particle energies and occupation probabilities of the corresponding odd-mass systems have been obtained within the constrained HFB approach. Those building blocks are then used as a microscopic input to build the IBFM Hamiltonian. The coupling constants of the boson-fermion interaction terms are taken as free parameters, fitted to reproduce experimental low-lying spectra. The diagonalization of the IBFM Hamiltonian provides the spectroscopic properties for the studied odd-mass nuclei. The procedure has been applied to compute low-energy excitation spectra and electromagnetic transition rates, in the case of the $\gamma$-soft odd-mass systems $^{129-137}$Ba, $^{127-135}$Xe, $^{129-137}$La and $^{127-135}$Cs. The calculations provide a reasonable agreement with the available experimental data and agree well with previous results based on the relativistic mean-field approximation.