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$β$ decay of odd-A nuclei with the interacting boson-fermion model based on the Gogny energy density functional

The low-energy excitations and $β$ decays of odd-A nuclei are studied within the interacting boson-fermion model (IBFM), based on the Gogny-D1M nuclear energy density functional (EDF). The constrained Hartree-Fock-Bogoliubov (HFB) approximation is employed to compute potential energy surfaces in terms of triaxial quadrupole degrees of freedom for even-even Xe and Ba nuclei in the mass $A\approx 130$ region. The mean field approximation also provides spherical single-particle energies and occupation probabilities for the neighboring odd-A nuclei. Those quantities represent a microscopic input for spectroscopic calculations in odd-A Xe and Ba, Cs and La isotopes. The Gamow-Teller (GT) and Fermi (F) transition matrix elements, needed to compute $β$-decay $\log{ft}$ values are obtained without any phenomenological fitting. It is shown that both the low-lying states and $β$ decays of the studied odd-A systems are described reasonably well within the employed theoretical framework.