Shape-phase transitions in odd-mass γ-soft nuclei with mass A ≈ 130

Quantum phase transitions between competing equilibrium shapes of nuclei with an odd number of nucleons are explored using a microscopic framework of nuclear energy density functionals and a fermion-boson coupling model. The boson Hamiltonian for the even-even core nucleus, as well as the spherical single-particle energies and occupation probabilities of unpaired nucleons, are completely determined by a constrained self-consistent mean-field calculation for a specific choice of the energy density functional and pairing interaction. Only the strength parameters of the particle-core coupling have to be adjusted to reproduce a few empirical low-energy spectroscopic properties of the corresponding odd-mass system. The model is applied to the odd-A Ba, Xe, La, and Cs isotopes with mass A approximate to 130, for which the corresponding even-even Ba and Xe nuclei present a typical case of gamma-soft nuclear potential. The theoretical results reproduce the experimental low-energy excitation spectra and electromagnetic properties, and confirm that a phase transition between nearly spherical and gamma-soft nuclear shapes occurs also in the odd-A systems.