2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/175601We investigate phase transitions in boson-fermion systems. We propose an analytically solvable model (E(5/12)) to describe odd nuclei at the critical point in the transition from the spherical to $γ$-unstable behaviour. In the model, a boson core described within the Bohr Hamiltonian interacts with an unpaired particle assumed to be moving in the three single particle orbitals j=1/2,3/2,5/2. Energy spectra and electromagnetic transitions at the critical point compare well with the results obtained within the Interacting Boson Fermion Model, with a boson-fermion Hamiltonian that describes the same physical situation.Phys. Rev. Lett. (in press)Nuclear Theorytext