Shape phase transitions in odd-A nuclei

We investigate shape phase transitions in odd nuclei within the Interacting Boson Fermion Model. Special attention is given to the case of the transition from the vibrational behaviour to the stable axial deformation. The odd particle is assumed to be moving in the three single particle orbitals j=l/2,3/2,5/2 with a boson-fermion Hamiltonian that leads to the occurrence of the SU^^(3) boson-fermion symmetry when the boson part approaches the SU{3) condition. Both energy spectra and electromagnetic transitions show characteristic patterns similar to those displayed by the even nuclei at the corresponding critical point. The role of the additional particle in characterizing the properties of the critical points in finite quantal systems is investigated by resorting to the formalism based on the intrinsic frame.